heat & temperature - learning by doing for secondary school

Heat and TemperatureA learning-by-doing module for secondary schools

Bhas Bapatand the Eklavya Team

an eklavya publication


12pt

14pt

an eklavya publication18pt


Text : Bhas Bapat, Uma Sudhir, Sushil Joshi, Kamal Mahendroo,Rama Chari, Urjit Yajnik

Illustrations: Bharat Jamra, Nishith Mehta, Boski Jain and Bhas BapatCover Design: Boski Jain

Typeset by the author using LATEX

©Eklavya – September 2013Any part of this publication can be used under a similar copyleft markfor free distribution for non-commercial, educational purposes. For any

other kind of permission, please contact the publisher.

September 2013 / 2000 copiesPaper: 100 gsm maplitho and 220 gsm paper board (cover)

ISBN: 978-93-81300-67-1Price: 130

Developed with financial assistance from the Sir Dorabji Tata Trustand the Parag initiative of

the Sir Ratan Tata Trust and the Navajbai Ratan Tata Trust, Mumbai.

Published byEklavya

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Contents

Preface v

Notes for the Teacher vii

1 Hot and Cold 11.1 Common experience of hot and cold . . . . . . . . . . . . . . . . . . . . . . . 11.2 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Temperature of objects in mutual contact . . . . . . . . . . . . . . . . . . . . 61.4 Does equal heating make things equally hot? . . . . . . . . . . . . . . . . . . 91.5 What flows, heat or cold? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2 Transfer of Heat 142.1 Transfer of heat in solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2 Transfer of heat in liquids and gases . . . . . . . . . . . . . . . . . . . . . . . 172.3 Heat transfer in the absence of a medium . . . . . . . . . . . . . . . . . . . . 192.4 Conductors and insulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.5 Prevention of heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3 Effects of Heat 273.1 Heat and expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2 Change of state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.3 Vaporisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.4 Does heating always lead to increase in temperature? . . . . . . . . . . . . . 34

4 Heat and Work 374.1 Some observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.2 Expansion and mechanical energy . . . . . . . . . . . . . . . . . . . . . . . . 384.3 Mechanical equivalent of heat . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

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4.4 Cooling by expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5 What Makes Things Hot 475.1 Early ideas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.2 Is everything within a substance static? . . . . . . . . . . . . . . . . . . . . . 505.3 Modern model of matter and heat . . . . . . . . . . . . . . . . . . . . . . . . 54

6 Temperature and the Particulate Nature of Matter 586.1 How large are particles of matter? . . . . . . . . . . . . . . . . . . . . . . . . 586.2 Representative properties of a large group . . . . . . . . . . . . . . . . . . . . 606.3 A measure of the random motion of a collection of particles . . . . . . . . . 626.4 Absolute temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.5 Thermal energy and heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.6 Particulate model and pressure . . . . . . . . . . . . . . . . . . . . . . . . . . 676.7 Particulate model and expansion . . . . . . . . . . . . . . . . . . . . . . . . . 696.8 Particulate model and convection . . . . . . . . . . . . . . . . . . . . . . . . . 70

7 Some Remarkable Devices 737.1 The pressure cooker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 737.2 The steam engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 757.3 The internal combustion engine . . . . . . . . . . . . . . . . . . . . . . . . . . 777.4 Refrigerator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

Teasers 80

A Note on Units 83

Index 85

Acknowledgements 87

Preface

This module covers the topics heat andtemperature at a level appropriate to theending years of secondary school. It ismainly aimed at teachers, but studentsshould be able to follow most of it.

Commonly observed effects of heatand transfer of heat are covered atthe beginning. We then look into theequivalence of heat and work, and as anatural extension, look into pressure andexpansion in the context of gases. We nextcome to the question of what causes heatand what is meant by temperature andarrive at the kinetic theory of heat andtemperature. After this the applicabilityof the theory is discussed in the contextof gases. Finally, we briefly look at afew heat-based devices that have had asignificant impact on our lives.

The emphasis is on activity-basedlearning wherever possible. However,it has to be appreciated that physicsrequires a certain degree of abstractionbased on observation, which then leadsto building models to explain naturalphenomena. This module accepts thatapproach, and an attempt is made to leadthe reader from inferences drawn fromclassroom based activities to the moderntheory of heat based on particulate nature

of matter and random motion of theparticles. While this is by no means theonly viable or valid approach, we haveattempted to make it self-contained andpedagogically consistent. Experimentsthat drive home the justification for theparticulate model of heat and matterare suggested. We are aware thatmodel building based on a small setof observations may have gaps and, inplaces, only loosely justified leaps. Wherethis is done, it is clearly stated. Strictlyspeaking, building a widely applicablemodel requires distillation of severaldiverse observations and is necessarilya long drawn activity that would beimpractical in classroom teaching.

The module contains a large numberof activities than can be done with ease inthe classroom or school laboratory, withmodest tools and equipment. Questionsrelated to the observations are oftenleft unanswered, or are left with ahint, to stimulate thinking. We havealso made a conscious effort to dispelconfusing notions, and to avoid confusingterminology.

The activities should be approachedas follows. First the description should beread to understand the activity, without

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actually doing it. Wherever there arequestions in the descriptions, an attemptshould be made to estimate or predict theoutcome of the experiment. If there arequestions posed in the description, theseshould be thought over before the activityis done. After this the activity shouldbe performed, and the observations noted

down. Finally inferences should be drawnand the questions answered. Teasersbased on feedback from various teachers,students and other resource persons, andperceived misconceptions, are presentedat the end of the module.

We hope that this module isappreciated for the route it takes.

Notes for the Teacher

This module is based on performing manysmall activities. A single activity mayneed as little as a minute, but some mayneed as much as 15 minutes. A coupleof activities suggested in the module maynot be possible in school laboratories, butare needed for the development of thesubject. These are available as a videofilm. We have intentionally desisted frompreparing video films of all activities sincethey are likely to deter students fromperforming the activities and learning theskill of experimentation.

Like any scientific experiment,these experiments have to be donecarefully. This implies not just doingthem with accuracy, but also realisingthe shortcomings, and identifyingthe potential sources of errors andwork-arounds. We hope that the spiritof these activities is recognised, and withthese comes the realisation that it is notalways necessary to have sophisticatedexperimental set-ups to understand basicprinciples.

We have listed below some points toease the performance of the activities andsome practical hints and pointers.

1. Activities in this module often require asource of heat. Common sources of heatthat can be recommended are a candle,a spirit lamp, a stove, a small (250 W)electrical immersion heater. Gas-filledlighters with a metal body could also beused for small tasks. Their suitabilityfor a particular activity has to be judgedon a case-by-case basis.

2. Many experiments will need water andsuitable containers. Containers couldbe beakers, or steel tumblers or kitchenutensils. Students should be madeaware that while heating or coolingwater or other liquids, the containersalso likewise get heated and cooled,although we do not make an explicitmention of this.

3. All laboratory thermometers donot respond identically. They mayshow different readings for the sameobject (e.g. for the same sample ofwater)! This is due to manufacturingshortcomings. For the experimentsto be done here, it is necessary tomake sets of 3–4 thermometers whichhave similar responses. This can bedone as follows. Keep beakers of cold

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water and very hot water at hand.Dip thermometers pairwise in thetwo beakers one after the other, andkeep together thermometers that shownearly the same readings, both atthe low temperature and at the hightemperature.

4. In all activities that involve mixing andobjects in contact, there are factors suchas heat transfer to the surroundings,which affect the observations. Hencethe results of these experiments areapproximate.

5. In the activities on liquids in contact,they are actually separated by the wallof the container. Heat is transferred tothe container also and the temperatureof the container changes during theexperiment. The second activity inthis context suggests a way around thishitch.

6. Certain activities are best done using athermos flask. Since a thermos flask isexpensive, it is impractical to spare afew for these activities every time.

Two improvised alternatives to thethermos flask are suggested. (a) Usetwo disposable type thermocol cups,one placed inside the other (b) Makean insulated beaker by wrapping a thinsheet of packing foam a few timesaround a glass beaker, place a thickcircular disk of the same material underthe beaker, and secure the wrappingwith packing tape.

7. Some activities require the use of equalmasses of more than one liquid (e.g.water and kerosene). It is much easierto use a volume measure for liquidsthan a weight measure. Wherever afixed mass of a liquid is needed, wemay use a volume measure. In doingso, it is useful to know that the densityof water is 1 g/mL and that 10 gof kerosene and water have volumes12 mL and 10 mL, respectively. The useof vegetable oils is not recommended,because they are viscous and heat doesnot spread quickly enough in them.There are greater variations in theirdensities than in kerosene.

Chapter 1

Hot and Cold

1.1 Common experience of hotand cold

Two words that are frequently used inour day-to-day life are hot and cold. Wesometimes remark “Isn’t it hot today?”or “It’s cold today!”. If it is very cold,we cover ourselves up with a shawl orwe wear a sweater. On wintry daysthe floor of the house feels cold. Onthe other hand, on a hot summer day itbecomes impossible to sit upon a bicycleor a scooter left standing in the sun.

If we reflect a bit on the manner inwhich we use the words hot and cold,it will become clear that in our everydayuse, the terms can be quite imprecise,even confusing. Consider the followingexamples.

• If given a cup of lukewarm water andanother cup of lukewarm tea, we arelikely to say that the water is too hot (todrink) while the tea is too cold (to drink).So, here the sense of something beinghot or cold is related to the purpose.

• Oddly enough, it might happen thatanother person finds the same cup oftea hot enough. Another similar exampleis that of warm water for a bath. Oneperson might declare a bucket of waterto be too hot to have a bath with, butsomeone else might find it just right fora bath. So here, the perception or senseof hotness depends on the person.

• When a pan of just boiled milk is takenoff the stove and left standing, we sayafter some time that the milk has cooleddown, although it may not be as coolas another pan of milk that has notbeen placed on the stove at all. Infact the first pan will be declared to beeven more cool after some more timehas elapsed. To add to the confusion,somebody might declare it to be less hotthan it was earlier. In this case we areusing the term cool (or hot) in a relativesense.

Our idea of hot and cold (in commonusage) is usually based on the sense oftouch, that is, on our skin acting as

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Figure 1.1: Comparison of sensation of hotness by palms dipped earlier in cold or hot water.

a sensor. Our sense of touch is notvery reliable, and there can be conflictinginterpretations of the terms hot and coldeven for the same person. This can beeasily seen by a simple experiment.

A 1.1 Hot or Cold?

Take three identical containers (large tumblersor pans would be fine). Fill the first with waterfrom a water cooler, or a refrigerator, or anearthen pot. Fill the second with tap water, andthe third with tap water that has been heatedfor a few minutes. Dip one of your palms firstin cold water for 15 s, and the other palm inwarm water for 15 s. Then dip both palmssimultaneously in tap water (See Fig. 1.1).On the basis of the sensation in your palmsin the two cases, can you say whether the tapwater is hot or cold?

In common practice, the use and themeaning of the terms hot and cold isoften subjective, i.e., it depends on thecontext or purpose, it may be relative tosomething, it depends on the person, andalso on the conditioning of the sense oftouch. The examples and the activityabove indicate that the sense of hot andcold is relative, not absolute. How can wethen meaningfully say that one object ishot while another object is cold?

Let us examine the pan of boiled milkonce again. To begin with, we declaredit to be hot but some time after it wasleft standing, we declared it to be cooleror less hot. As time passes, we findthat the hotness of the milk is continuouslyreducing, or the coolness is continuouslyincreasing. The process of reductionof its hotness, or increase in coolness

Chapter 1. Hot and Cold 3

is a continuous one. In a contrastingsituation a tumbler containing chilledwater becomes less cool or becomeswarmer as time goes by; here too, thereduction of its coolness or, equivalently,the increase in its hotness, is continuous.

The inferences from our observationscould be stated as follows:

• We could equally well say that allobjects are cold, but some are colderthan others, or that all objects are hot,but some are hotter than others.

• Hotness and coldness are notcompartments or distinct categories.They merge into each other, or changecontinuously from one to another.Hotness and coldness are like twovalues on the same scale, one large andone small.

1.2 Temperature

The degree of hotness is given the nametemperature and its value changes in acontinuous manner. A ‘hotter’ body has ahigher temperature while a ‘colder’ bodyhas a lower temperature. One of theearliest successful attempts at establishinga method of measuring the degree ofhotness was that of Galileo (around 1610CE). He constructed a device called a gasthermoscope, which can be considered asthe forerunner of the thermometer. Athermoscope is based on the expansionof a gas due to change in the degree of

hotness. We will construct a thermometerlater.

Thermometers are now commonlyused devices. We come across variousthermometers: in the laboratory, in adoctor’s clinic, or in a weather bureau.We frequently come across reports oftemperatures, such as in a weatherreport, or the body temperature of apatient, or the temperature of a solutionin the laboratory. These temperaturesare variously reported as “so manydegrees Celsius”, or “so many degreesFahrenheit”. We will use the Celsiusscale for all our work, and treat thenumber indicated by the alcohol ormercury column as the degree of hotness, ortemperature.

A 1.2 Examine a thermometer

A laboratory thermometer is a long glass tubesealed at both ends, inside which there isanother very fine tube with a fat bulb atone end, partly filled with a liquid. Theliquid could be mercury (a shiny substance) oralcohol (mixed with a red or blue dye). Observethe mercury column. There is a scale along thetube which shows markings in ◦C, or degreesCelsius. Take a look at its initial reading. Whatis it showing the temperature of? Hold it in atumbler of water. Note the reading. Next putthe bulb of the thermometer in cold water orin crushed ice and watch what happens to themercury column. Then hold the thermometerin a saucepan containing water and placed


Galileo Galilei (1564–1642)Galileo was very versatile and did seminal work in many areas, and he is best known for

championing the heliocentric theory proposed by Copernicus. He also laid the foundations

of kinematics (the study of motion) by recognising that under ideal conditions an object

would continue in its state of rest or uniform motion till an unbalanced force acts on it.

This, along with his work on the pendulum and falling bodies, was a strong challenge to

the views proposed by Aristotle which had been accepted for almost two thousand years.

What did he contribute to our understanding of heat and temperature? He not only invented

the thermoscope (in which the expansion or contraction of an enclosed volume of a gas

indicated increasing or decreasing temperatures respectively), but also proposed that a

higher temperature might be attributed to the constituent particles of that object moving

faster. But since this came before the particulate nature of matter came to be widely

accepted, it was largely ignored.

over a flame. Find out the temperature atwhich water boils.

A 1.3 Temperatures of objects aroundus

You will need a beaker with tap water, asmall pile of dry sand which has been keptin the room for a long time and a fewthermometers1. Take one of the thermometersand place it in a beaker containing tap water.Take another thermometer and place it ina pile of sand. Leave one thermometer incontact with air. Note down the reading inall three thermometers after approximately 5min. Are the temperatures noted in the threethermometers identical? If not, why?

You might wonder about questionssuch as: is there a limit on how cold or

how hot something can be? What is thehighest possible temperature? Can thetemperature be negative? How low can itget? We will try to answer these questionsin due course.

A 1.4 Hot or cold re-visited

Take two identical thermometers. Mark themas A and B. Now repeat the palm-dippingactivity with three beakers of water using thethermometers A and B, instead of your leftand right palms. What reading do you expecton the thermometers in each case? In whatway has the use of a thermometer helped ourinvestigation, compared to the case when weused our palms to gauge the degree of hotness?

It should be clear from this activitywhy a thermometer is a more precise and

1. See ‘Notes for the Teacher’ at the beginning.


Two temperature scales

Our laboratory thermometer has a Celsiusscale, but there is another scale oftemperature, called the Fahrenheit scale. Itis commonly used by doctors to measurethe body temperature. The normaltemperature of the human body is around98 ◦F or 37 ◦C, and it varies from personto person. The freezing point andboiling points of pure water are 0 ◦C and100 ◦C, respectively, when the surroundingair pressure is 1 atmosphere. On theFahrenheit scale these points are 32 ◦F and212 ◦F, respectively. (The previous activitymight have led to different values. Try toreason out why.) Thus 100 degrees onthe Celsius scale equal 212−32, or 180degrees on the Fahrenheit scale. Hence1 degree on the Celsius scale equals 1.8degree on the Fahrenheit scale. 0 ◦Cequals 32 ◦F, 1 ◦C would be [32 + 1.8] ◦F,2 ◦C would be [32 + (2×1.8)] ◦F, and soon. If C and F denote the temperatures

on the two scales, we can write thegeneral relationship, F = 1.8 × C + 32.Can you find out at what temperaturethe Fahrenheit and Celsius scales readthe same? To find out more about theinteresting history of thermometers, see thearticle ‘taapmaapii mein paaraa kyon?’ bySushil Joshi, Sandarbh, Issue 67, p 7–18.

reliable indicator of the degree of hotnessthan touch.

Temperature of Parts

We often use warm water for a bath,and we take the water out of the bucketmug-by-mug. That is, we take waterpart-by-part. Is the temperature of eachpart of the water that we take thesame as the temperature of the waterin the bucket? Would it matter, as

far as temperature is concerned, whichpart of the bucket we take the waterfrom? Instead of the example above,consider a situation in which we take twohalf-filled mugs of hot water at the sametemperature and pour the contents of oneinto the other. The amount of water isequal to the addition of the amounts ofwater in the separated portions. Does thetemperature of the water also add up in asimilar manner?

If we imagine a substance to have


been divided into equal or unequal parts,each part will have the same temperature.It does not matter whether you considerthe whole substance or part of it. Ifyou combine two parts of water, thetemperature of the sum of parts is notequal to the sum of the temperatures.We say that temperature is an intensiveproperty2. By contrast, if we combinetwo parts of water, the volume of thecombination is equal to the sum of thevolumes of the parts. The same is trueof the mass of the substance. These areexamples of extensive quantities. Can yousay whether the density of a substanceis an extensive or an intensive quantity?Recall, that density is mass per unitvolume.

