temperature

Fundamental Physics I by Dr. Abhijit kar Gupta (email: [email protected]) 1

Temperature The sense of temperature comes primarily from touch. Our common experience tells that ice is cold and boiling water is hot. Many other objects spread all around, may be neither hot nor cold. Temperature is a relative measure which is to express the degree of hotness or coldness of matter. The temperature is indicated by a number according to some chosen scale. Definition of Temperature: The quantity that tells how hot or cold an object is with respect to some standard is called temperature. [Note: When we touch something and say that it is either hot or cold with respect to some ‘standard’, the standard is our own body.] Our temperature sense is somewhat unreliable and limited due to the following reasons:

• There is a limited range of temperature which can be sensed by us. We can not touch too hot or too cold a thing.

• We can not have a quantitative idea of temperature. Also the feeling of temperature may vary from one person to another. (This depends on the difference of body temperature of the person involved.)

• Two things having same temperature can sometimes be mistaken to be at different temperatures. As for example, if we remove a metal tray and a packet of vegetables from the refrigerator, it appears that the metal tray is colder even though they have the same temperature.

When we touch a hot iron rod, energy enters our hand from the hot rod and we can sense that to be hot. When we touch a piece of ice, energy passes out of our hand to the colder ice and we sense that to be cold. Energy is always transferred from a warmer object to a colder object when in thermal contact*. (This energy transfer is a natural process which happens in various ways.) Definition of Heat: The energy transferred from one object to another because of temperature difference between the objects is called heat. [Note: Matter does not contain heat as it is energy in transit from an object of higher temperature to one of lower temperature. Matter contains internal energy in the form of atomic and molecular motions and vibrations etc. The analogy can be drawn with work. Work is done to transfer energy. But a body does not contain work.]

* Thermal contact: when heat is transferred between two objects, whether or not they are touching, they are said to be in thermal contact.


Concept of thermal equilibrium: When our thermal sensation appears to be the same as we touch different things, we can say that the things are at thermal equilibrium. The household things in a room are usually found to be in thermal equilibrium. (The precise definition of thermal equilibrium will be given later.) A tray of ice when left open in a room for a sufficient time, the ice melts and subsequently the ice-cold water in the tray does not remain cold. On the other hand a pot of hot water when left open, it cools down and attains a temperature which is that of other objects in the room. In both the cases water finally turns to be in thermal equilibrium with other things in the room. To understand thermal equilibrium in a better way, we have to know the interior of a matter how it changes when heat flows in or out of the system. Internal (microscopic) state of a system can be understood by measuring some external (macroscopic) physical properties like temperature, pressure and volume etc. These are called thermodynamic coordinates. Thermodynamics: A system that is described in terms of thermodynamic coordinates is called thermodynamic system. The subject is called thermodynamics. Under the purview of thermodynamics we can attach a more precise meaning of the word, ‘equilibrium’. A state of a system in which the independent thermodynamic coordinates that remain constant as long as the external conditions are unchanged is called an equilibrium state. The Zeroth Law of Thermodynamics: Two systems in thermal equilibrium with a third one are in thermal equilibrium with each other. The above statement is basically a postulate which results in after considering experimental facts. Experiment shows that the existence of an equilibrium state in one system depends on the proximity of other systems and on the nature of the thermal interactions among them. The concept of temperature can be derived from the zeroth law of thermodynamics. We may conclude that two systems when in thermal equilibrium may have some common property. When a system A is in thermal equilibrium with another system C and also another system B is in thermal equilibrium with C then the systems A and B are in thermal equilibrium with each other. Therefore, there is some common property between A and C which is also common between B and C. This property is temperature. Thus we can define temperature in the following way: The temperature of a system is a property that determines whether or not a system is in thermal equilibrium with other systems.


[Note: The concept of temperature can be derived in a more concrete and mathematical way which is beyond the scope of this syllabus. There are three more fundamental laws of thermodynamics. The first law and second law of thermodynamics will be discussed in a subsequent chapter. The zeroth law was postulated after all other laws were discovered and the name was suggested by R.H. Fowler.] Thermometer: We have already discussed that temperature of a substance can only be merely sensed by touching. But we need to quantitatively measure temperature. A thermometer is a device which is used to measure temperature by using some property of a substance that changes with temperature. Examples⇒

• The Clinical thermometer: the mercury thermometer, we use at home. The column of mercury expands with temperature. The property of thermal expansion (or contraction) is used here. This is a common thermometer, in general, liquid-in-glass type. Coloured alcohol is also used for the same purpose. These substances (mercury or alcohol) are chosen because of their large thermal expansion and also because they remain liquids over normal temperature ranges.

• The platinum resistance thermometer: this is used at laboratories. The property of the change of electrical resistance of platinum wire with temperature is used here. This is usually used for measuring a wider range of temperature and also for more accurate measurements.

• The property of a thermo-couple is also used as a thermometer.

How does a thermometer work? A thermometer records its own temperature. When a thermometer is in thermal contact with some substance whose temperature we wish to know, energy is exchanged (heat flows) between the thermometer and the substance. This energy exchange continues until a thermal equilibrium is established between the two when the temperature of the thermometer is equal to the temperature of the substance. The practical use of thermometer is based on the zeroth law of thermodynamics which is nothing but a law of equilibrium. Temperature Scale:

Picture of a Clinical thermometer to be included


A number is assigned when a temperature is measured with a thermometer. This is called calibration. To calibrate a thermometer for different temperatures we have to have a numerical scale. How do we fix a scale? To obtain a standard scale or unit, two fixed reference points are required. The ice point (the temperature at which the water freezes) and the steam point (the temperature at which water boils under standard atmospheric pressure) of water are usually considered to be two standard fixed points. Several scales of temperature are in use:

• The Celsius scale:

o This scale is commonly used in laboratories. The number 0 is assigned to the ice point and the number 100 is assigned to steam point.

o The space between two fixed points is divided into 100 equal parts and each division is called one degree.

o Such a thermometer is called a centigrade thermometer (The name is obtained from centum which means hundred and gradus which means degree.). This is now referred to as Celsius thermometer as the Swedish astronomer Andres Celsius (1701-1744) first suggested such a scale.

o The readings of temperature in the scale of thermometer is written as C0 . The temperature differences are usually written as 0C .

• The Fahrenheit scale:

o In America, the number 32 is assigned to the ice point and the number 212 to the steam point. The space between two fixed points is now 180 and this is divided into 180 equal intervals or degrees.

o A thermometer with such a scale is called Fahrenheit thermometer. This is named after its originator, the German Physicist Gabriel Daniel Fahrenheit (1686-1736).

o The temperature readings are written as F0 and the temperature differences are usually written as 0F .

Note: Fahrenheit was the first to choose mercury as the substance to be used in thermometer. There are many advantages of mercury over many other substances, e.g., it does not wet glass, can be easily obtained pure, remains liquid for a fairly large range of temperature, has a low specific heat and high conductivity. Also, mercury is opaque and its expansion is approximately regular and uniform.


The advantage of Fahrenheit scale over Celsius scale: The number of divisions in Fahrenheit scale is more than that in Celsius scale. So the value of each division is smaller in Fahrenheit scale compared to that of Celsius scale. Therefore, the temperature can be measured with greater accuracy in Fahrenheit scale. For small variations in temperature like in weather reporting and our body temperature, this scale is convenient to use.

We can write, 180 0F = 100 0C which means, 1 0F = 95 0C or 1 0C =

59 0F .

Relation between two scales: Suppose, F is some temperature measured in Fahrenheit scale and the same temperature measured in Celsius scale is denoted by C . Then the relation between two measurements can be written as following:

3259

+= CF . (1)

Alternatively,

9

325

−=

FC . (2)’

From equation (1) or equation (2) it can be easily verified that when 0=C (which corresponds to ice point), we have 32=F . When 100=C (which corresponds to steam point), we have 212=F . Equation (1) is similar to an equation of straight line of the form:

cmxy += where the slope is equal to 59

=m and the intercept of line with

y-axis is equal to 32=c .