1.3 Temperature of objects inmutual contact

We know from common experience, asfor example, the pan of hot milk leftstanding, that hot objects gradually cooldown. Likewise a cold object, saychilled water in a glass, left standing,becomes warm. Now examine thefollowing activity, which is a variation ofa commonplace kitchen trick for coolingdown a pan of hot milk.

A 1.5 A water bath

Take a boiling tube partly filled with very hotwater. Close the boiling tube with a stopper

Figure 1.2: A boiling tube containing hot waterin a cold water bath.

or a thermocol cap, which has a hole for athermometer. Stand the boiling tube in alarge beaker that contains tap water. Suspenda thermometer each in the boiling tube andthe beaker (Fig. 1.2). How do you expectthe thermometer readings to change as timeelapses? Repeat the above activity with the hotwater in the boiling tube replaced by the sameamount of chilled water. Make a simultaneousnote of the readings shown by the twothermometers at intervals of 30 seconds. Howfar do you expect the thermometer readings to

2. There may be a real confusion among studentson this point. If so, the activity with parts of watershould be done and analysed properly.


go? Note the readings of the two thermometersas before. Compare the changes in temperaturewith the previous activity. What happensafter a long time, say 1 h later? How fardo you expect the thermometer readings togo? It would be instructive to plot graphs oftemperature versus time. You will have fourplots in the same graph.

Is cooling of one object accompaniedby warming up of something else? Whatwas warming up as the hot water inthe boiling tube cooled down? Assessthe following statement in the context ofchilled water in a glass: air is cooling downwhile the water is warming up, and thenperform the next activity.3

A 1.6 Liquid in contact with gas

Take a thermos flask, or improvise one.4 Leaveaside the lid. Make a tight-fitting lid ofthermocol or packing foam with a hole toinsert a thermometer to fit whichever thermosyou use. Take some chilled water anddetermine its temperature. Fill approximatelythree-quarters of the thermos with chilledwater and shut the lid with the samethermometer inserted in it. Ensure that thethermometer does not touch the water (SeeFig. 1.3). Note the thermometer readingas time lapses. What does the thermometershow the temperature of? After approximatelyhalf an hour, push the thermometer graduallyinwards so that its bulb dips in water. Whatdo you expect the temperature of the water tobe?

Figure 1.3: Cold water and air in contact witheach other and isolated from the surroundings.

A 1.7 Temperature of liquids in mutualcontact

Fill a beaker to about half with water at about60 ◦C. It would be good if you can use a beakerwith a jacket as in the previous case. Suspenda thermometer in it. Note the temperature.Keep another thermometer ready. Very gentlypour kerosene at room temperature over the

3. It should be noted that when we say liquidsare in contact in this activity, they are actuallyseparated by the wall of the container. Heatis transferred to the container also and thetemperature of the container changes during theexperiment. The activity on the next pageeliminates this hitch.

4. See ‘Notes for the Teacher’ at the beginning.


Figure 1.4: Two liquids, kerosene (above) andwater (below), at different temperatures and incontact with each other.

water in the beaker. Pour gradually along thewall; do not splash. You will have kerosene atroom temperature floating on top of hot water(See Fig. 1.4). Make sure that the volumeof kerosene is sufficient for a thermometerbulb to be completely immersed in kerosenealone. Suspend the second thermometer in thebeaker such that its bulb is entirely in kerosene,and does not touch the water. Predict thetemperatures shown by the two thermometersas time elapses. What do you conclude?

In the activities above, we noticedthat a hot object cools down if the

surroundings are cooler than theobject, and a cold object heats up if thesurroundings are hotter than the object.Objects in contact gradually come to thesame temperature if their temperaturesare different to begin with. The changein temperature is continuous, till thetemperatures of the two objects becomeequal. The temperature of the hotterbody falls, while that of the cooler bodyrises. While one body cools down, bodiesin contact with it heat up. Even whensomething happens to cool down (e.g. apan of just boiled milk left standing) orwarms up (e.g. chilled water in a glass leftstanding) by ‘itself’, the surrounding airis getting warmer or cooler, respectively.It is only that we do not generally noticethis change in the temperature of air. Whydo we not? Can you describe a situationwhere you actually feel it?

The first conclusive experimentsto determine what happens to hot orcold objects when kept in contact witheach other were done by Joseph Black,who, using a thermometer, came to theconclusion that objects which are incontact with each other acquire the sametemperature. This is true whether thebodies are solids, liquids or gases, andirrespective of what temperatures theyare at to begin with. Of course, it has to bestressed that there should be no externalfactors hindering the contact betweenthe bodies for this to happen. The idealsituation of no external hindrance is not


Joseph Black (1728–1799)Black studied ice-water mixtures and observed that the application of heat does not always

cause a rise in the temperature. He also found that continued supply of heat to boiling

water only increases the amount of steam produced, and does not lead to an increase

in the temperature of the water-steam mixture. Thus, he was the first to recognise the

latent heat during change of state. He also showed that different substances have different

specific heats. Black’s work led to the development of efficient steam engines, and he is

also credited with the discovery of carbon dioxide.

generally attained in practice, so normalobservations might appear to not conformto this conclusion. Contact between twobodies may not be exclusive, there maybe a third body, such as the surroundingair. This observation is significant in thedevelopment of our understanding ofheat and temperature. So significant,that the state of achievement of the sametemperature by two bodies is given aspecial name; the bodies are said tohave reached a thermal equilibrium. Theterm equilibrium indicates that no furtherchange in temperature can take place. Infact, if a body A is in thermal equilibriumwith a body B, and body B is in thermalequilibrium with a body C, then thebodies A and C are also in thermalequilibrium.

1.4 Does equal heating makethings equally hot?

When we heat a substance, do we findthat the rates of rise of temperature of all

substances are the same? Are they thesame for different quantities of the samesubstance? We know from our day-to-dayexperience, that a small amount of waterin a pan becomes hot quickly, as comparedto a large amount of water in the samepan, when heated on the same stove. Ifwe take the same quantity of oil andwater, would heating them for the sametime under same conditions increase theirtemperature identically? Let us perform afew activities to check and quantify theseideas.

A 1.8 Rate of change of temperature indifferent substances

Fill a large beaker or saucepan with waterand heat to around 60 ◦C (pan can be lefton the stove). In the meantime prepare twoidentical test-tubes with corks, containing 10 geach of water and kerosene, respectively. Alsoset aside two thermometers having identicalresponses. Make an arrangement to immersethe test-tubes with the thermometers in the


Figure 1.5: Testing the rate of change oftemperature in different liquids.

pan of hot water as shown in Fig. 1.5. Takecare that the level of the test-tubes is suchthat the liquid inside is fully immersed. Notethe temperature of the two liquids in the test-tubes every 30 seconds. Compare their rates ofchange of temperature.

A 1.9 Rate of change of temperature fordifferent amounts of a substance

Similar to the previous activity, but insteadof different liquids, take different amounts ofwater: 10 g in one test-tube, 20 g in the secondand 40 g in the third. Dip them in the pan ofhot water for the same period of time. Do notstir. Observe the change in temperatures in thethree samples of water. Repeat the experimentwith three samples of kerosene instead of water.

Does the same amount of heatsupplied to different substances of thesame mass lead to the same rise intemperature, or is the rise different fordifferent substances? If a fixed amountof heat is supplied to different massesof the same substance, is the change inthe temperature of the samples the same,or does it depend on the quantity of thesubstance? The amount of heat required toincrease the temperature of 1 g of a substancethrough 1 ◦C is called its specific heat, andis denoted by the symbol s. The amountof heat required to raise the temperatureof 1 g of water through 1 ◦C is calleda calorie (cal), i.e., the specific heat ofwater is 1 cal/g/ ◦C. If the specific heatof a substance is s, we can determinehow much heat (Q) is needed to raise thetemperature of a substance (whose mass ism) by a certain amount (say the change is∆T). These quantities are related by

Q = ms∆T.

Water has a high specific heat amongcommonly occurring substances. Table 1.1gives the values of specific heat of somesubstances.

With the help of the concept ofspecific heat and rate of change oftemperature that we just discussed, canyou predict the temperature of the mixturewhen two different quantities of waterat two different temperatures are mixed?Read the next activity, but perform it aftermaking the prediction.


Table 1.1: Specific heat of some commonsubstances

Materials Specific Heat[cal/g/ ◦C]

Silver 0.06Copper 0.09Glass 0.21Granite 0.19Air 0.24

A 1.10 Temperature of mixtures

Take two beakers of the same size and heat200 mL of water in each of them to the sametemperature. If you pour the two into a largerbeaker, what do you expect the temperature ofthe mixture to be? Suppose now that you heatthe water in one beaker to 80 ◦C and the otherto 60 ◦C. What will be the temperature of themixture? Test it out. Now take 100 mL ofwater at 80 ◦C and 200 mL of water at 60 ◦Cand mix the two. What is the temperature ofthe mixture?

Check your prediction as follows.5

Let the initial temperatures of the samplesof masses m1 and m2 be T1 and T2 (thehigher of the two temperatures is calledT1, the lower is called T2). Let T be thefinal temperature of the mixture. Thetemperature of the mixture is lower thanthe temperature of the hotter sample, buthigher than the temperature of the coldersample. This means that the hot samplehas lost heat, and the cold sample has

gained heat. The amount of heat lostby the hotter sample Q1 is m1s(T1 − T).The amount of heat gained by the coolersample, Q2, is m2s(T − T2). Since heatlost by the first sample is equal to the heatgained by the other sample, Q1 = Q2,which can be written as

m1s(T1 − T) = m2s(T − T2)

and can be simplified to

T =m1T1 + m2T2

m1 + m2

Repeat the experiment with differentmasses and temperatures of the samples.How close are the experimental valuesand the predicted values of T? If there is adifference, try to explain why.

Using the above analysis, solve thefollowing problem: You have two beakerscontaining identical masses of water andoil. Both are at the same temperature andwell insulated from the surroundings.Two identical blocks of the same metalat the same temperature (which is lowerthan the oil/water temperature) arelowered into the oil and the water,respectively. Will the temperatures ofthe oil and water be the same after sometime?

5. Do keep in mind that this exercise isapproximate, because there is heat loss to thesurroundings and containers, not just between thewater samples.


1.5 What flows, heat or cold?

A commonly asked question, when wewish to keep something cold (e.g. toprevent ice from melting), is: Do we wishto prevent cold from escaping, or preventheat from entering? In a contrastingsituation, we might wish to keep tea warmin cold weather, and ask the question, dowe wish to prevent the cold from enteringor the heat from escaping? Consider alsothe following: A tumbler of cold waterdoes not become colder and thereby heatthe surroundings, nor does hot oil leftstanding become hotter while cooling thesurrounding air.

In our common usage, saying that anobject is hot merely means that it is hotterthan some reference object, such as ourbody, and when we say that an object iscold, it is colder than the reference object.It is possible to say that all bodies are cold,but some are colder than others, just as it ispossible to say that all bodies are hot, butsome are hotter than others.

We can summarise all the aboveobservations by saying that in all cases,heat is transferred from a body at highertemperature to a body at a lower temperature.What we really wish (in the previousexamples) is to prevent transfer of heatfrom the surroundings to the object if theobject of interest is [to be kept] colderthan the surroundings, and we wish toprevent transfer of heat from the object tothe surroundings if the object of interest is[to be kept] hotter than the surroundings.Heat moves towards colder objects, notcoldness towards hotter objects.

Henceforth, we will avoid using theterms hot and cold in an absolute sense.When we use them, we will rememberthat they are relative, and imply higherand lower temperatures, respectively. Wewill also abandon the term flow that causesmuch confusion in the context of keepingheat in/cold out etc. Instead, we shalluniformly use the term transfer of heat,which is the next topic of discussion.


Summary

• The terms hot and cold in daily use are relative terms. Temperature is thequantity used to describe how hot a body is, and a thermometer is a deviceused to measure temperature. Hotter the body, higher is its temperature.

• Objects in contact with each other, and initially at different temperatures,gradually reach a common temperature due to transfer of heat from the bodythat has the higher initial temperature to the one that has the lower initialtemperature. This is true of solids, liquids and gases.

Chapter 2

Transfer of Heat

In the activities in the last chapter,we observed that objects initially atdifferent temperatures when kept incontact, gradually come to a commontemperature. It takes some time for thisto happen, or for thermal equilibrium to beestablished. When we heat a substance, ittakes some time for it to become warm.Does the entire object become warm allat once? Does heat take time to gettransferred from one point to another? Letus do some experiments to find answersto these questions. We will look separatelyat the transfer of heat in solids, in liquids,and in gases.

2.1 Transfer of heat in solids

A 2.1 Heat transfer along a strip

Take a metal strip roughly 15 cm long and 2 cmwide. You may use a metal ruler or even a cyclespoke, instead. Using wax stick several paperpins along a straight line at equal distances(approximately 3 cm apart) on it as shown inFig. 2.1. With the pins hanging down, holdone end of the strip to a candle flame. Note the

Figure 2.1: Transfer of heat from one end of asolid to the other.

order in which the pins fall. Why do the pinsfall?

Once again fix pins to the metal strip.This time leave the central spot empty and heatthe strip at the centre, as shown in Fig. 2.2.What is the order in which the pins fall?

What is the explanation for the orderin which they fall? Heat is transferredequally in all directions from the source.That is why in the first case the pinclosest to the candle falls first, while in thesecond case, pins at equal distances fromthe candle fall at almost the same time.In which direction is heat transferred

14

Chapter 2. Transfer of Heat 15

Figure 2.2: Transfer of heat in differentdirections in a solid, away from the source.

more rapidly? Does it make a differencewhether the strip is horizontal or vertical?Try out the above activity with strips heldin different orientations.1

Does the rate at which heat istransferred in a solid body depend on itssize and shape? Let us find out.

A 2.2 Factors affecting heat transfer ina solid

Take a saucepan or a beaker. Take three pipesof aluminium of the same length (length ofthe pipes should be about twice the depth ofthe pan), same wall thickness, but differentdiameters. Make an arrangement using acardboard lid with three holes of the right size,to suspend the three pipes in the pan as shownin Fig. 2.3. You may use a couple of tight turnsof a rubber band around each pipe to preventit from slipping. Ensure that the lengths ofthe pipes in the water are the same, and thatthey do not touch the bottom. Place a smalldrop of wax close to the upper end of the pipes.Make sure that the drops are identical in size.Heat the water. After some time drop somewax in the water. Continue heating for a few

Figure 2.3: Transfer of heat through solids andthe effect of size and shape.

minutes after the wax melts, while you stir thewater gently. Stop heating and stirring. Letthe water become still. Quickly place the pipeswith the lid in the water and start a stop watch.Note the times at which each drop of wax startsmelting. Repeat your experiment, but with thewax drops now placed closer to the hot water(i.e. closer to the lid) than before. Compare thetime needed for the wax drops to melt in thetwo cases.

Let us put together our observations.Does the time taken to melt increase as thedistance of the wax blob from the surfaceof the water is increased? How does thetime taken to melt change with the changein the diameter of the strip? If the time

1. While turning the metal strip to point indifferent directions, make sure that the flame of thecandle does not spread out. Also ensure that thepoint at which the strip is being heated does notchange.


ProportionalityWe often come across situations where one quantity depends on another. An example

might be that the volume of paint (x) required to cover a wall depends on the desired

thickness of the layer of paint (y ); if the thickness is doubled, the volume of paint required

also doubles. Or, if a tank is being filled with water, the mass of the water in the tank (x)

increases as the height of the water column (y ) increases; if the tank is being emptied, the

mass decreases as the height of the water column decreases. In both these examples, the

quantities in question were directly varying with respect to the other. The amount of paint

doubles if the thickness doubles, the mass of the water doubles as the height of the water

doubles, etc. We say that the first quantity is directly proportional to the second (x ∝ y ).

On the other hand, if you were to fill a fixed amount of water in a cylinder, the height of the

water column (x) in the cylinder would be large if the cross-section area of the cylinder (y )

were small, and vice-versa. Doubling the cross-section area of the cylinder would halve

the height of the water column, and so on. This is an example where the first quantity is

inversely proportional to the second (x ∝ 1/y ). For direct as well as inverse proportions, we

can specify a (fixed) number which will convert the proportionality relation to an equation.

This number is called the constant of proportionality. In the first example, the constant of

proportionality is the area of the wall, in the second it is the cross-section area of the tank,

in the third, it is the volume of water given to you.

to melt is shorter, then we say that heat isconducted well.

It has been found after repeatedexperiments of the type we justperformed, that the amount of heattransferred per unit time (q) between twopoints with a temperature difference∆T is directly proportional to thecross-sectional area (A) of the stripand the temperature difference (∆T), andinversely proportional to the length ofthe strip. Note the distinction betweenthe heat transferred per unit time and thetotal heat transferred, for which we had

used the symbol Q earlier. We can thuswrite three relationships

q ∝ ∆T, q ∝ A, q ∝ 1/l.

If the above experiment wererepeated with pipes of different materials,but of the same diameter and length,would you expect the time taken formelting to be the same for all materials?What would have happened had wechosen glass instead of a metal as thematerial of the strip? Recall, that you feelthe heat due to the hot tea faster when thetea is in a metal container, as compared


to a glass container. All other factors,namely ∆T, A, l remaining the same, theheat transferred varies from material tomaterial. This variation is specified by theconstant of proportionality in the aboveequation. Heat transfer through solidsis called conduction, and the constantof proportionality is called the thermalconductivity of the material and denotedby σ. Thus,

q = σ ∆T A/l.

Materials with small values ofconductivity are commonly calledinsulators while those with large valuesof conductivity are called conductors. Theunits of σ are cal·cm/s/ ◦C. It is generallyseen that good conductors also have smallvalues of specific heat.

2.2 Transfer of heat in liquidsand gases

In solids heat is transferred in alldirections. Does that happens in liquids?

A 2.3 Heat transfer in a liquid

Take a boiling tube and fill it 3/4th with water.Hold it inclined to a flame such that only theupper part of the water gets heated as shown inFig. 2.4. Once the water starts boiling, touchthe bottom of the tube. Surprised? Why doesthe water at the bottom remain cool, even whenthe upper half is boiling away?

Figure 2.4: Transfer of heat in a liquid.

Consider a situation where we heata beaker of water using a small electricalimmersion heater as shown in Fig. 2.5.Notice that the bulb of one thermometeris above the lower end of the heater andthe bulb of the other is below it. Predictthe temperatures that would be measuredby the two thermometers after the heateris turned on and then perform the activity.

Figure 2.5: Temperature of water above andbelow the source of heat.


A 2.4 Heat transfer in a liquid

Make an arrangement as shown in Fig. 2.5.Ensure that the immersion heater is welldipped and not touching the beaker or thethermometer bulb. Then turn the heater on.Observe the change in temperature indicatedby the two thermometers at 30 s intervals andexplain the readings.

When heating water to make tea,we generally heat the pot only from thebottom. Yet, the water at the top (andeverywhere within the pot) also becomeshot in a short time. What is the process bywhich the entire mass of water becomeshot, even though heat is supplied onlyfrom the bottom? Will the water becomehot everywhere if we heat it only near thetop as it would in a solid? Let us revisitthe ‘normal’ water heating process, as inwater being boiled for tea, but with someaids for observation.

A 2.5 Movement within a liquid due toheating

Let us place a beaker filled with cold wateron a hot plate or over a spirit lamp. Dropa crystal of potassium permanganate in thewater. Switch on the hot plate or light thelamp and observe the motion within the liquid.The motion will be indicated by the movementof the solution of potassium permanganate.Observe carefully the motion of the liquid,with particular attention to the pattern of itsflow.

Find out, or reason out, what mighthappen when the shape of the containeris changed. Heat transfer in a liquidoccurs by the movement of the liquiditself. Portions of the liquids closest to thesource of heat get hot first. Portions of theliquid that become hot rise to the surfaceand their place is taken by portions ofthe liquid from the top, thereby heatingthe liquid all through. This movement ofportions of the liquid in a loop patternis called convection, and thus we saythat heat transfer in a liquid is due toconvection. Contrast this mode of heattransfer, with that in a solid. In a solid wediscerned no net movement of the matterconstituting the solid.

What might be the mechanism fortransfer of heat in gases? Is it similar tothe case of solids, or the case of liquids?Or something else? We cannot see air.But if the lighting is appropriate, we cansee smoke or dust moving and mixing inair. We will utilise the motion of smokefrom an incense stick as a tracer for themovement of air in our experiments.

A 2.6 Convection in gases

A broken test tube can teach us somethinginteresting. Take a broken test tube and twolighted incense sticks. Hold the test tubeinclined, while a friend holds two incensesticks close to the two ends of the test tube asshown in Fig. 2.6. Watch the incense stickscarefully as you heat the test tube at its centre.


Figure 2.6: Transfer of heat in air.

When we burn an incense stick,the smoke does not immediatelyspread everywhere. Which way doesit preferentially move? Try to see it!Does this observation have a link to thecommonly made statement, that warm airis light, and hence rises upward?

In gases, as in liquids, transfer of heattakes place through the movement of thematter itself. Why does the movementof the liquid or the gas start off mostlyonly in the upward direction? Why doesthe liquid or the gas that has moved upreturn towards the bottom? What wouldhappen to transfer of heat in liquids hadthere been no gravity?

In the examples and discussions here,we looked into heat transfer in solids,which we called conduction, and thenin liquids and gases, which we calledconvection. The distinguishing featurebetween the two was that in convection,

there is movement of the medium asa whole, which is not the case in asolid. It is found from rather difficult andcarefully performed experiments2 that asmall amount of heat does get transferredby conduction in liquids, similar to thatin a solid, but for most purposes, we canassume that convection is the dominantmode of heat transfer in gases and liquids.

2.3 Heat transfer in theabsence of a medium

In the discussions so far, we have alwayshad a medium through which heat istransferred. Is a medium always neededto transfer heat? When you stand beside abonfire (Fig. 2.7), you feel hot. A similareffect is observed if you place (withouttouching) your palm below a hot pan kepton a stand. Recall that convection onlytransfers heat upwards, neither sideways,nor downwards. This implies that, whenyou are standing level with a fire, or belowa hot body, there must be some meansother than convection that transfers heatto you.

On a winter day when the sky is clearand the sun is shining, if you step out ofshade into the sun, you immediately feelwarm. This is due to the heat from the sun.Now if the heat from the sun were beingtransferred via air as the medium, there

2. See, for example, the internet resource,http://fluidproperties.nist.gov/thermal.html


Figure 2.7: Heat may be transferred in all directions, as we notice around a bonfire.

could not have been a dramatic differencein the temperature of air in a distance asshort as a step. Since air is in constantmotion, the temperatures of two portionsof air should be nearly equal. Moreover,the air around you feels cool, but if youstay in the sun long enough, your skin getsquite hot. This means that your body isabsorbing heat from the sun more rapidlythan the air surrounding you. Heat fromthe sun is reaching you without the air inbetween getting hot.

A 2.7 Temperature in sun-n-shade

Make an arrangement to suspend athermometer from a portable stand. Make twosuch arrangements, and place one of themin the shade of a building or a tree, and the

other in direct sunlight. Keep a watch onthe thermometer left in direct sunlight. If itsreading increases rapidly, bring it back intoshade quickly, otherwise it may break! Are thetwo readings different? If the thermometersare left in place for a long time, how dothe temperature readings shown by the twochange? Why?

The examples that we just sawsuggest that in addition to convection,there is another way of transferring heat,which transfers heat in all directions.In fact, in all these cases heat can betransferred even in the absence of amedium. This mode is called transfer byradiation. Radiation, like light, can bereflected, in particular from shiny metallicsurfaces, as we will see next.


Figure 2.8: Using a canopy to reflect heatfrom a light bulb.

A 2.8 Reflecting Heat

Take a 100 W light bulb with a reflectorcanopy. If it does not have a canopy, you canimprovise one using thick aluminium foil, butdo make sure that the foil does not touch thewires or other electrical contacts. Take a smallamount of solid ghee and place it in a spoonunder the lamp as shown in Fig. 2.8. Switchon the light bulb and record the time it takes forthe ghee to melt. Next, put the canopy on thebulb and again record the time it takes to meltthe ghee. Compare the two readings. Whatrole would you say the aluminium canopy hasplayed in warming up the ghee?

When placed in the sun, black or darkobjects get hotter quickly, as compared toan object that has a shiny, white surface.A dull or rough surface gets hotter more

easily than a shiny surface of the samematerial. This is because a smooth surfacereflects heat from the sun better than arough surface. To get an idea of howstartling the difference in the ability ofdifferent bodies to absorb heat in theabsence of convection or conduction is, letus perform a small experiment.

A 2.9 Dull and Shiny, Black and White

Take tinfoil, or thick aluminium foil. Make twocups out of it, either using origami ideas orsome of your own. The cups should be almostidentical, and approximately 50 mL in volume.It is preferable if the mouth of the cup is smallerthan the overall diameter. Hold one of themwith tweezers over a candle or kerosene flame,such that the flame does not touch the cup butthe soot from the flame gets deposited on theoutside of the cup. Now place a small blobof wax in each cup, and place the cups in thesun. Watch what happens, and explain yourobservations.

2.4 Conductors and insulators

We always use a metal saucepan forcooking. We do not use a glass bowl.However, when we drink tea, we usuallyuse a glass or a ceramic cup, not a metalcup. What is the reason for that? Can youthink of more cases where we use to ourbenefit the ability of certain materials toresist transfer of heat? Such materials arecalled insulators.


Table 2.1: Thermal conductivity of somecommon substances

Materials Conductivity[cal/cm/s/ ◦C]

Silver 1.01Copper 0.99Steel 0.012Glass 0.0025Polyethylene 0.00006

Being able to prevent conduction ofheat is vital in many cases. When wego out on a cold day, we wear a sweater.In cold regions of the world people wearseveral layers of warm clothes. Veryoften, it is necessary to prevent loss ofheat in factories, to conserve fuel. Withexperience we have been able to devisemany insulating materials. Table 2.1gives the values of conductivity of somesubstances.

The data in the table might suggestthat we use polyethylene tongs instead ofmetal tongs. But we do not find such tongsin use. However, pans or pressure cookersoften have plastic covered handles. Whyis this so? What would happen if thetongs were short, or if we had to hold apan on a stove using a pair of tongs for along time? The usefulness of a substance,or design of devices is based on multipleconsiderations. Reason out the case oftongs by taking into account conductivityand melting point of the material of the

tongs, distance of the hot object from theuser, ease of use and robustness.

Touch sensation of cold and hot

From our earlier experiments, we knowthat objects in a room gradually reachthe same temperature. However, youmust have noticed, even when objectshave been left in the same surroundingsor conditions for a long time, we do notsense them as being equally cold or hot. Ametal pan, for instance, feels colder than aplastic container. A polished floor tile feelscolder than a floor mat, but a rough stonetile feels less cold. A metal bench left inthe sun feels hotter than a wooden benchleft in the same place.

These common observations resultfrom several factors coming into play.We will first note these factors and thenapply them to the situations above. (a)We find something hot to touch whenheat is transferred to our skin, and coldto touch when heat is transferred fromour skin to the object. (b) Metals aregood conductors of heat and have smallervalues of specific heat than non-metals.(c) The rise in temperature depends onthe specific heat of the substance. (d)Rough, hard surfaces make poor contactwith our skin in comparison to smooth,hard surfaces.

A rough tile feels less cold thana polished tile because the roughnessreduces the area of contact with the skin


so less heat is transferred from the skin. Amat feels less cold than a floor tile becauseit is a poor conductor and hence there isless heat transfer from the skin. A metalpan feels colder than a plastic containerbecause heat gets transferred very quicklyto it from our skin, not because of atemperature difference – the temperatureof the two objects is almost the same –but because of the higher conductivity ofthe metal. In the case of benches keptin the sun, apart from the differencesin sensation due to conductivity, therecan be a difference in the temperatureitself. A metal bench could in facthave a higher temperature than a woodenbench. When placed in sun they heatup by radiation. The temperature of themetal may increase more than that of thewooden bench, owing to the lower specificheat of the metal, even though it absorbsless radiation than wood.

2.5 Prevention of heat transfer

We wear woollen clothes in winter to keepourselves warm. Ice is covered in a gunnybag or covered in saw dust or straw toprolong its melting. What is the roleof the covering material? Suppose youtake two identical blocks of ice and placethem in two saucers, and cover one ofthem up by sawdust, or woollen strandsor coconut husk powder. Which cube willmelt faster? Why?

In the examples above, we are

preventing heat from being transferredto or from the object of interest, as thecase may be, by covering it with a poorconductor of heat. Since heat can betransferred by conduction, convection andradiation, a scheme for prevention of heattransfer, or insulation, must minimise allthree modes of transfer.

Let us examine the choice of woollenclothes in winter to keep ourselveswarm. Air is a poor conductor, butconvects easily – so one can achieveheat insulation using air, provided theair is still or trapped! This happensvery effectively in the so-called warmclothes. Wool has many minute poreswhich trap air. Cotton too is porous,but less so, and is usually densely spunand woven, leaving very little trappedvolume. Moreover, cotton fibres havefewer empty spaces than wool fibres.So for a given thickness wool insulatesbetter than cotton. A woollen pulloveris therefore more effective than a cottonpullover of the same thickness in keepingthe body warm, and two thin blankets(one over the other) more effective thana single blanket of double thickness.Bird feathers form another superb systemof insulation based on trapped air andporous non-conducting natural polymer(keratin) to protect themselves from cold.It might appear surprising, but certaincommunities use blankets made of animalfur to insulate themselves from the harshsun. In colder climes, it is very important


to protect oneself from the wind, as windcan carry away a lot of heat from anexposed body. Whatever clothing wewear has to allow sweat to evaporate,otherwise we will end up being clammy!Wool scores well in this respect too.

There are several cases at home, in theindustry, and so on, where it is importantto be able to conserve heat, or preventtransfer of heat. Pipelines carrying coldwater in the industry, or even thosein large air-conditioning plants, have aninsulated casing made of a porous orspongy material with a reflective outerlayer. This prevents heat transfer from theoutside to the cold water in the pipe. Evena simple thing like covering the saucepanwhen boiling water for tea prevents loss ofheat by convection of air above the watersurface. List a few situations where youfind various means of preventing heat lossbeing employed!

A Thermos Flask

A thermos flask is used to keep thingscool or warm for a long time. It iscommonly used for food, but in thelaboratory it is used for storing othersubstances too. How should an idealthermos be? A thermos has to preventtransfer of heat from either inside to theenvironment, or the other way round.This implies that its design should preventconduction, convection, and radiation.Conduction can be reduced by choosing

outer casing

double-walled,silvered glassbottle

insulatingsupports

insulatingstopper

Figure 2.9: The construction of a thermosflask.

an insulating material, and reducing thearea of contact between the inside andthe outside. Convection can be reducedby preventing a contact between thecontainer and the surrounding air. Thissuggests that a thermos should ideallyconsist of two containers, one inside theother, with the air in the gap removed.To reduce radiation loss, the surfaces ofthe container should be made smooth andhighly reflecting. A practical and closeto perfect thermos took time to develop,and the thermos flask, as is known today,is credited to James Dewar. A Dewarflask consists of a double walled glasscontainer, the top rims being fused to eachother. The inner surface of the outer walland the outer surface of the inner wall aresilvered, the air in the gap is removed,and the evacuated gap is sealed off. The


glass container has a stopper lid made ofan insulating material. The glass is thenplaced in a larger plastic container, leavingan air gap. Small supports hold the glassin place, while minimising the area ofcontact. Figure 2.9 shows a sketch ofsuch a flask. Thermos flasks of the Dewar

type are being replaced by containers thatare double walled (usually stainless steelinside, and plastic outside), with a thicklayer of an insulating, porous polymerin between. These are more robust anduseful from a practical point of view, butare less effective than a Dewar flask.


Summary

• Heat is transferred within a body from a region of higher temperature to theone at lower temperature.

• The mode of transfer of heat in solids is called conduction. While conductioncan occur in liquids and gases too, the dominant mode of transferring heatin these is convection, which involves an overall movement of the matter inthe medium.

• Heat can also be transferred in the absence of a medium. Such heat transferis called transfer by radiation. Light coloured and shiny objects mostlyreflect the heat falling on them while dark coloured and dull or roughsurfaces tend to absorb most of the heat falling on them.

• Certain substances prevent heat from being transferred quickly throughthem as compared to others, and they are called insulators. Metals conductheat effectively, and also reflect radiation effectively.

Chapter 3

Effects of Heat

In this chapter we will look at the physicaleffects heat has on a substance. From ourday-to-day experience, we are aware ofchanges such as expansion of an object orthe change in the state of an object, e.g.ice changing to water or water changingto steam. We will look at these in detail.

3.1 Heat and expansion

Let us begin by looking at the effect of heaton gases.

A 3.1 Expansion of gases

Take an empty ball-pen refill and an emptyinjection bottle with a tight stopper. Removethe refill tip. Pierce a hole in the stopper usinga thick needle and push the refill through it.Slide in a drop of coloured water into the refill.You may use a pin to ‘guide’ the drop. If youquickly open and shut the stopper, the waterdrop will slide in easily. Make sure that thedrop does not fall into the bottle. Now rub yourpalms together vigorously and hold the bottletightly between your palms (See Fig. 3.1).Observe what happens to the water drop and

explain your observations. What is the changein the volume of the air inside?

Some fun is in order. Take a usedPET water bottle. Remove the cap andadd a little water to it. Press a coin onits mouth and invert the bottle to wetthe coin sufficiently. Verify that no waterleaks out. Now place the bottle in anupright position without disturbing thecoin. Warm up your palms by rubbingand then hold the bottle gently, but firmlyin your palms, so that there is adequatecontact between the palms and the bottle,ensuring that the bottle is not compressed.

Figure 3.1: Expansion of air in a bottle by thewarmth of a palm.

27


Watch what happens! Explain what yousaw. Explain the role of water in theexperiment.

Do liquids behave in the samemanner as a gas when heated?

A 3.2 Expansion of liquids

Let us now do a similar experiment, but withwater. Simply fill the previously used injectionbottle fully with the coloured water that wasused earlier for blocking the refill. Make surethat there is no air left in the bottle, and thatthe liquid level is clearly seen in the refill.Now warm your palms by rubbing and holdthe bottle in your warm palms for some time.Watch what happens. Do you see any changelike you did in the case of air? Next, hold thebottle with a pair of tongs and hold it over acandle (See Fig. 3.2). Does the level of theink in the refill change? Find the reason forthe difference seen between warming up usingyour palms and using a flame.

In both activities, you would haveobserved that the level of water in thesmall tube rises. Why does it rise?Why did it not rise in case of water,when the bottle was held between warmpalms? What happened to the volumeof the air or water in the bottle when itwas heated? What happened after youstopped heating?

A 3.3 Expansion of a solid

Let us now see what happens to a solid when it

Figure 3.2: Expansion of water on heating bya candle.

is heated. Collect a few items: a bicycle spoke,few short wires, a battery and a bulb, a candleand matches, a square piece of aluminiumor tinfoil wrapped over a small rectangularpiece of wood, and a couple of stones or paperweights. Build an electrical circuit with thespoke as one of the components as shown inFig. 3.3. In the beginning let the spoke touchthe coin and check that the circuit is completeand the bulb glows. If it does not, checkall contacts and clean them using sand paperor a blunt blade. Now create a small gapbetween the coin and the spoke by slipping astrip of paper in between. Does the bulb gooff? Remove the paper gently, taking care notto disturb the arrangement. Heat the spokeand watch what happens. Does the bulb glowagain?

Can you explain why the bulb glowsagain after the spoke is heated? What

Chapter 3. Effects of Heat 29

Figure 3.3: Increase in length of a solid on heating.

change in the spoke caused the circuitto be completed? What happens a shortwhile after you stop heating?

In the experiment with a spokeand a bulb, you saw that the spokeexpands when heated. Let us repeat theexperiment after increasing the gap veryslightly. You may set the gap first byslipping a strip of paper, and in the secondstage, set the gap by inserting two strips,or a thicker strip. Does the gap get bridgedby the heating with the same candle forthe same time? What if you heat for alonger time? Can we increase the gapindefinitely, as we heat the spoke everlonger?