• The Kelvin Scale:

C

F


Why do we need Kelvin scale? The zero or lowest fixed point considered so far in the Celsius or Fahrenheit scale is the freezing temperature of water. While the highest fixed point is taken to be the temperature at which water starts boiling at standard atmospheric pressure. However, there are many natural systems or phenomena on and outside earth where we come across a temperature well beyond the above range. Very high temperature is likely to be found in deep inside Sun or other stars which can be of the order of several million degrees. Although it is hard to set a upper limit of temperature when we consider all kinds of phenomena in the entire universe. Research in Physics shows that there exists a lower limit of temperature below which we can not think of matter. This can be termed as absolute zero. Thus a temperature scale is set up where the lower fixed point is this absolute zero. This is Kelvin scale, named after British Physicist Lord Kelvin (1824-1907). This is also called absolute scale.

o This scale is more fundamental and is favoured in scientific and research works.

o The number 0 is assigned to the universal zero of temperature which is the lowest possible temperature: absolute zero.

o Absolute zero corresponds to C0273− in Celsius scale ( C015.273− to be precise).

o There are no negative numbers on the Kelvin scale. o The temperature and the difference in temperatures are denoted by K (not

K0 ). The relation with Celsius scale: The relation between Celsius and Kelvin scale is 273−= KC where C is some temperature measured in Celsius scale and K is that in Kelvin scale. For a more precise measurement, 273.16 is used in place of 273. Primary and Secondary Thermometers: Kelvin scale of temperature is independent of the property of any particular substance. This is the standard scale of temperature and is known as the thermodynamic scale. Further, it is seen that this scale is quite identical with the perfect (or ideal) gas scale (where the thermometer scale is determined using the properties of perfect gas). Thus one can say that the ideal gas thermometer scale which actually depends on the properties of ideal gas, now becomes independent of the properties of any particular substance. Thus this is called thermodynamic scale and is a standard or primary scale. The thermometer which uses primary scale is primary thermometer. This is used in scientific works. Gas thermometers are difficult to use as they require several corrections. Thus in laboratories, they are replaced by secondary standard thermometers. Any thermometer standardized with the help of primary thermometer is called secondary thermometer. Except ideal gas thermometer, all other thermometers e.g., the resistance thermometer, the thermo-couple etc., are secondary thermometers.


Triple point of water is the standard fixed point used in primary thermometer. Triple point of water: The triple point of water is the equilibrium state of pure water existing as a mixture of ice, liquid and vapor. This happens at a temperature of 273.16 K (0.01 C0 ) and at a pressure of 610 Pa* (or 4.58 mm of Hg column). This is used as a standard fixed point.

Discussions Q.1 The temperature of a room is 25 C0 . What can you say about thermal equilibrium when someone enters in that room? Ans. Our normal body temperature is 37 C0 (98.6 F0 ). Biologically, through metabolism, our body tries to maintain this temperature. If we enter into a room of 25 C0 , we will feel cold as the room temperature is below our body temperature. Energy will flow out of our body to the air of the room to establish equilibrium. But our body will resist and the equilibrium will not be reached. [Note: However, if we keep an object of temperature 37 C0 in that room, it will eventually reach in equilibrium state after exchanging energy with the air of the room.] Q.2 When in winter, we cover our body with a blanket or a quilt, initially we feel cold but after a while we get warm. What is the reason? Ans. Our normal body temperature is 37 C0 . The blanket or the quilt assumes the temperature of the room which is usually below our body temperature. So they appear cold at the beginning. After a while the inner side of the cover and the trapped air surrounding our body reach equilibrium with our body. Thus we feel comfort. Q.3 Do you have same temperature sense when you touch a steel chair and a wooden chair? Ans. If the two chairs are kept in a same room, they will have same temperature due to thermal equilibrium of them with the room. However, when we touch them, the steel chair appears colder than the wooden chair (in winter). This is because the steel being a metal, removes energy more quickly from our hands. But after some time, when the thermal equilibrium is established, we feel no difference. Q.4 Can you have an idea of atmospheric pressure with the help of a thermometer? Ans. Boiling point of water is 100 C0 at standard (normal) atmospheric pressure. When the pressure above water surface increases the boiling point also increases and the boiling point decreases as the pressure decreases. Therefore, if the boiling point of water is found to be more than 100 C0 , this gives an indication that the atmospheric pressure is

* Pa = Pascal (unit of pressure); 101.3 kPa = 1 atm (1 kPa = 10 3 Pa); 1 atm = standard atmospheric pressure = the pressure corresponding to 760 mm of Hg column.


more than the normal. Likewise, when the boiling point is found to be less than 100 C0 , the atmospheric pressure can be assumed to be less than the normal.