Suppose you heat the spoke usingtwo candles instead of one. How doyou expect the observations to change?Repeat the experiment with two candlesto test your prediction. The length of

the spoke increased when heated. Whathappened to its thickness (diameter)? Hadyou replaced the spoke by a shorter, butthicker rod (both made of steel, and of thesame mass), and repeated the experimentexactly in the same manner, would theelectrical contact be re-established uponheating for the same time?

A 3.4 A simple thermometer

Take the bottle and refill as was done inearlier activities. Fill the bottle completelywith kerosene and shut it tight with thestopper in which the refill is fixed. Do itgently, so the kerosene will not spill, insteadit will rise into the refill (see Fig. 3.4).Our thermometer is ready! Compare ourthermometer with the laboratory thermometer.What are the similarities and differences?Hold both thermometers in hot water. Does


Figure 3.4: An improvised oil-basedthermometer compared with a laboratorythermometer.

our kerosene thermometer take longer toreach the maximum height, or the laboratorythermometer? What could be the reason forthis? What properties should a substance haveto be suitable as a thermometric medium?

Let us compare our results concerningexpansion of solids, liquids and gases.Recall that the tiny amount of heatsupplied by rubbing the palms wasenough to appreciably expand air, but notwater, even though the volume of the airand the water was the same. That is,a small change in temperature led to anoticeable change in volume in case ofgases. Also note, that the mass of air is

much smaller than the mass of water forthe same volume. Solids need to undergoa much larger change in temperature thanliquids for a noticeable expansion. Wecan summarise our observations by sayingthat for a given rise in temperature, solidsexpand less than liquids, while liquidsexpand less than gases, the volumes beingequal in all cases. Can we now say thatexpansion is a measure of how hot thesubstance is?

3.2 Change of state

What happens when we heat a solid suchas wax or ghee long enough? Try it out.You will find that it melts, but would ithave melted had it not been heated? Whathappens to a block of ice if you leave it ina saucepan? It turns into water, so, we saythat ice is the solid form of water. Wheredid the heat that converted ice to watercome from? Would the ice have melted ina shorter, or in a longer time had it beenheated as in the case of wax?

Take some soldering wire or a smallpiece of tin (which you can obtain from atinsmith), and hold it to a flame. Observewhat happens. Does it turn from solid toliquid? Does the saucepan in which youheat the water also melt?

Take a small saucepan of water andcover it with a dry lid. Make sure thatthe lid sits firmly, but is not too tight.Heat the pan on a stove and pay attention.Do you hear a faint sound which goes


Figure 3.5: Some examples of change of state from solid to liquid.

on increasing? When this happens, stopheating and carefully lift the lid. What doyou see on the underside of the lid? Wheredid the water come from? What happenswhen you heat longer?

In the examples above, we saw thatsubstances changed their state – solid toliquid, or liquid to gas – when heated, orwhen left in a surrounding with a differenttemperature. Let us note some contrastingissues in what we saw. The metal panin which water was being heated didnot melt, but tin, which too is a metal,did melt. Wax melted only when heatwas supplied, but ice, apparently, meltedwithout any additional supply of heat!Can you assess the situation, not in termsof the heat supplied, but in terms of thetemperature of the substance when thechange took place?

It is found that most materials change

state when heated. However, they do soat vastly differing temperatures. Water[liquid], for example, turns into ice [solid]at 0 ◦C and into steam [gas] at 100 ◦C.Aluminium [solid] turns into liquid at570 ◦C, while nitrogen [gas] turns intoliquid at −196 ◦C. The temperature atwhich a solid turns to liquid is called itsmelting point, while the temperature atwhich a liquid turns to a gas is called itsboiling point.

Densities of solids and liquids

What happens to the density of a solidwhen it melts? When we melt ghee (athome) or wax (as in the activity in theprevious chapter), we find that the solidstays at the bottom of the container. Thisimplies that the liquid has a lower densitythan its corresponding solid.


The thermometer re-visited

We have seen that when exposed to hot surroundings, the mercury or alcohol column ina thermometer becomes longer, i.e., the substance expands. Expansion is taken as ameasure of the degree of hotness. An ideal thermometer based on expansion should havethe following properties:

• It should expand or contract significantly for small changes in temperature, so thattemperatures can be precisely measured.

• The substance should take up little heat from the object of interest to come to the sametemperature as the object of interest, otherwise the thermometer will show a lowertemperature than what it was before inserting the thermometer.

• The expansion should be uniform over a wide range of temperatures.

• If the thermometer can be made compact and reusable and provides accuratemeasurements each time, it is ideal.

Thus, the ideal thermometric substance has a high expansion coefficient which remains

the same at all temperatures of interest, and should have a low specific heat. It should

not change its state over the temperature range of interest. A gas based thermometer,

or a thermoscope, satisfies most of these criteria, but it is voluminous, and cumbersome

to use. A mercury thermometer satisfies most of these criteria, while also permitting a

compact and robust construction. However the more commonly used substance is alcohol

rather than mercury. The reason is not because it is superior based on the ideal criteria,

but because mercury is a poisonous substance, while alcohol is not, and also because

mercury is very expensive compared to alcohol. An alcohol thermometer is useful over

the temperature range −70 ◦C to 110 ◦C, while a mercury thermometer is useful over the

temperature range −20 ◦C to 300 ◦C. A dye is added to alcohol to improve readability.

The strange case of water

Have you noticed that when ice meltsit floats on the water resulting from themelting? What do you conclude about thedensity of water compared to the densityof ice? The case of water is a rare caseof a solid having a lower density than thecorresponding liquid. In most substances,

the liquid has a lower density than thecorresponding solid.

Solids that have a smaller densitythan the corresponding liquids exhibitanother anomalous phenomenon, namelythat their melting point is lowered underthe application of pressure. A niceillustration of this is the gradual splitting


Figure 3.6: Melting of ice under pressure.

and re-joining of ice along the track of awire exerting a force on the ice. This canbe easily effected by hanging weights by awire as shown in Fig. 3.6. A corollary ofthis effect is that two blocks of ice pressedtogether for a while will stick togetherwhen the pressure is released.

3.3 Vaporisation

If an open pan of water is left standing, thewater level keeps falling, and ultimatelythe water disappears completely. Wheredoes this water go? Observe this underdifferent conditions – at different timesof the day, at different times of the yearor at different locations. If you wereto leave a covered pan of water with alid standing for a long time, you willnotice fine droplets of water sticking tothe underside of the lid. A similar, and amore dramatic effect is seen when water isheated with a lid on the pan.

What happens is that some of thewater leaves the bulk liquid and havingtransformed to the gaseous state mixes

with the air around. This process iscalled vaporisation. How do changesin the surrounding conditions affectvaporisation?

In most cases, the liquid and vapourphases exist together. Some liquids,such as alcohols and ethers evaporatereadily, compared to water or oils. Thereason why you smell alcohol when abottle is left open is because the alcoholevaporates in copious quantities (even atroom temperature) and reaches your nose.Air contains some water vapour, whoseamount varies with temperature and thepresence of large water bodies, such aslakes or rivers. Have you not noticedthat the air feels moist in the vicinity of alake or a river? A term called humidityis usually used to denote the amount ofwater vapour in the air.

Humidity is a significant factor indetermining the weather. As the vapourcontent in the air keeps on increasing,there comes a point when the vapourcondenses and forms droplets of water.The formation of droplets depends


on both, the amount of water and thetemperature of the surrounding air.The process of evaporation followed bycondensation, when the water vapourand air temperature conditions are right,is responsible for phenomena such as theformation of dew and rain.

The effect of a fall in temperature onhumid air can be seen easily. When abottle of chilled water or a container froma refrigerator is left in the open, we findwater collecting on the outer surface of thebottle or the container. This effect is morewhen the air is humid, and is due to thevapour in the air condensing on the coldsurface.

Sublimation

Some solids undergo significantvaporisation. Two examples arenaphthalene and camphor – we smelltheir presence by their vapours. All solidsdo vaporise to some extent, but the effectis very small. Ammonium chloride is apeculiar solid that does not vaporisesignificantly at room temperature,but when heated sufficiently, it getscompletely converted to vapour, withoutundergoing a change to the liquidstate. This process is called sublimation.Vapours of ammonium chloride can bedangerous, so do not try to sublimateit unless there is plenty of ventilation.Children should not do it without adultsupervision.

3.4 Does heating always leadto increase in temperature?

In the activities above and in the previouschapters we found that heating generallyleads to a change in temperature, althoughthe change may differ from substance tosubstance. But, is it always true thatheating leads to change of temperature?Let us check it out.

A 3.5 Latent heat of evaporation

You will need two laboratory thermometers,a saucepan full of water, and a stove.Keep the saucepan on a stove and suspendthe thermometers through slightly over-sizedholes in a lid as shown in Fig. 3.7. Make surethat one of the two thermometer bulbs is wellunder water, but does not touch the pan, whilethe other is above the water. Now light theflame and note the temperature of the waterevery few minutes, until well past the time thewater starts boiling. Record the temperature ofthe water vapour rising from the pan.

What is the most striking point in yourobservations? Can you explain theobserved patterns of the readings in thetwo thermometers? Let us try out a similaractivity, but with a solid.

A 3.6 Latent heat of melting

You will need: a laboratory thermometer, someice and a small bowl or cup. Take someice and crush or grate it. Fill up the cup


Figure 3.7: Change in temperature of wateras it turns into steam.

completely with the crushed ice and standthe thermometer in it such that the bulb iscompletely enclosed by ice but does not touchthe cup. Note the temperature shown by theice. Now leave the cup in the sun or heat itgently. Keep a record of the temperature whileyou watch the ice melt. Does the temperatureof the water formed rise continuously?

In both the above cases, heat wasbeing supplied continuously, but thetemperature did not rise continuously. Itrose for a while, and then for some time itremained unchanged. At this juncture theentire substance was undergoing a changeof state, from liquid to gas (or from solidto liquid). This change of state is differentfrom the case of vaporisation, where onlythe liquid (or solid) from the surface waschanging to gas. In other words heatwas used for effecting a change of state,without increasing its temperature. Likespecific heat, the amount of heat requiredto effect a change of state varies fromsubstance to substance. The amountof heat per unit mass needed for thechange is called latent heat of melting[solid–liquid change] or latent heat ofevaporation [liquid–vapour change].


Summary

• Heat causes expansion in all states of matter. For a given substance,expansion is a measure of how hot that substance is.

• Heat can transform matter from one state to another: solid to liquid to gas.

• Some substances may be directly transformed from the solid to the gas phase.This phenomenon is called sublimation.

• Change of state requires heat, but that does not lead to a change oftemperature.

• Most substances contract upon cooling and expand upon heating, and thedensity of the solid is greater than that of the corresponding liquid.

• Water shows anomalous behaviour, in that it expands upon freezing, unlikeother solids, and the melting point of solid water (ice) is reduced by theapplication of pressure.

Chapter 4

Heat and Work

4.1 Some observations

We have already seen a connectionbetween heat and expansion – supplyingheat leads to an increase in volume. Inthe experiment on expansion of air in aninjection bottle, we found that the drop ofink in the stopper moved outwards. Inthe experiment with the PET bottle with acoin as a lid, we found that the coin movedwhen the air in the bottle became warm.

Such movement from a state of restimplies that there is a force acting on theink drop or the coin. Since pressure isforce per unit area, we can say that thelid, or the ink drop, moved due to anincrease in the pressure exerted by theair inside the bottle, which in turn was aconsequence of heating of the air. In otherwords, heating, or change in temperature,not only led to an increase in volume of thegas, but also an increase in the pressureof the gas. Can it happen the other wayround? Will an increase in pressure of agas lead to an increase in its temperature?

A 4.1 Compressing Air

Find a bicycle pump, and push the piston backand forth a few times. Feel the barrel forchange in temperature. Next, close the nozzle(or ask someone to press a finger against thenozzle) and pump again as shown in Fig. 4.1.Feel the barrel for change in temperature.Compare the two cases. Note that in the lattercase air is not escaping the barrel, and itsvolume is reducing.

Figure 4.1: Increase in temperature of airupon compression.

37

38 HEAT AND TEMPERATUREV

olum

e

Temperature

Charles’ Law for an Ideal Gas

Pre

ssur

e

Volume

Boyle’s Law for an Ideal Gas

Figure 4.2: Graphs depicting Charles’ and Boyle’s laws for gases.

In the above experiment, with thenozzle closed, you exerted force on theair inside the barrel causing its pressureto increase, as a result of which itstemperature increased and its volumedecreased. Pressure, Temperature andVolume of a gas are related. Therelationships between the three werestudied by the scientists Charles, Boyleand Gay-Lussac, as early as in the 17th

and 18th centuries. The inferences fromtheir investigations are summarised intwo important laws.

Charles’ Law: At constant pressure, thechange in the volume of a given mass ofan ideal gas changes in proportion to thechange in its temperature.

Boyle’s Law: For a fixed mass of anideal gas kept at a fixed temperature,pressure and volume are inverselyproportional to each other.

The laws are depicted as graphs inFig. 4.2. These laws are idealisations,or approximations, and all gases showsome deviation from this behaviour. Thebehaviour of helium is closest to ideal gasbehaviour.1 Many gases come close toideal gas behaviour at low pressures andhigh temperatures.

4.2 Expansion and mechanicalenergy

In the air expansion experiment usingthe injection bottle, the force that pushedthe ink drop outwards does not cause itto move for ever. Explain why. Whatdoes the distance moved by the ink dropdepend on?

1. An ideal gas is one whose molecules have zerosize, and no internal structure, and scatter fromeach other without loss of energy. The significanceof the concept of an ideal gas will be clear in thenext two chapters.

Chapter 4. Heat and Work 39

Robert Boyle (1627–1691) andJacques Alexandre Cesar Charles (1746–1823)Boyle got to know of the vacuum pump invented by Otto von Guericke and worked on

improving its design with the help of Robert Hooke. He was able to conduct many studies

using this pump, which led to the enunciation of the law which states that the volume of

a gas varies inversely with its pressure. In addition, he was also able to discover the role

of air in the propagation of sound. He also laid the foundation for modern chemistry by

giving the first modern definition of an element and differentiating between compounds and

mixtures. Charles was lucky to have a law named after him. The law which states that the

volume of gases is proportional to the absolute temperature under constant pressure was

in fact formulated by Gay-Lussac, who credited it to unpublished work by Charles. Charles

had carried out an experiment in which he filled the same volume of different gases in five

balloons. When he raised the temperature of all the five balloons to 80 ◦C, he found that the

increase in volume was the same in all cases. Charles was also the first to use hydrogen

in balloons where previously only hot air had been used. The first balloon managed to lift a

weight of approximately 9 kg.

Recall from mechanics, that energy isspent when an object is displaced againsta force. Mechanical Work is defined asthe product of the displacement of a bodyalong the direction of the applied forceand the magnitude of applied force. In thesituation described above, heating of air leadsto work being done on the ink drop. In thecase of the PET bottle, work is done on thecoin.

Let us look more closely at the workdone when a gas expands with the aid ofan example.

A 4.2 Expansion and work done

Take an injection syringe with its needle

removed. Press the plunger nearly half wayin and seal the tip by an airtight plug, or yourthumb, or by using a sealant or an adhesive(See Fig. 4.3). Draw the plunger out. Whathappens when you stop drawing? Why does

Figure 4.3: Pulling a piston (i.e. a syringeplunger) atmospheric pressure.


Joseph Louis Gay-Lussac (1778-1850)Gay-Lussac did important work in both Physics and Chemistry. But we generally hear of

him in connection to the law named after him which states that under constant pressure,

the volume of a gas is directly proportional to its temperature. Gay-Lussac improved the

design of common laboratory equipment like the burette and pipette along with playing a

part in the discovery of boron and recognising iodine as a separate element. He also went

up in hot-air balloons to study the composition of the atmosphere at different altitudes.

the plunger move into the barrel? It movesin because the air outside exerts pressure onthe plunger. In drawing out the plunger ofthe syringe, the air inside expanded to occupythe increased volume, and the pressure insideis lowered in comparison to the pressure of theair outside. In pulling the plunger out workhas been done by you against atmosphericpressure. When you release the plunger, the airoutside does work on the plunger – and in turnon the gas inside it. Repeat the above exercise,but instead of drawing out the plunger byhand, stand the syringe in a hot water bathafter sealing the tip. What do you expect?

In mechanics, the work done equalsthe amount of energy spent by the agentapplying the force. Thus, if you push ablock, you are doing work on the block,and spending energy. When you liftsomething, you apply a force. You needto spend more energy to lift a heavy objectthan a light one. In other words, you needto do more work.

How much is the work done when thebarrel moves out? Let us find out. The

force on the piston is P × A, where P isthe air pressure and A is the area of theplunger. If the plunger moves a distanced, the work done is

W = P × A × d

Since A × d is the change in the volume,∆V, of the gas, the work done is P × ∆V.This is true whether the barrel moves outby your pulling on it, or because the airinside is heated. When the gas expands,it loses heat, which is converted intowork.2 That means energy is expended.This suggests a relationship between heat,work and energy. Indeed, heat is oftencalled thermal energy, a term we shalldiscuss in the next chapter.

Recall the activity with blockedbicycle pump at the beginning ofthis chapter. There it was found thatcompression leads to heating, which is theexact opposite of heating leads to expansion.To reduce the volume of the gas, you hadto perform work on it, whereas, when

2. The relation between the heat supplied andwork done forms the basis of the steam engine!


a gas expands due to heating, the gasdoes work on the stopper. As anotherexample, consider an empty, stopperedinjection bottle held over a candle flame.In a short time the stopper flies off thebottle – try it out! Once again, heatingof a gas is causing displacement of anobject in contact with the gas. Thus heatperforms work, or heat can be convertedto mechanical energy. A common exampleof this conversion is when water is boiledin a saucepan, and the lid of the saucepangets lifted.

A 4.3 Displacing objects using heat

Take a test-tube filled partly with water andclose it with a cover-slip and set it on a flame.Note how long you have to heat until thecover-slip moves up and down. Record thistime and throw away the hot water. Let thetest-tube cool down completely. Add exactly

Figure 4.4: Work done by supplying heat to agas.

the same amount of fresh water as before.Cover the test-tube, and place a small weighton the cover-slip, such as a few coins, as shownin Fig. 4.4. Heat once again. Note the time ittakes for the cover-slip and coins to show somemovement, and compare it with the previousexperiment. This experiment could also bedone with a saucepan having a close fitting lid.

What is the relationship between theweight displaced by the steam and thetime for which heat is supplied? Since thesteam arising from boiling water exertsforce on the lid, and displaces it, it is doingwork against gravitational force. Thusheat performs work.

4.3 Mechanical equivalent ofheat

The equivalence of heat and mechanicalwork was demonstrated and establishedby the efforts of Joule. He spuna tight-fitting paddle in a cylindercontaining water by applying a weightto a string wound over the axle of thepaddle as shown in Fig. 4.5. Since thecontainer is made water-tight, watercannot escape when the paddle turns.The spinning paddle churns the waterand the kinetic energy of the spinningpaddle is transferred to the water. Theeffect of constant churning of the watertrapped in the water-tight container isto make the motion of water quickerand more irregular. Eventually, the


Figure 4.5: Joule’s apparatus for demonstrating the equivalence of heat and (mechanical) work.

kinetic energy imparted by the paddles isdistributed throughout the water, therebyincreasing the thermal energy, and hencethe temperature, of water.

If we measure the change, ∆T, intemperature of the water, then knowingthe mass of the water mw, and the specificheat of water s, we can calculate the heattransferred to the water Q:

Q = mw × s × ∆T

As the block accelerates under gravity, itskinetic energy increases. However, theacceleration of the block is less than g, thegravitational acceleration of a free-fallingobject, because the paddle in the wateris resisting the motion of the block. Ifthe acceleration of the block is a, mb

is the mass of the block, and d is itsdisplacement, then mb × a × d is the workdone by gravity on the paddle.

Having measured the rise in thetemperature of water and the accelerationof the block, Joule could show that theheat generated Q was proportional to thework done, or,

Q ∝ mb × a × d

The constant of proportionality in SI unitsis 4.184 joule/calorie, and is called themechanical equivalent of heat. You wouldremember, that 1 J is the work done whena body of mass 1 kg is accelerated by1 m/s2 and is displaced through 1 m.


James Prescott Joule (1818-1889)Joule was one of Dalton’s pupils, and that might explain his ready rejection of the calorific

theory which was widely accepted at that time. He was convinced that temperature was a

measure of the motion of the constituent particles and made three different measurements

of the mechanical equivalent of heat. Though his work was not immediately accepted

(maybe because of the precision with which he claimed to have made the measurements),

the SI unit of energy is now named after him. In addition to this work, he also found the

relationship between the resistance and the amount of heat dissipated in a circuit.

4.4 Cooling by expansion

So far we have concerned ourselves withdeveloping a relationship between anincrease in temperature of a gas and work,by way of expansion. Let us now look athow expansion can lead to cooling.

A 4.4 Cooling trick

Take a bicycle tyre-tube. Pump it up hard.3

Now rapidly pull out the valve. Compare thetemperature of the air rushing out, relative tothe air outside. To do this you could placeyour finger on the neck of the valve as shownin Fig. 4.6, or even better, place the bulb of athermometer in the air jet.

The air rushing out does Workagainst the atmospheric pressure.Part of the thermal energy of the airinside is converted to work, therebyreducing its thermal energy and hence thetemperature4.

The air inside the tube and the airoutside have the same temperature since

Figure 4.6: Expanding air cools when it doeswork against atmospheric pressure.

the tube is in contact with the outside air.So, cooling by expansion appears to be acase of transferring heat from a body ata certain temperature, to another similarbody at the same temperature. Is thisconsistent with our inferences from earlierchapters?

3. If you wish to pump up the tube very hard,it is safer to have a tyre encasing the tube in thisactivity. Explain the role played by the tyre.

4. This cooling effect is called the Joule-Thomsoneffect, or the throttling effect, and is usefulfor liquefying gases and for refrigeration andair-conditioning.


Julius Robert von Mayer (1814-1878)Mayer took an indirect route to Physics, he studied and practised medicine and got

interested in Mathematics and Physics only later. In spite of this, he made valuable

contributions to the field of thermodynamics which were not immediately accepted. He

was the first to state that energy can neither be created nor destroyed. Not only this,

he described oxidation as the source of energy for living things and proposed that plants

converted light into chemical energy.

Now suppose, instead of letting outthe high pressure air from the tube toatmosphere, we had placed an airtight,evacuated container snugly on the nozzle,as shown in Fig. 4.7, and then opened thevalve. Would there be a change in thetemperature of the rushing air? Why orwhy not?

It is found that when a gasexpands freely, there is no change in

evacuated container

air at highpressure

valve

Figure 4.7: Expansion of air at high pressureinto an evacuated container.

its temperature. This can be understoodin terms of the work done – since thepressure in the evacuated container iszero, there is no force opposing themotion of the air particles rushing intoit. So, at the beginning of the expansionno work is done and no heat is lost bythe gas. As the gas starts filling theevacuated chamber, the pressure in theevacuated chamber starts building upand work is done as time goes by. In theearlier example, work was done by theexpanding air against the surrounding air,causing it to lose heat and consequentlythe temperature of the expanding air wasreduced.

Heat transfer between bodies at thesame temperature

As we have seen in the earlier chapters,objects at different initial temperatures,when kept in contact, gradually cometo a common temperature, and heat istransferred from the object at a highertemperature to the object at a lower


temperature. But, in the precedingexample we found that heat was lostfrom the gas! Transferring heat froman object at a lower temperature to anobject at a higher temperature, or betweentwo objects that are initially at the sametemperature, is impossible unless some

energy is spent by an external agent. Thephenomenon of cooling by expansion thatwe saw is an instance where energyis spent in reducing the temperature ofan object (a gas) whose temperature isinitially equal to the temperature of thesurroundings.


Summary

• Heat and work are related, and they can be transformed into each other; thusheat is a form of energy.

• Pressure, volume and temperature of an isolated gas are related to each other.Pressure is directly proportional to temperature, and inversely proportionalto volume for a fixed amount of gas.

• When a gas expands, it performs work and loses heat.

Chapter 5

What Makes Things Hot

In the previous chapters we accepted thenotion that temperature is a measure ofhow hot a substance is. We observed thatobjects which have different temperaturescome to the same temperature when theyare in contact with each other, as the bodywith higher temperature loses heat. Wealso looked at some effects of heat, andat how heat is transferred. We have notyet answered the question What is it thatmakes things hot? Of course in our dailylives, we use a gas stove or a coal stove, oran electric heater to generate heat for ourdaily needs, while in our experiments weused candles or Bunsen burners, but theseare merely means of heating a substance.We still do not have an idea of what is it in abody that makes it hot, and what determinesthe temperature of a body.

5.1 Early ideas

The question ‘What is heat?’ keptscientists of the past centuries busy. Oneof the prominent beliefs of the scientistsuntil the middle of the nineteenth century

was that heat is an invisible substance(called the caloric) that is present insideall matter. Joseph Black, an Englishscientist, was a proponent of this idea. Hecould explain many phenomena basedon the caloric model. The plausibilityof the caloric probably arose fromphenomena related to the transfer ofheat. As we have seen, heat is nottransferred instantaneously across anobject. Moreover, it is always transferredfrom a hot object to a cold object. Thusarose the notion, that hot objects havesomething in excess over a cold body.By postulating that when this excessis transferred, the deficit in the coldbody is balanced, one could explain theobservation that equality of temperaturesis achieved between hot and cold bodiesin contact.

The idea of a caloric was also usefulin explaining expansion of an object uponheating. Expansion is explained bythe spreading of the caloric between theparticles of the material the object is madeof, thereby increasing the gaps between

47


the particles. This model of heat is ableto explain phenomena such as transfer ofheat and expansion due to heat, but it failsin certain respects.

There was one phenomenonconcerning heat where the caloric theoryfailed spectacularly. It was a matterof common observation that rubbingobjects against each other (such as one’spalms), creates heat, and increases thetemperature of the objects being rubbed.Explaining this effect satisfactorily wasa challenge for the caloric theory. If thecaloric theory were true, then the amountof caloric in each of the palms wouldremain unchanged unless some heatwere explicitly supplied from outside(we leave aside the issue of what wouldhappen to a person’s palms if held overa flame). Merely moving them back andforth against each other should not haveincreased the amount of caloric withinthem. Experience tells us that heat can begenerated by rubbing almost any pair ofobjects against each other, and the amountof heat generated depends not so muchon the objects themselves, as on the forcewith which they are rubbed against eachother.

A 5.1 Heat by friction

Take a flat iron strip (such as a hacksaw bladeor a knife) and rub it against a rough surface(such as a large stone or the underside of atawa). Another option is a marble rubbed

against the floor. Is heat generated by rubbing?Does only one of the two surfaces in contactbecome hot? What happens when you rub fora longer time, without changing how rapidlyyou rub? Compare the temperatures of theheated surfaces when the rubbing is rapid andwhen it is slow, but for the same durationof time. Several commonplace examples ofgeneration of heat by friction can be cited:the tyre of a vehicle gets hot while in motion,a stone or a piece of metal being cut by asaw-wheel or a cutting disc gets hot.

Is there a limit on how much heat youcan generate by rubbing as in the aboveexperiment? Suppose we keep rubbing fora minute, cool the object by dipping it inwater and start rubbing it once again. Inprinciple, you could repeat this process asmany times as you want. So, there is nolimit on how much heat you can generateby this means. If the caloric theory werecorrect, and the heat generated was dueto the caloric being released, then at sometime all the caloric would flow out, and itwould be impossible to generate any moreheat in that object by further rubbing.

Rumford’s experiments

Very elaborate experiments concerningthe generation of heat by friction weredone by Benjamin Thompson (laterknown as Count Rumford), who was asupervisor in a gun factory. He observedthat a great amount of heat is generatedwhen the barrel of a gun is bored. So

Chapter 5. What Makes Things Hot 49

Sir Benjamin Thompson, Count Rumford (1753-1814)Rumford tried his hand at many things during his life – served in the army, invented the

coffee percolator and recognised that heat generated by friction was a refutation of the

calorific theory. He was also the first to appreciate the role of convection in the heating and

cooling of fluids and that air and water were poor conductors of heat.

Figure 5.1: Heat generated by cannon boringin the experiment done by Rumford.

much, in fact, that the boring of a gunimmersed in water could lead to theboiling of water, as demonstrated usinga specially built apparatus, shown inFig. 5.1. He noticed that heat was onlygenerated when the borer was moving,and when boring was stopped the gunbarrel gradually returned to normaltemperature. He found that the piecesof metal that were expelled in the boringprocess were quite hot. This meant, ifthe caloric model were true, that caloricwas being lost from the barrel, and thatthe barrel should never again becomehot. This was not true, for when the

boring process was resumed the barrelbecame hot once again; the supply ofheat was apparently endless. Rumfordconfirmed that no physical change hadtaken place in the material of the gunbarrel by comparing the specific heatsof the material removed by boring andthe material that remained. He measuredthe mass of the metal filings emergingfrom the boring while they were stillhot, and after they had cooled down,in order to examine whether the loss ofcaloric appeared as a change in mass. Hisobservations did not show a change inmass due to heating. This was a strongpoint against the caloric theory, for if thecaloric were a substance, it ought to havea mass, but none of the carefully repeatedmeasurements showed that it did.

He examined these observations verycarefully and came to the conclusion thatthe concept of the caloric must be wrong.The most significant point emergingfrom his experiments was that motion isnecessary for heat to be generated byfriction. He therefore asserted that the rootcause of heat was related to motion. Butwhat kind of motion could be associated


with heat? Clearly not any kind ofmotion, for two identical objects, one leftstationary and the other moving around,do not show a difference in temperature!To stress the point that not any arbitrarymotion can be linked to heat, let us do thisthought experiment.

A 5.2 A Thought experiment

What if in Rumford’s experiments at the gunfactory, the borer were left in the barrel andthe entire assembly were moved, instead of theborer moving within the barrel? Would suchmotion lead to heating of the barrel?

Although Rumford was convincedthat motion was the only tenable sourceof heat, he could not say decisively whichkind of motion was responsible for theobserved heat. It was clear that ordinarymotion, (such as movement of the cannonas a whole) could not be linked to heat.Moreover, heat was only being generatedwhen objects were rubbed against eachother. The nature of the surfaces incontact and the rapidity of the relativemotion were two significant factors thathad an influence on the amount of heatgenerated. The hypothesis of motion andheat being related needed investigation asto which kind of motion was responsible forheat.

With Rumford’s hypothesis in mind,let us perform some experiments and seewhether they give us any clue about thekind of motion that can be linked to heat.

5.2 Is everything within asubstance static?

A 5.3 Mixing in liquids

Take two identical beakers and fill one of themwith water at room temperature. Fill theother with the same amount of water, butat approximately 60 ◦C. The hot water usedhere should be pre-heated, stirred and allowedto become still. Add to the two beakersone drop each of ink that has already beendiluted. A drop of red fountain pen inkdiluted by about 10 drops of water at roomtemperature is suitable. Make sure that yourdropper dispenses drops of the same size at alltimes. Watch how the ink spreads gradually(Fig. 5.2). Compare the rate at which theink spreads throughout the water in the twobeakers.

Figure 5.2: Spreading of ink in water.


We know from our day-to-dayexperience that salt or sugar dissolve inwater more quickly when the water is hot,compared to the case when it is cold. Toconfirm this, let us do a small experiment.

A 5.4 Mixing salt in water

Measure out one spoonful of salt each intwo identical beakers with insulation (or useinsulated cups), containing the same amountof water, but one chilled (say at about 10 ◦C)and the other hot (say around 80 ◦C). Do notstir the mixture. Cover the cups and leavethem standing for 2 min. Without stirringor shaking the solutions, check how salty thewater at the top of the two beakers is, by gentlyscooping a little water and tasting it.

In the two activities that we justperformed, try to assess the factor(s) thatmight have led to the observed differencesin the mixing of the added substance (inkor salt) in the solutions while also makinga note of the temperatures. Pay attentionto the observation that at the beginningof both activities the substances that wereadded to water were present in one place(or close to one point within the liquid),but as time passed, they were no longerconfined close to that point. The substancehad moved to different locations within theliquid. Examine your inference in the lightof Rumford’s assertion about heat beingrelated to motion. Assess the followingstatements.

• Ink spreads in water randomly,until there is equal amount of inkeverywhere, i.e. it is spread outuniformly and mixed with water.

• Uniformity is achieved faster if thewater is warmer.

• The above observations suggestdivisibility of the ink drop or saltgrains, and not mere expansion, orspreading out, of the drop or the grainas a whole.

• We call the divided units particles.

• Warmer the water, more rapid is themotion of the particles.

• Heat influences the motion of theparticles.

Let us turn to gases. Do we observeany internal motion in gases? We usuallydo not, since many gases, and in particularthe air surrounding us, are transparent.But there are cases when we do get a hintof internal motion in air. For example,when we see light streaming into a roomthrough a gap or a hole in the wall ora window, we see dust suspended in airilluminated by the light. These particlesare generally seen to move in randomdirections. What causes this motion? Weknow that dust particles often settle on thefloor and other surfaces, and exhibit nomotion, in contrast to the situation whenthey are in air. Could the air have somerole in their motion?


NH4OH

swab

HClswab

reaction occurs here

Figure 5.3: Difference in the diffusion of two gases.

Have you noticed that when youenter a freshly painted room, you smellthe paint? Why is that so? If youleave a petri-dish filled with alcohol in aclosed room, does the air in the room startsmelling of alcohol after a while? Doesthe quantity of alcohol in the petri-dishreduce after a while? Does this suggestthat alcohol is spreading throughout theair?

Is there motion within a gas? Do gasesspread and mix with each other? Let usfind out.

A 5.5 Diffusion in gases

Take a long glass tube. Hold it horizontallyand insert wads of cotton dipped inhydrochloric acid and ammonium hydroxidesolutions into the two ends respectively asshown in Fig. 5.3. Be careful here, bothchemicals are harmful to the skin, so itis recommended that you wear gloves oruse tongs to handle the wads. A whitecloud starts appearing at a definite positionwithin the tube which is due to the formationof ammonium chloride. Mark the position atwhich the white cloud begins to form. Repeatthe experiment with the tube held vertically,taking care that the ends corresponding to thehydrochloric acid and ammonium chloride

wads are not interchanged. Relative to themark made in the first case, where doesthe cloud form in the second case? Do theexperiment yet again, with the tube vertical,but upside down. If a long glass tube is notavailable, one could use a stiff transparentplastic sheet, rolled up and kept rolled bysticking a sellotape along its length.

The white cloud of ammoniumchloride was formed at some distancefrom either wad. This implies thatammonia from ammonium hydroxide andhydrogen chloride from the hydrochloricacid solution have moved away from thewads and spread through the air to reactwith each other. Does the ammoniumchloride cloud have a regular shape? Canyou describe where it is formed, how itgrows, how it spreads?

Consider the assessments made inthe context of mixing of liquids onceagain, but now in the context of paint,alcohol, hydrogen chloride and ammoniaspreading in air. Would the motion of theparticles of these substances be different, ifthey were to spread in empty space, i.e. ifthe surrounding air were removed?

Let us now do an experiment inwhich we try to compare the spreading of


a substance in air, and in empty space.1

A 5.6 Smoke in Vacuum

Take a bell jar with an airtight baseplatewhich has a provision for a stopcock or avalve. Place a petri-dish on the base platein which a matchstick is stuck vertically ina blob of wax and cover the baseplate withthe bell jar. Place the bell jar in directsunlight. Take a large convex lens and burnthe matchstick by focusing sunlight on it (SeeFig. 5.4). How does the smoke from thematchstick travel? Open the bell jar andreplace the burnt matchstick with a new one.Cover again and pump out the air. Thematchstick will burn even when the jar hasbeen evacuated because the mixture on thematch head contains potassium chlorate thatreleases oxygen. Repeat the burning activityusing the same convex lens. How do you

Lensto focus sunlight

To vacuum pump

Bell jar

Base plate

Match-stick

Figure 5.4: Experiment to observe theunhindered motion of smoke in partial vacuum.

expect the smoke from the matchstick to travelnow?