Questionnaire Very short questions:

1. How much is the temperature -273 C0 in Kelvin scale? [H.S.(XI)’06] Ans. 0 K

2. Our normal body temperature is indicated to be 98.6 in a Clinical thermometer. How much is it in Celsius scale? Ans. 37 C0

3. From the zeroth law of thermodynamics we get a definition of some physical property. What is that? Ans. temperature

4. We can say something is same between two bodies if they are in thermal equilibrium. What is that? Ans. temperature

5. What is the device that can measure temperature? Ans. thermometer 6. Some energy is transferred between two bodies only because of temperature difference

between them. What is that energy of transit? Ans. heat 7. What is the lowest value of temperature that is possible? Ans. 0 K 8. Where can we possibly find the highest temperature? Ans. Stars 9. How much is our standard body temperature in Kelvin scale? Ans. 310 K 10. What is the property of matter that is exploited in a clinical thermometer?

Ans. thermal expansion Multiple answer type:

1. Triple point of water is at (i) 273.16 K , (ii) 273.16 C0 , (iii) 273.16 F0 , (iv) 0 C0 .

2. The pressure at the triple point of water is (i) 4.58 mm Hg , (ii) 4.57 mm Hg, (iii) 4.59 mm Hg, (iv) 4.56 mm Hg. 3. The primary thermometer is

(i) Liquid-in-glass thermometer, (ii) Platinum resistance thermometer, (iii) Ideal gas thermometer, (iv) Alcohol thermometer

4. A difference in temperature measured with a Fahrenheit scale is unity (1 0F ). The measured value in Celsius scale is

(i) 0

59 C , (ii) 0

95 C , (iii) 1 0C , (iv) none of them.

5. There is no negative number in (i) Celsius scale, (ii) Kelvin scale, (iii) Fahrenheit scale, (iv) all of them.


Descriptive type:

1. What do you mean by thermal equilibrium? 2. Write the zeroth law of thermodynamics. 3. How do you interpret the zeroth law of thermodynamics? 4. How does one derive the definition of temperature from the zeroth law of thermodynamics? 5. What is temperature? 6. What is heat? 7. What is a thermometer? 8. How is the scale of a thermometer determined? 9. What is a fixed point? Give examples.

10. Is the solar system is in thermal equilibrium? 11. Give an example of a system where there is thermal equilibrium. Explain why. 12. Why do you feel comfort after a certain time when you cover your body with a blanket in winter. 13. Can there be equilibrium when somebody is in a cold room? 14. Explain your feeling when you simultaneously touch a wooden chair and a metallic chair kept for a long time in the sun. 15. What is primary thermometer? 16. Why is it that the ideal gas thermometer be called primary thermometer? 17. What is triple point of water? What are the temperature and pressure at this? 18. What do you mean by ideal gas scale of temperature? 19. What is secondary thermometer? Give examples. 20. ‘Heat is energy in transit’ – explain this statement. 21. What are ice-point and steam-point? 22. What will happen if we mix some water of 80 C0 with some of 20 C0 ? 23. How can you determine whether the atmospheric pressure is higher or lower compared to the standard value? 24. What is absolute zero? 25. What is thermodynamics? 26. What is the advantage of measuring our body temperature in Fahrenheit scale? 27. What do you mean by thermal contact? 28. What is responsible for whether heat will flow between two objects? What are the things responsible for how much heat flows between two objects? 29. What is thermal energy? 30. What is the basic principle by which a thermometer measures temperature?

temperature

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