In the experiment above, it is seenthat when smoke is formed with air stillin the bell jar, the smoke rises up and thengradually spreads all through the bell jar.When the bell jar is evacuated, however,the smoke travels in all directions moreor less equally, and directly away fromthe matchstick. Compare the two caseswith two situations in the game of carrom.If you place the queen coin at the centre,pack six coins around it, and strike them,they mostly move directly away from thecentre. If, on the other hand, a largenumber of coins are spread randomly onthe board, then a randomly struck coinwill scatter here and there. Does thedifference in the motion of smoke particlesin the air-filled and the evacuated bell jarsuggest what influence air particles haveon the motion of smoke particles?

With the above observations in mind,examine the following statements.

• Smoke particles move aroundrandomly in the presence of airbecause they collide with air particles.

• When the air particles are removed,the smoke particles emerging fromthe matchstick move in straight lines,without any collisions.

1. This activity may not be possible in schools.A video recording of this activity is available fromhttp://www.eklavya.in/616


John Dalton (1766-1844)To Dalton goes the credit of creating a theoretical framework which could explain all

the empirical laws explaining the behaviour of gases and also the laws of chemical

combination. He was drawn into chemistry because of his interest in meteorology – he

was studying the amount and distribution of various gases in air (which led to his law of

partial pressures) and he was led to conclude that the particulate nature of matter best

explained the observations. Though this idea had been proposed more than two thousand

years earlier by Democritus and periodically resurrected by Lucretius, Galileo and Boyle

amongst others; Dalton was able to make it a fruitful scientific idea by linking the concept

of weight to each atom, thus measurements could be linked to theory. With some simple

assumptions, he was able to calculate the atomic weights of various elements. Of course,

his work had to undergo further refinements before being finally accepted, but he deserves

the credit for postulating the modern atomic theory.

5.3 Modern model of matterand heat

In all experiments that we have discussedin this chapter, we found that some kindof motion constantly occurs within liquidsand gases. When some other liquid orsolid material is introduced in the liquid,the foreign material tends to spread aboutin all directions randomly, and over timemixes completely in the liquid or gas. Wealso found that mixing is more rapid in ahot liquid or gas, as compared to a coldone.

A word of caution is necessary here.In all our discussions concerning themotion within a substance, whether itwas mixing or diffusion, the scale of themotion, i.e. the amount of liquid thatappeared to be moving, or the distances

over which the motion was observed,was large enough to be perceived by oursenses. That scale is, however, far largerthan the scale of motion giving rise toheat. Nonetheless, it reflects to someextent the motion on a smaller scale thatis the cause of heat. We shall see in thenext chapter how tiny the ‘particles’ areand how densely packed they are in asubstance. It will also give us some ideaof how tiny the scale of the motion of theparticles is.

Based on various experiments andobservations – some of which we havediscussed – scientists have put forth thehypothesis, that all matter is made up oftiny particles that are in persistent randommotion. By postulating that matter is madeof tiny, identical, indivisible particles, itis possible to explain the phenomenon


Brown, Einstein and Brownian MotionRobert Brown (1773–1858) was a botanist who gave one of the earliest descriptions of

the nucleus and cytoplasmic streaming. He finds a place in this module because the

continuous jittery motion of suspended microscopic particles is called Brownian motion

even though it was first reported by Jan Ingenhousz in 1784–85. Ingenhousz observed

this using charcoal particles while Brown was observing tiny particles released by ruptured

pollen grains which are suspended in water. The pollen particles in Brown’s experiment

moved about due to collisions with the water molecules, as they are light but large enough

to be seen under a microscope. Brown later observed this with the particles of non-living

matter too, leaving him to conclude that life was not generating this motion.

The explanation of this motion had to wait about three-quarters of a century, and it came

from Albert Einstein (1879–1955), who is easily the most famous and easily identified

scientist and is almost synonymous with genius. He is best known for his work on special

and general relativity, but he got the Nobel Prize for his work on the photoelectric effect.

His work on the problems of statistical mechanics led to the explanation of Brownian motion

as evidence for the existence of particles, and this forms the basis of the modern kinetic

theory.

of heat as being related to the motion ofthe constituent particles in random directionsaccompanied by collisions amongst theparticles, which leads to motion not onlyin all directions, but also with varyingspeeds. An approximate idea of themotion of particles in a gas can be hadfrom Fig. 5.5. The critical points arerandomness of the motion, and collisionsbetween particles – to be contrasted withdirected motion, such as that when aparticle moves along a well-defined pathwithout colliding with other particles, ormotion of the object as a whole.

This hypothesis explains most of theobservations regarding heat, temperature,

Figure 5.5: A representation of randommotion of gas particles. The size ofthe molecules is greatly exaggerated incomparison to their separation.


pressure and diffusion. As a substanceis heated, particles in the substance movemore rapidly. In a liquid or a gasthe motion is completely random, but insolids the constituent particles move backand forth, like the bob of a pendulum,or a weight attached to a spring. Inother words, they oscillate about a pointin random directions. They do notleave the solid, unless the temperatureis very high. The hotter a substancebecomes, the more rapidly its constituentparticles move. When the substance

cools down, the motion of its constituentparticles becomes less rapid. Left ina particular surrounding, a solid, liquidor gas will achieve an equilibrium withthe surroundings by exchange of energybetween its particles and the particlesof the surrounding medium. In thenext chapter we will build on the ideathat heat is nothing but motion of theseparticles and see how we can understandtemperature in terms of the particulatemodel of matter and the motion of theparticles.


Summary

• Modern model of matter postulates tiny particles oscillating back and forthin solids, and moving randomly in liquids and gases.

• Heat is related to persistent random motion of the particles. The hotter asubstance is, the faster is the random motion of the particles it is made of.

• Heat is not related to the motion of a substance as a whole.

Chapter 6

Temperature and the Particulate Natureof Matter

Our model of matter and heat comprisestiny particles which are in constantmotion, in random directions or inan oscillating manner. We have seenexamples in which heating a mediummakes the motion faster. Thus, thesense of an object being hot or cold mustbe related to how rapid the motion ofthe constituent particles is. In otherwords temperature should be related to themotion of the particles. How do we definea single quantity (temperature) that willrepresent the motion of all particles?

6.1 How large are particles ofmatter?

To begin with, let us make an estimate ofhow many particles we have to deal with.As a first step, let us estimate how smallthese particles might be and from thatmake an estimate of how many particleswe have in 1 mL of a liquid. We assume,for simplicity, that particles are cubes.

A 6.1 Number of particles in a givenvolume

The idea in this activity is to determine thethickness and volume of an oily film on waterand use that information to determine the sizeof a single particle and the number of particlesforming the layer, assuming, that the film isformed of a single layer of oil particles. Itworks best with oleic acid dissolved in hexaneor benzene, but other oil–solvent combinationsmay also work.

Dissolve 0.2 mL of oleic acid in 20 mL ofan organic solvent such as hexane or benzene.Select a graduated syringe (2 mL volume)and a fine needle (gauge 28 or finer) andconfirm that it dispenses drops of uniformsize. Establish conditions under which youcan dispense a single drop at a time. Nextdetermine the volume of one drop of thesolution by finding out how many (say m)drops are formed from 0.2 mL of the solution.The volume of the drop is therefore 0.2/m mL,and the volume of oleic acid in the drop (V) is(0.2/20)× (1/m), or 1/(100m) mL.

58

Chapter 6. Temperature and the Particulate Nature of Matter 59

As shown in Fig. 6.1, fill a large flatplate (approximately 50 cm in diameter) withwater and sprinkle ordinary talcum powder onthe surface. The talcum powder will aid indemarcating the area of the oil film.

Precautions: Fans should be turned offand the talcum powder should be sprinkled on

syringe

water withtalcum powdersprinkled on it

pattern formed on waterafter the drop falls

Figure 6.1: [Top] Creating a thin film of ameasured amount of oil over a still watersurface. [Bottom] Oil film formed on water,demarcated by the talcum powder. Theboundary may not be very smooth, but weapproximate it by an inscribed circle.

the water surface only when it is still and justbefore adding the oil drop. If done in advance,the powder becomes wet and is not useful fordemarcating the oil film.

Add a drop of the oleic acid solutiongently on the surface of the water using thepreviously established technique. The solventevaporates as soon as the drop spreads over thewater surface, leaving behind a film of oleicacid of a near circular shape. Measure thediameter (d, in cm) of the film and determineits area (A = πd2/4).

Let us now calculate the size of theoleic acid particles.

• If the particles are cubes of side s, thenthe thickness of the film, assuming itis formed by a single layer of particles,will also be s. The volume of the layerwill be V = sA. V and A are measuredin the experiment, so we can calculate s.

• The volume of each particle is s3, so thenumber of particles (N) in the oil filmwill be given by N = V/s3.

• Hence the number of particles in 1 mLof oleic acid is mN.

In general liquids have more closelypacked molecules than gases, while solidsare slightly more densely packed thanliquids. Typical numbers per mL are 1019

for gases, and roughly 1022 for liquids andsolids. Thus, any quantity of matter thatwe can perceive with our senses containsa very large number of molecules.


Avogadro and his numberLorenzo Romano Amedeo Carlo Avogadro di Quaregna e di Cerreto (1776–1856) was

another scientist whose work was not appreciated in his own life-time. Based on

Gay-Lussac’s work on the volumes of combining gases, Avogadro recognised that the

relationship between the masses of the same volume of different gases (under identical

conditions of temperature and pressure) is the same as their respective molecular weights.

He was the first to appreciate the difference between the atoms and molecules of elements,

or that atoms of the same element could be combined to form molecules. He proposed,

around 1821, that all gases contain roughly the same number of molecules in a given

volume (the temperature being the same). This proposal was verified in due course, and

generalised. The number of particles (atoms or molecules) present in one mole of any

substance has been named the Avogadro number in his honour. A mole is that amount of

a substance that corresponds to its atomic or molecular weight in grams. If, for example,

you take M grams of a pure substance, where M is its molecular weight, then it contains

the same number of molecules, no matter what the compound is. That means, 2 grams

of H2, 18 grams of H2O or 63.5 grams of Cu all contain the same number of molecules or

atoms. That number is approximately 6×1023. A mole is often used as a unit to simply

specify Avogadro number of particles.

6.2 Representative propertiesof a large group

In building further our model of heatbeing related to the motion of particleswithin a substance, we are now faced withan immediate problem. The problem isthat we need to take into account thesimultaneous motion of a collection of avery large number of particles. How dowe describe the simultaneous, collectivemotion of such a large number of particlesin a simple manner?

To sort this out, let us ask whether weneed the exact motion of each one of the

particles. How important is the behaviourof individual particles when describingthe property of the collection of particles?Is it possible to derive a single number, ora single parameter that can be consideredas representative of a property of a groupconsisting of several members?

Let us consider the followingsituation. A factory has a large number ofworkers, who are to be given a shirt andtrousers as uniforms. Clearly not all ofthem have the same measurements. Somemay be tall and thin, some short andthin, some tall and fat etc. Can we (moreprecisely, a tailor) make an estimate of


how much cloth will be needed to clotheall workers, without really measuringeach person up? Since clothes have beenmade for several generations, and byseveral people by now, tailors have a verygood idea of how much cloth is needed,by and large, for a person. That estimateof size is behind the fact that cut piecesof cloth ready to be stitched usually havethe same size. For convenience of storing,transporting and pricing, a commonlyaccepted size of cut pieces has beenestimated and accepted by traders, andsuits most people. Of course there mightbe some individuals who are either tootall or too fat to be accommodated in thestandard size, but such cases are rare, andby-and-large the cut-piece system seemsto work well.

The reason for this can be found in thefact that if we survey a large populationand tabulate the heights (or girth, orany measurement of the body) of theindividuals, we will, by and large, findthat although there is a range of heights,within this range the heights of a largenumber of people lie close to a certainvalue. This value lies approximatelymid-way between the extreme valuesof the heights in the population. Ifwe were to add up the heights of allindividuals and divide it by the numberof individuals, we get a rather usefulvalue that can be considered to be arepresentative height of the population.This value is called the mean, in the

0

200

400

600

800

1000

162 163 164 165 166 167 168

num

ber

of p

eopl

e

height in cm

Women Men

Figure 6.2: Distribution of heights of men andwomen in a population. The graphs show thaton the average women are shorter than men,but not all men are taller than all women.

present case the mean height, and takesinto account, to some extent, the variationin individual heights. In some senseit represents the characteristics of theentire population and can help in makinguseful estimates, as seen in the precedingexample.

See the graph in Fig. 6.2 and saywhether it tells you something aboutthe cloth requirements for women incomparison to that for men (assumingsimilar dresses). Does the estimate matchyour intuition about the difference in thecloth requirement for men and women?

A single value, the mean height inthis example, does not tell us how widelyspread the heights in the population are.It can happen that the mean heights oftwo populations are the same, but in onepopulation the heights are close togetheras compared to the other population.In this case another measure, called the


0

200

400

600

800

1000

162 163 164 165 166 167 168

num

ber

of p

eopl

e

height in cm

Population A

Population B

Figure 6.3: The distribution of heights ofmembers of two populations. Although themean heights are the same, the spreads ofheights is different in the two populations.

variance is useful. The variance is ameasure of the spread of values aboutthe mean. In the graph in Fig. 6.3,you will notice, that values in populationB are more widely spread out than inpopulation A, although the mean valuesare the same. We then say that thevariance of B is greater than that of A, andthis single value brings out the fact, thatthe two population distributions are notquite the same, even though their meansare identical.1.

These concepts about the mean valueof a property and the spread of the valuesamong the members of a population willbe useful to us in describing the motionof the large number of particles of matterthat are in persistent random motion.Our goal is to relate the motion of allparticles within a substance to the degreeof hotness.

6.3 A measure of the randommotion of a collection ofparticles

The property relevant to us at the levelof the individual particle in the contextof heat is how rapid its motion is.Taking that as the basis, we will assign arepresentative quantity for the rapidnessof the motion of all particles taken together.

For a single particle, the motion iscompletely described by its velocity. Fora collection of particles in a substance thevelocities of the particles are random, sothe average velocity of the entire collectionwill be zero, irrespective of how smallor large the individual velocities are. Tosee how the average velocity is zero,consider any direction you like. Someparticles will be moving approximatelyin this direction. But, you could havechosen exactly the opposite direction andseen an equal number of particles movingin the newly chosen direction. If youtake the velocities along the first directionto be positive, the velocities along theopposite direction will be negative. Sothe sum, and hence the average of thevelocities for the chosen pair of directionsis zero. This argument can be repeatedfor any pair of opposite directions. So

1. The mean is defined as the sum of all valuesdivided by the number of values; µ = ∑i xi/N.The variance is defined as the sum of the squares ofthe difference of values from the mean, divided bythe number of values; σ2 = ∑i(xi − µ)2/N


the average velocity of a large collectionof particles is zero, no matter how rapidlythe molecules may be moving. Thus, theaverage velocity does not tell us anythingabout how rapidly the individual particlesare moving. In other words, no useful linkcan be made between the average velocityof the particle and the degree of hotness.

Let us trace the motion of a particle. Itmoves, collides with some other particle,as a result of which the direction andspeed of both particles may change. Hadthere been no collisions, the particlewould keep moving along a straight line,and finally escape from the substance.This is not what most particles do(although in the case of evaporation someparticles do escape). When a substancebecomes hotter, as seen in the examplesof mixing in the previous chapter, themotion within the substance becomesmore rapid. But higher speeds alone arenot a characteristic of a hot substance.A necessary consequence of the morerapid motion is that the time betweensuccessive collisions reduces, or in otherwords, the number of collisions in agiven time, i.e., the rate of collisions,must increase. Thus, something becominghotter implies two consequences at thelevel of the particle motion: increasein velocity and increase in frequency ofcollisions. A quantity that is used to definetemperature must take into account bothfactors, the speed of the particle and thefrequency of collisions. In other words,

the quantity that we could consider asrepresentative of the degree of hotnessmust necessarily depend on the productof two factors, speed of the particles andthe frequency of their collisions. But, asa little reflection shows, the frequency ofcollisions itself depends directly on thespeeds of the particles involved: the morerapidly particle moves, the greater is therate at which it encounters other particles.

Hence the quantity that represents thedegree of hotness must be proportionalto v × v. Notice that if we add thequantity v2, particle after particle, the sumwill not be zero, because v2 is alwayspositive, and is unaffected by the directionin which an individual particle is moving,while simultaneously reflecting the factthat the motion has become more rapid.Hence the average value of v2, ratherthan the average of the velocity, is theappropriate quantity for conveying thedegree of hotness within the model of heatthat we are building.

The quantity v2 is closely related tokinetic energy. The kinetic energy of anobject of mass m moving with a velocityv is given by mv2/2. The average kineticenergy of N number of particles is:

KEave =1N

[m1v2

12

+m2v2

22

+. . .+mNv2

N2

]

The average kinetic energy is a non-zeroquantity that takes into account thechange in the rate of collisions and thechange in the velocity of the particles


Ludwig Eduard Boltzmann (1844–1906) andJames Clerk Maxwell (1831–1879)Boltzmann was also a firm supporter of the particulate nature of matter and his suggestion

that the energy levels of a physical system are discrete could be considered the foundation

of quantum mechanics. He worked extensively on heat and temperature, or what is more

generally called thermodynamics. His major contribution was in providing a statistical

description of the motion of particles in gases. Together with James Clerk Maxwell, he

formulated a description of the speeds of these particles, upon which the modern idea of

temperature is based.

Maxwell is best known for his equations of classical electromagnetic theory which brought

together the fields of electricity, magnetism and optics. But he also worked on what is now

known as the Maxwell–Boltzmann distribution. This explained the observations and laws

of classical thermodynamics and is a statistical method of understanding the distribution of

particles moving with different velocities.

simultaneously. Hence it is chosen fordefining temperature.

The temperature T of a collectionof molecules is defined to be aquantity directly proportional tothe average kinetic energy of thecollection of molecules. The constantof proportionality, kB, is called theBoltzmann’s constant. The temperaturethus defined is called the absolutetemperature, defined by the expression:

T =1kB

KEave

6.4 Absolute temperature

The absolute temperature defined interms of KEave has units of Kelvin (K).Absolute zero, or zero on the Kelvin

scale, is the temperature where allinternal or particulate motion within asubstance stops. The above equationsuggests that temperature can neverbe negative (since the kinetic energy isalways positive). How is it then thatwe hear of negative temperatures incold regions of the world? For historicalreasons, there exist other scales oftemperature which are commonly used,and are different from the Kelvin scaleof temperature. It is on such scalesthat negative temperatures exist. Weare familiar with the Celsius scale oftemperature, on which temperaturesbelow the freezing point of water arenegative.

The magnitudes of a unit on theCelsius and Kelvin scales are the same.


William Thomson, or Lord Kelvin (1824-1907)Kelvin can be counted amongst the few scientists who made immense contributions in both

theory and practical applications. His work on the relation of heat and work (with Joule) led

to the first and second laws of thermodynamics and the recognition of the absolute zero

temperature – the Kelvin scale being named after him. But he also did important work in

telegraphy and in improving the compass to make it more reliable.

The zeros of the two scales are different.Temperature on the Kelvin scale equalsthe temperature on the Celsius scale plus273.15. The Kelvin unit is written withoutthe customary ◦ for temperature. Acomparison of the two scales can bemade from the hypothetical thermometersshown in Fig. 6.4.

Temperature lower than absolute zerodoes not exist, as all motion stops at this

100 ° C

0 ° C

−273 ° C

373 K

273 K

0 K

Celsius Kelvin

Boiling point of water

Freezing pointof water

Absolute zero

Figure 6.4: Comparison of Celsius and Kelvinscales of temperature.

temperature. Most substances solidify attemperatures much higher than absolutezero. Helium is an exception, it remainsgas until 4.2 K and is expected to solidifyonly at absolute zero. Temperatures aslow as a few 10−6 K have been reachedunder controlled conditions for a smallcollection of atoms, while temperatures ashigh as 104–105 K are routinely achievedin plasmas. Room temperature is close to300 K, while human body temperature isapproximately 310 K.

6.5 Thermal energy and heat

We now understand heat and temperatureas being related to the kinetic energy ofthe particles constituting the substance.We have seen above how temperatureis defined. In defining temperature, wesummed the kinetic energies due to theinternal motion of all particles. This sumis given a special name, Thermal Energy,and is denoted by the symbol U. Whatis heat, then? Recall various uses of theterm heat. In all uses the term heat is usedin a relative context – i.e., when there is a


temperature difference, or when we speakof hot and cold objects. We do not use it inthe sense of being a property of an objector a substance itself.

A 6.2 Addition of thermal energies

You have a cupful (180 g) of nearly boilingwater and a bucketful (18 kg) of nearly freezingwater. (18 g of water contains Avogadronumber of molecules!) Compare the absolutetemperatures and the thermal energies of thetwo samples. If you mix the two, what will bethe thermal energy of the mixture? What willbe the temperature of the mixture?

Consistent with our particulate modelof matter, we understand heat as thermalenergy that is being transferred due todifference in temperatures. Thus, theparticulate model of matter yields thefollowing fundamental concepts:

1. All matter is composed of tiny particlesthat are in constant random motionwithin the substance. The kineticenergy of the particles due to thisrandom motion is not the same for allparticles.

2. The sum of the kinetic energies of allparticles is called the thermal energy ofthe object or the system.

3. Thermal energy is due to random motionof particles within a substance, and is notinfluenced by directed motion, such aswhen the object moves as a whole.

4. Temperature is proportional to theaverage kinetic energy of particlesmoving in random directions withina substance. As in the case of thermalenergy explained above, it is notinfluenced by directed motion.

5. Thermal energy in transfer from anobject to another, due to the differencesin temperature, is called heat.

The last point needs some elaborationwith respect to terminology: since thermalenergy in transfer is understood as heat,strictly speaking the expression transfer ofheat is improper, as transfer (of thermalenergy) is implied in the term heat.

In our model of matter and heat,particles are constantly in motion andcollide with each other, and transfer ofheat is to be understood in terms ofenergy exchange in these collisions. Asan example, let us consider the case ofhot water brought in contact with coldwater. The molecules in the cold waterhave a lower average kinetic energy thanthe molecules in the hot water. Whenthe two samples are brought in contact,molecules in a sample not only continueto collide with each other, but also startcolliding with molecules from the othersample. During collisions the kineticenergy of a given molecule may change,but the sum of the kinetic energies ofall molecules together remain constant.The result of several collisions is thatthe average kinetic energy of a collection


of molecules in any part of the entireliquid is the same, no matter which partof the liquid you choose. As was thecase before the samples were brought incontact, not all molecules have the samekinetic energy, but the average kineticenergy is the same all throughout. Atthis point, the temperature of the liquidis the same throughout and heat transferis complete. We can understand in asimilar manner heat transfer within a solid(the difference being that the particles ofthe solid do not move randomly, onlyback and forth about a mean position), orwithin a gas or between a solid and a gasor a solid and a liquid.

A 6.3 Temperature of a mixture

You can work out whether the temperature oftwo water samples in the previous activity,which are initially at temperatures T1 and T2

and are mixed together, will eventually becomesteady at a value less than both values, greaterthan both values or some intermediate value.All you need to remember is that the netthermal energy is number of particles timesthe absolute temperature. The thermal energyof the first sample, U1, is N1kBT1, while thatof the second sample U2, is N2kBT2, whereN1, N2 are the numbers of particles in the twosamples respectively. The combined thermalenergy is U1 +U2. Upon mixing, this thermalenergy is shared by all particles. So, whenmixing is complete, the temperature of themixture is (U1 + U2)/(N1 + N2).

Transfer of thermal energy from oneobject to the other is determined by thetemperature, not the total thermal energyof the objects. Our model does not entirelyexplain why, when two bodies at differenttemperatures are in contact, thermalenergy does not get transferred from thecolder body to the hotter one. Basedon various studies, this phenomenon isformulated as a law: there cannot be aprocess whose sole result is the transfer ofthermal energy from a cold body to a hot body.

Let us try to see how the relationbetween pressure, temperature andvolume of a gas can be explained withinthe particulate model of heat and matter.

6.6 Particulate model andpressure

Our model of matter has particles movingabout continuously, in random directions,and colliding with one another. In thecourse of this random motion, they willcollide not only with one another but alsowith the walls of the container. Let us seehow the model explains the relationshipbetween pressure, temperature andvolume of a gas.

A 6.4 An imaginary game

Suppose many of you stand near a wall andthrow balls at it. What happens to the wall?Not much, but every time the ball hits it, andrebounds, the momentum of the ball changes,


Figure 6.5: Balls striking a wall or any membrane exert pressure on it. The effect is more readilyseen if the membrane is flexible, as seen in the second picture. Molecules exert pressure on thewalls of a container in a similar manner.

i.e., a force is exerted on it. If you now doublethe rate at which balls are thrown, will theforce be greater? What if you throw the samenumber of balls, but with greater speed? Inboth these situations, the force on the wallincreases. We know that pressure on the wallis simply the force exerted (by the balls on thewall in this case) divided by the area. Thus,increasing the number of balls colliding withthe wall in a given time, or increasing thespeed of the balls striking the wall, results inan increase in the pressure on the wall. Theeffect on a surface by the striking of particleson it is more obvious if the surface is not rigid.Compare the two situations shown in Fig. 6.5.

The situation with molecules of a gasand the wall of the container is verysimilar. Let us consider a fixed number

of molecules of a gas. If the moleculescollide with greater kinetic energy, on theaverage, the force on the wall, and hencethe pressure, increases; if the frequency(rate) of collisions increases, that tooincreases the pressure. Thus increasein pressure is a consequence of increasein the average kinetic energy and rateof collisions of the molecules. In theparticulate model, an increase in averagekinetic energy and increase in the rate ofcollisions are identified with an increase inthe temperature of the gas, so we concludethat increase in temperature leads to anincrease in pressure. This is in conformitywith the gas laws stated earlier, and werebased purely on observations.

Let us think of what will happen


if we increase the number of moleculesin our container, without increasing thevolume of the container? As in the caseof balls being thrown at the wall, anincrease in the number of molecules willincrease the force on the walls of thecontainer, which implies an increase inpressure. What should be done to keepthe rate of collisions the same as before? Astraightforward solution is to increase thevolume of the container. Thus, increasingthe volume occupied by a gas reduces itspressure, while reducing its volume willincrease its pressure, again in conformitywith the laws stated earlier.

A 6.5 A Thought experiment

In the previous case, we increased pressure byincreasing the number of molecules. The keypoint was that the number of collisions wentup. What if we had increased the temperatureof the gas, while keeping the number ofmolecules constant? How would that haveaffected the number of collisions? What wouldhave been the effect of the increased number ofcollisions on pressure?

6.7 Particulate model andexpansion

Having seen evidence for the dependenceof the volume of a gas on its temperature,let us see how it fits in within theparticulate model. When heated, the

particles in a gas or a liquid gain kineticenergy, while simultaneously the rateof collisions between the particles alsoincreases. Since particles in a liquid ora gas are in continuous random motion,the (geometrical) extents of a gas arenot fixed, as we know from commonexperience. The extents are determinedby the surroundings – i.e., the shape andthe size of the container, or the pressure ofthe surrounding air. So the phenomenonof expansion is related to the interactionbetween the molecules of our sample gaswith the surroundings. In particular, ifthe surrounding is a solid container, thenthe molecules continue to collide withthe walls ever more frequently and withgreater kinetic energy on the average, asthe temperature increases.

If the force due to collisions is notlarge enough to damage or break thewall, the net effect is to transfer thermalenergy to the walls of the container,leading to an increase in the temperatureof the container itself. Of course, aswe have seen in our activities earlier,heating of the solid leads to its expansion,so the container itself expands in theprocess. Of course, this expansion isrelatively small. On the other hand, ifthe container is not very rigid, or somepart of it is a flexible/movable partition,then the flexible part of the containeris pushed out, so we very clearly seethe volume increasing. An example ofthis might be a balloon that is inflated


and then kept in contact with warmwater, or a hot air balloon, in whicha gas burner heats the air inside tocreate a lift. As discussed earlier, theair outside also exerts a pressure on the‘partition’, so the expansion is in fact dueto the pressure of the gas inside becominggreater than that of the surrounding air. Inthis case, the phenomenon of expansioncannot be seen in isolation, we have totake into account simultaneous changesin pressure, temperature, volume and thework being done against the boundary.

The situation with expansion ofliquids is very similar to the case ofgases, and the arguments based on theparticulate model are identical. Particlesin a solid do not move randomly, but onlyback and forth about a mean position.An increase in temperature implies anincrease in the extent of their oscillationon the average, so the effective spacingbetween any pair of particles increases.This in turn implies that the volume of thesolid increases.

6.8 Particulate model andconvection

We have seen that heating of a liquidor a gas happens mostly by convection.Let us examine convection in view ofthe particulate model of heat and matter.When a liquid is heated at the bottom,the kinetic energy of the molecules close

to the base increases rapidly. Some ofthe molecules that move in the upwarddirection now have sufficient kineticenergy that they can transfer to themolecules above them, in turn enablingsome of the molecules above to overcomethe gravitational force, and move furtherupward. No single molecule is likely tomake a trip all the way up to the surface,but because of the heat supplied frombelow, an ever larger number of moleculesis gradually able to rise upwards, againstgravity, and towards the surface of theliquid.

As the collection of these moleculesmoves further upward, their kineticenergies decrease (similar to a ball losingits upward velocity when thrown againstgravity). A small number of them reachthe surface with excess kinetic energy andmay leave the surface. This is consistentwith the observation that heating leadsto greater evaporation. The collection ofmolecules that move upwards is replacedby molecules with lower kinetic energythat tend to move downward due togravity, constantly colliding with othermolecules, and a loop pattern of motionis set up. The shape of the loop canbe quite complex. The shape of thecontainer, the extent of the source ofheat and the nature of the liquid comeinto play. If gravity were absent, therewould be no convection. However, therandom, persistent motion of moleculeswill still be there and heating a gas will


increase the kinetic energy of moleculesin the vicinity of the source of heat,thereby increasing the probability of theircollisions with other molecules, and

enhance their transport to other regions ofthe container. The mode of heat transfer ina gas or a liquid in zero gravity would bea mix of diffusion and conduction.


Summary

• The average kinetic energy of the molecules due to the random motion is ameasure of the temperature of the substance. The temperature scale basedon the average kinetic energy, called the absolute scale, or Kelvin scale, isalways positive.

• When two objects are brought into contact, thermal energy flows from theobject at higher temperature to the object at lower temperature. The thermalenergy keeps flowing till the two bodies are at the same temperature, that is,till thermal equilibrium is achieved.

• Pressure of a gas is due to collisions between the particles and the walls ofthe container. Increase in temperature increases the average kinetic energyof the particles and the rate at which they strike the walls, thereby increasingthe pressure of the gas.

• The conversion of heat into mechanical work can be understood in termsof the kinetic energy transfer from the randomly moving particles to thesurroundings, and is readily observed in case of expanding gases.

• Transfer of heat within liquids and gases is by a combination of randomand directed motion of particles within the substance, and is influenced bygravity.

Chapter 7

Some Remarkable Devices

We use heat for many of our day-to-dayactivities. The commonest example isthat of cooking; we can hardly imaginecooking without a source of heat. Weuse a variety of heating devices for this.Stoves based on the burning of a fuel suchas petroleum gas or kerosene, electricalheaters, microwave ovens are examples ofsuch devices. Devices based on the useof heat are also employed for a varietyof purposes outside home. Many ofthe effects of heat that we studied inthe earlier chapters are exploited in theconstruction of different devices.

Perhaps the most significant ofdevices using heat are based on theequivalence of heat and work, andtheir relationship with pressure andtemperature in the context of gases.Examples are the steam engine – usedin the past for a whole lot of tasks infactories, in shipping and railways, andfor generating electricity by driving agenerator, and the internal combustionengine – now the overwhelminglycommon engine for powering vehicles of

all descriptions from the scooter to trains,ships and aeroplanes. Odd as it mayseem first, even cooling needs heat, as inrefrigeration and air-conditioning. Thesedevices have had a major impact on thesociety. They are remarkable because ofthe way they exploit our understanding ofheat, and perform useful and contrastingtasks. The steam engine and the internalcombustion engines exploit the increase inthermal energy of a substance to do work,whereas a refrigerator exploits work toreduce the thermal energy of a substance.We shall look at these devices in detail ina while, but first we will look at a simplerdevice that is just as significant, because itis directly connected to the most basic ofhuman needs – food.

7.1 The pressure cooker

There are many methods or techniquesof cooking such as boiling, roasting,frying. Of these, boiling occupies a majorplace in routine cooking – for cookingrice, daal, etc. Boiling is the process of

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Safety Valve

Pressure Vent

Lid with gasket

Cooking Pot

HandleandLidClamp

Figure 7.1: Structure of a pressure cooker.

immersing in water the substance to becooked, followed by heating the water,bringing it to boil, and leaving it on theboil until food is cooked. The boilingpoint of water is approximately 100 ◦C,so food immersed in water cooks atthat temperature. All cooking cannotbe accomplished at 100 ◦C; differentsubstances need different temperaturesfor cooking well. Moreover, most cookingcan, at least in principle, be accomplishedfaster at a higher temperature. If asubstance needs a higher temperaturefor cooking, this cannot be achieved byboiling, since no matter how much heatyou provide to the water in a saucepan,its temperature will not rise beyond theboiling point.

If the boiling point of water couldbe raised by some means, then it willbecome possible to heat the water tohigher temperature, and achieve faster

cooking. Of course, the source of heatmust have a much higher temperaturethan 100 ◦C to achieve this, but this ishardly a problem, as the temperature ofstove flames, although dependent on thefuel used, is much higher. How do weraise the boiling point of water? Thetrick is to increase the pressure of theair surrounding the water. This is donein a pressure cooker, which is a sealedvessel that does not permit air or othervapours from inside it to escape to theambient air, unless the pressure insideexceeds a certain value. The idea of apressure cooker dates to 1670 CE, thefirst commercial venture dates to 1864 CE,while the modern pressure cooker can betraced to the year 1938 CE. A sketch ofthe essential features of a modern pressurecooker is shown in Fig. 7.1.

When food is placed for boiling in apressure cooker, the steam arising from

Chapter 7. Some Remarkable Devices 75

water and the hot air inside it lead toa pressure build up within the cooker.This in turn suppresses further boiling ofwater. The heat from the stove now causesthe temperature of water to rise beyondits normal boiling point and eventuallystart boiling at a higher temperature. Thesteam resulting from boiling is trappedin the cooker until the pressure exceedsthe set value. This arrangement has twoadvantages. First, the food cooks at ahigher temperature. Due to the increasedtemperature, the food cooks quickly withheat from the steam. Thus, much lesswater is needed than when boiling in anopen saucepan. Cooking via steam alsopreserves nutrients which might be lostduring prolonged cooking by immersionin boiling water in a pan. The net effect issavings on fuel and time. Most domesticpressure cookers are set to operate at apressure twice the normal atmosphericpressure, which raises the boiling point toabout 120 ◦C.

What is the ideal way to use apressure cooker? First, one should use aslittle water as is possible – just enoughto create an adequate amount of steam.Second, once the steam pressure hasbuilt up, the flame should be reduced –excess heating will only create more steamwhich will keep escaping periodically asthe pressure increases beyond the setvalue. Escaping steam represents heat lostto conversion of excess water to steamand eventually to the surrounding air!

So, the principle that so many whistles(i.e., pressure releases) are needed to cooka certain food item is a wasteful one. Itis better to let the steam build up to theset pressure (just below escape), and thenreduce the flame and cook for as longas is needed for the particular item. Infact, even after the flame is turned off,cooking continues due to the transfer ofheat from the steam to the food item, untilall steam condenses to water inside thecooker. A rule of thumb is that a correctlyused pressure cooker will not give out awhistle.

7.2 The steam engine

The idea that steam, created by heatingwater, can be used to displace objectswas cleverly exploited in the 17th century.A steam engine is a device that usesheat to create steam from water anduses the steam to perform mechanicalwork, usually by moving a piston backand forth. Steam engines have beenused in locomotives and poweringmachines such as looms in factories.In fact, the association of the steamengine with a railway locomotive isso strong, that rather inappropriately,the steam locomotive is called a steamengine. The steam engine is consideredto have been one of the most importantindustrial inventions, and the herald ofthe industrial era.

Figure 7.2 shows the essential parts


Sliding Valve

intake exhaust

Centrifugal Governor

Crank

PistonPiston Rod

Cross head bearing Connecting Rod Eccentric Valve Motion

Flywheel

Figure 7.2: A steam engine, with the main parts labelled.

of a steam engine. Steam is generatedat a very high pressure in a boiler byburning coal or some other fuel, such aspetroleum oil or gas. When the steampressure crosses a limit, it escapes intoa cylindrical chamber inside which thereis a tight fitting piston that can movealong the axis of the cylinder. Thehigh pressure, super-hot steam expands,pushing the piston out, or working thepiston. The expanded steam has lost heat(it is converted into the motion of thepiston) and is cooler, so will condense.The condensed steam can be recycled backto the boiler.

In the meanwhile the piston hasbeen set into motion. Connected to thepiston is a crankshaft (a shaft that movesback and forth synchronous with themovement of the piston) and a flywheel (aheavy, supplementary wheel that rotates

as the piston moves). The crankshaftalso converts linear motion of the pistoninto circular motion of the wheel of alocomotive or the propeller of a ship or thespindle of a loom. The rotary action of theflywheel ensures that the piston is pushedback into the expansion cylinder after theexpanded steam has returned to the boiler.

The invention of the steam engine isoften considered the starting point of theindustrial era. The steam engine was thefirst device which enabled conversion ofheat into mechanical work in a practicalmanner. Compared to the work that canbe done using human or animal power, asteam engine can do much more work ata lower cost and in less time. This madesteam engines very popular for all kindsof machines – from spinning and weavingmachines to locomotives.


James Watt (1736-1819)Most of us have heard of Watt in connection with the steam engine, and he is usually

credited with inventing it when he only improved it enormously. The steam engine was

actually invented by Newcomen, but the fuel efficiency attained by Watt’s engines and their

versatility (the Newcomen engine was only used for pumping water) led to the linking of

Watt with the industrial revolution and the steam locomotive. Two of the innovations that

he introduced were (i) a separate condenser so that energy was not wasted in repeatedly

heating the cylinder and (ii) using the engine to generate rotatory motion. He introduced

the concept of horsepower and the unit of power is named after him.

7.3 The internal combustionengine

In a steam engine fuel is used to createsteam from water, which then works apiston. Burning of the fuel, or combustion,occurs outside the cylinder in which steamexpands. In contrast to this arrangement,there are engines in which a mixture of afuel (generally a fossil fuel such as petrol,diesel, kerosene or compressed naturalgas) and air is ignited inside a cylinder,and the gases resulting from combustion(mainly oxides of carbon and watervapour) expand in the same cylinder,working a piston. Such engines areclassified as internal combustion engines.IC engines deliver far more power for thesame size of the engine compared to anexternal combustion engine. The pistoncan then be made to drive a crankshaftand a wheel as needed.

IC engines are of two kinds,two-stroke and four stroke. A two-stroke

engine performs repeated compressionand expansion strokes. Admission of theair-fuel mixture and its ignition occurs inthe compression stroke, while expulsionof the combustion products occurs inthe expansion stroke while the piston isbeing pushed out. In a four-stroke engine

CamshaftValve Cover

Intake ValveIntake Port

Head

Coolant

Engine Block

Oil PanOil Sump

Spark PlugExhaust Valve

Exhaust Port

Piston

Connecting Rod

Rod BearingCrankshaft

Figure 7.3: Structure of an internalcombustion engine.


CompressorCooling Fan

Blower

Low Press.Low Temp.Gas

Cooled Air

LiquidRefrigerant

ExpansionValve

DrierHigh Press.High Temp.

Gas

Forced Air

Evapo-rator

High Press.High Temp.Liquid

Low Press.Low Temp.Liquid

Con-densor

Figure 7.4: A schematic diagram of the refrigeration cycle based on expansion and compressionof a gas.

the compression and ignition operationsare sequential, such that ignition takesplace after the mixture is completelycompressed. Expulsion of the expandedgases takes place after the piston is fullypushed out. Not only is combustion moreefficient in a four-stroke engine, but alsothe expansion of the combustion productsis more efficiently converted to work.IC engines are usually configured withtwo or more (generally even) number ofcylinders performing alternate strokes.

Due to their compact size, highpower output and robustness, they arethe engines of choice for vehicles of alldescriptions, whether on land, or sea, orin air. In fact, heavier-than-air poweredflight was possible only after IC enginescame along.

7.4 Refrigerator

Recall the cooling effect of air escapingfrom a pressurised cycle tube. If one hadmeans of compressing the air repeatedlyand filling it in an enclosure, whilealternating the compression by expansion,it would be possible to cool the air –and in turn cool the object in the regionof expansion. This is the principle ofrefrigeration. It uses mechanical energy(during compression of the gas) to transferheat from a region of interest to thesurroundings, even when the temperatureof the surroundings is not lower than thetemperature of the region of interest.

In a refrigerator, a gas is circulatedbetween two units, the condenser and theevaporator, by a compressor (Fig. 7.4).


Internet resourcesApart from the pressure cooker, we do not usually get an opportunity to see the internal

workings of the devices described in this chapter. Computer animations are often useful in

understanding such devices. Several resources are available on the internet. We mention

some of them here.

For the steam engine see

http://en.wikipedia.org/wiki/Steam engine

For the IC engine see

http://www.howstuffworks.com/engine1.htm

and

http://en.wikipedia.org/wiki/Cylinder (engine)

See a picture explaining the refrigeration cycle at

http://en.wikipedia.org/wiki/Heat pump and refrigeration cycle

The compressor does work on the gas,for which it uses electrical energy. Therefrigerant vapour is compressed, and inthe process its pressure and temperatureincrease. This compressed vapour ispassed on to the condenser, where itloses heat to the surrounding air andcondenses to a liquid. The liquid is forcedthrough a fine valve, which is the keyelement. It consists of a fine orifice,which opens and closes synchronouslywith the compression. As the liquefiedgas is forced through the orifice into theevaporator, it expands rapidly (just as wesaw in the case of the bicycle tube) therebycooling the evaporator,which in turn cools

the air around it. The hot and cold areasof the refrigerator are well insulated fromeach other, and the valve demarcates thetwo zones. In effect, heat is transferredfrom a cold region to a hot region, bymeans of a gas and a compressor.

Air conditioners work on the sameprinciple as refrigerators. The compressorin an air conditioner is driven by anelectrical motor (in buildings) or by anIC engine (in vehicles). The work that isneeded to transfer heat is thus effected bya supplementary source of energy.

Can you explain why a refrigerator issometimes called a heat pump?

Teasers

There are several situations in real lifeconcerning heat and temperature whichare not readily explained, and leave usconfused. Here is a collection of teaserswhich we hope you will find stimulating,and will be able to solve based on theexposition in this book.

1. Does a warm blanket provide youwith heat when you wrap yourselfup in it? Can the blanket also be usedto keep something cold?

2. When a window is accidentally leftopen on a wintry night, do you feeluncomfortable because the cold isgetting in, or because the heat isescaping from the room?

3. When you are faced with a glassbottle with a metal lid that is verytight, it becomes easier to unscrewthe lid if it is warmed up. Explainhow this happens.

4. A thin-walled plastic bottle is filledto the brim with water and its cap istightly closed. The bottle is left in afreezer. What is the likely outcomeof the freezing?

5. What do you understand by thestatement warm air is lighter?

6. If you wish to keep a block of ice forlong in winter, would you choose towrap it in a blanket, in an aluminiumfoil, or simply leave it in the open?What if you have to do the same insummer?

7. In winter a metal surface feels colderto touch than other surfaces. Explainwhy. How would the cold sensationchange if the surface were rough? Ifthe surface were smooth?

8. What difficulties might an astronautface in boiling water to make tea?

9. Suppose your normal bodytemperature were lower than what itis. How would the sensations of hotand cold change?

10. In view of the activity Reflecting Heat,can you say why food (especiallychapati) is wrapped in an aluminiumfoil if it is to be kept for some timebefore being served?

11. A room has a west-facing glass

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Teasers 81

window, and you wish to preventthe room from getting very hot onsummer afternoons. Three methodsare suggested below. Rate theireffectiveness, giving reasons.

(a) covering the outside of the glasspanes with an aluminium foil,

(b) covering the inside of the glasspanes with a thick thermocolsheet,

(c) covering the inside of the glasspanes with black chart paper orblack curtains.

12. What is the reason for your shiveringwhen you have a fever?

13. When you perspire and the windblows, you feel cold. Why?

14. What is the difference betweencooling a pan of hot milk by standingit in a pan of cold water, and byblowing on it or stirring it?

15. Does a refrigerator violate ourconclusion that a body at a lowertemperature cannot transfer heat toa body at a higher temperature? Ifit does, explain what will happen ifthe compressor is removed from therefrigeration cycle.

16. Can you cool a room by leaving arefrigerator in the room with its dooropen?

17. If you heat a circular disk with ahole, what change do you expect inthe diameter of the hole? Rememberthat the effect of heating is to increasethe separation between any pair ofparticles.

18. You have a glass full of water keptinside a large chamber. The air inthe chamber is (suddenly) removed.Describe what will happen to thewater.

19. A short plastic rod and another shortmetal rod of the same mass are left ina refrigerator for a long time. Theyare removed and given to you tograb in the fist. Which one feelscolder? Which one feels colder for alonger time?

20. Why might clothes dry quicker incold dry air than in hot humid air?

21. On the basis of the kinetic theory,explain the bursting of a tyre insummer.

22. What would you recommend asideal clothing when going out in thesun? Black or white? Short clothesor covering up in loose clothes(e.g. kurta-pyjama or salwar-kameez)?Might it explain why people indesert countries usually coverthemselves completely in white?


23. A raincoat is made of a non-woven,water-proof, insulating material.How would you rate it for use as aprotective garment on a cold day?On a windy day?

24. On a rainy day, a dry glass is filledwith ice, covered and left standing.As the ice melts, water collects onthe outer surface of the glass. Wheredoes this water come from?

25. Why is the water in mountainstreams usually cooler than thesurroundings?

26. If instead of the theory of heat, weconstruct a theory of coldness, i.e.instead of speaking in terms of heattransferred, Q, we talk of coldnesstransferred, −Q, what quantity mightreplace the absolute temperature T?

27. Why does M gram of any purecompound (M being the molecularweight of the compound) alwayscontain Avogadro number ofmolecules?Hint: Avogadro number is roughlythe reciprocal of proton mass (or theatomic mass of hydrogen) in grams.

A Note on Units

It is recommended that one uses SIunits for all physical quantities. Thetwo physical quantities central to thismodule are Heat and Temperature, whilea few other quantities also find mention.We look at SI units for the quantitiesappearing in this module, and theirrelation to the units that have beenmentioned, or used, in this module, or areoften used in practice.

• Heat is a form of energy, and the SI unitfor energy is Joule (J), so the SI unit ofheat (thermal energy) is Joule.

• The SI unit of temperature is Kelvin (K).

• We used the unit calorie (moreprecisely, the thermochemical calorie)for heat earlier. A calorie is equal to4.184 J.

• The unit of specific heat is defined interms of the amount of heat required toraise the temperature of a unit mass ofa substance per ◦C, so the SI unit ofspecific heat is J/kg/K. The commonlyused unit cal/g/ ◦C is equal to 4.184 ×10−3 J/kg/K.

• Rate of transfer of heat is anotherquantity we encountered. Its unit is

Joule per second, which is given aspecial name, Watt (W).

• Conductivity, which is defined asthe rate of transfer of heat per unitdifference in temperature per unitlength, therefore, has the SI unitW/m/K. In terms of the practicalunits calorie and cm, it has the unitcal/s/cm/ ◦C, which is equal to 4.184×10−2 W/m/K.

• Pressure is force per unit area, and itsSI unit is Pascal (Pa), or Newton/m2.Non-SI units that are in common useare bar (1 bar = 105 Pa) and torr (1 torr= 133.32 Pa). The standard atmosphericpressure is 1.013 × 105 Pa.

The Nutritional Calorie is a frequentlymisunderstood unit of heat. One oftenhears, for example, that an adult needs2500 Calories per day. Does this numbersound right? To answer this, let usestimate how much energy is spent in aroutine activity, such as walking. Walkingspeed is 5–6 kmph or 1.5 m/s. In walkingwork is primarily done against gravity,but the force is not vertical, it is at asmall angle (say 10◦) to the ground. So,the force applied by a person weighing

83


60 kg when taking a step is approximately60 kg × 9.8 m/s2 × sin(10◦), or 80 N.Hence the power expended is 80 N ×1.5 m/s, i.e. 120 W. In walking for aminute, this is an expenditure of 7200 J,or 1700 cal. Surely 2500 cal of nutrition

is too little! This apparent contradictionarises because the nutritional Calorie is infact 1000 standard (or thermo-chemical)calories (or 4184 J). Note the capital C inthe nutritional Calorie, to distinguish itfrom the thermo-chemical calorie.

Index

Absolute temperature, 64Average velocity, 62Avogadro, Lorenzo, 60

Black, Joseph, 9Boltzmann, Ludwig, 64Boyle’s Law, 38Boyle, Robert, 39Brown, Robert, 55Brownian motion, 55

Caloric, 47Change of State, 30Charles’ Law, 38Charles, Jacques, 39Conduction, 17Conductors, 21Convection, liquids, 18Convection, particulate model, 70

Dalton, John, 54Dewar, James, 24

Einstein, Albert, 55Engine, internal combustion, 77Engine, Steam, 75Expansion, gases, 27Expansion, liquids, 28Expansion, particulate model, 69Expansion, solids, 28

Friction and heating, 48

Galileo, Galilei, 4Gay-Lussac, Joseph, 40

Heat transfer, prevention, 23

Ideal thermometer, 32Insulators, 21

Joule, James, 43Joule-Thomson effect, 43

Kelvin, Lord, 65Kinetic energy, average, 63

Latent heat, 35

Maxwell, J C, 64Mechanical equivalent of heat, 42Motion within a substance, 51

Number density of particles, 59

Particles, collective motion, 62Particulate matter, 54Pressure cooker, 73Pressure, particulate model, 67Properties, intensive and extensive, 6Proportionality, 16

Radiation, 20Refrigerator, 78Representative number, mean, 61Representative number, variance, 62Rumford’s experiments, 48

85


Rumford, Count, 49

Specific heat, 10

Temperature, Celsius scale, 65Temperature, common usage, 3Temperature, Fahrenheit scale, 5Temperature, Kelvin scale, 65Thermal conductivity, 17Thermal Energy, 65Thermal equilibrium, 9

Thermometer, improvised, 29Thermometers, choosing, viiiThermos flask, 24Thomson, Benjamin, 49Thomson, William, 65

von Mayer, Julius, 44

Water, 32Watt, James, 77Work, mechanical, 40

Acknowledgements

The inspiration and the starting point forthis module are chapters dealing withheat from Eklavya’s earlier publication,Bal Vaigyanik. This module attemptsto take qualitative ideas regarding heatand move towards the kinetic theory,while maintaining the level of abstractionaccessible at the high school level.Considerable guidance and feedback wasobtained in this endeavour from Eklavya’slarger resource group including VijayaS. Varma, Amitabha Mukherjee, PramodKumar Shrivastava, N. Panchapakesan,the late M. M. Kapoor, Sushil Joshi,Kamal Mahendroo, Patrick Dasguptaand Aamod Karkhanis. Past and presentteam members of Eklavya, Reva Yunus,Himanshu Shrivastava and Uma Sudhirhelped in trying out various activities andrefining them, as also in offering multiplepoints of view on the text. L. Mishra andR. Rangarajan gave critical inputs as themodule was taking its final form.

The organisation of the concepts andactivities was tried out in two teachertrainings organised by Eklavya in Indoreand again with students in a workshoporganised by the Vidya Bhawan Societyin Udaipur. Once the entire structureof the module was finalised, Rama Chariand Urjit Yajnik went through it to checkfor conceptual correctness and clarityand made some valuable suggestions toimprove the presentation of the ideas.Most of the illustrations were drawn byBharat Jamra, and some by Nishith Mehtaand Boski Jain. The Eklavya publicationsteam looked into the finer details of thelayout and look of the module, as well asthe editorial aspects.

Comments and suggestions on themodule are welcome by e-mail at theaddresses [email protected] [email protected].

– Bhas Bapat

87

Eklavya is a non-governmental registered society working in the fieldsof education and people’s science since its inception in 1982. Its mainaim is to develop educational practices and materials related to a child’senvironment that are based on play, activities and creative learning. Inthe past few years, Eklavya has extended its area of work to includepublishing. We bring out three periodicals: Chakmak is a monthly sciencemagazine for children, Srote is a weekly science and technology newsfeature, and Sandarbh is a bimonthly magazine on science and educationfor teachers. In addition to titles on education, popular science andcreative activity books for children, we develop and publish books on thewider issues of development.

Please send us your comments and suggestions about the content anddesign of this book. They will help us to make our future publicationsmore interesting, useful and attractive.

Contact:[email protected]

E-10, BDA Colony Shankar Nagar, Shivaji Nagar, Bhopal 462016

heat & temperature - learning by doing for secondary school

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