PHYSICS

Part I: Heat and Gases

Hong Kong Diploma of Secondary Education

(HKDSE)

Notes & Exercises

Chapter 1 to 4

ANDY WONG S.T.

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TABLE OF CONTENTS

CHAPTER 1 TEMPERATURE AND INTERNAL ENERGY ................................................................. 4 1. Temperature ................................................................................................. 4

2. Temperature scales ..................................................................................... 4

3. Thermometers .............................................................................................. 5

4. Heat and internal energy ............................................................................ 8

5. Heat capacity ................................................................................................ 8

6. Specific heat capacity .................................................................................. 8

7. Mixture ........................................................................................................... 8

8. Importance of high specific heat capacity of water ................................. 8

CHAPTER 2 CHANGE OF STATE ................................................................................................. 9 1. States of matter ............................................................................................ 9

2. Cooling curve ................................................................................................ 9

3. Latent heat .................................................................................................... 9

4. Specific latent heat of fusion ...................................................................... 9

5. Specific latent heat of vaporization ........................................................... 9

6. Evaporation and boiling .............................................................................. 9

CHARTER 3 TRANSFER PROCESS ............................................................................................ 10 1. Conduction .................................................................................................. 10

2. Conductivity of heat ................................................................................... 10

3. Molecular motion and conduction ............................................................ 10

4. Applications of conductors and insulators of heat ................................ 10

5. Convection .................................................................................................. 10

6. Examples of convection of heat ............................................................... 10

7. Radiation ..................................................................................................... 10

8. Absorbers and emitters of radiation ........................................................ 10

9. Greenhouse and vacuum flask ................................................................ 10

*CHAPTER 4 GAS LAW AND KINETIC THEORY......................................................................... 12 1. Pressure ...................................................................................................... 12

2. Boyle’s law .................................................................................................. 12

3. The pressure law ........................................................................................ 12

4. Charles’ law................................................................................................. 12

5. General gas law ......................................................................................... 12

6. Ideal gas law ............................................................................................... 12

7. Brownian motion......................................................................................... 12

8. Assumptions in kinetic theory model....................................................... 12

9. Kinetic theory of gas (statistical mechanics) .......................................... 13

10. Mean K.E. of a gas molecule ................................................................... 13

11. Some deductions from the kinetic theory ............................................... 13

12. Maxwell-Boltzmann distribution for molecular speeds ......................... 13

13. Intermolecular forces** .............................................................................. 13

14. van der Waals’ equation** ........................................................................ 13

15. Departure from Boyle’s law for real gas at high pressure ................... 13

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16. Isotherm of real gas** ................................................................................ 13

*These topics are not required in physics part of HKDSE Combined Science curriculum.

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CHAPTER 1

TEMPERATURE AND INTERNAL ENERGY

1. Temperature

Temperature is a physical property that measures the degree of hotness (or coldness) of an object.

Sense of touch (by skin) cannot detect the exact temperature, but only the differences in temperature.

It is also subjective and inaccurate, thus unreliable.

A. Thermometric properties

Thermometric properties are physical properties that change with temperature, e.g. volume of a gas,

solubility of a solute, resistance of a metal, etc.

B. As a measure of average kinetic energy of molecules

Matter is composed of atoms, molecules or ions. When temperature is above absolute zero, these

particles are constantly under random motion and have kinetic energy.

Temperature is a measure of average kinetic energy of the particles.

2. Temperature scales

A temperature scale can be obtained by:

(1) Choosing two fixed points, i.e. a lower fixed point and an upper fixed point. A stable fixed point

should be easily and accurately reproducible.

(2) The range between this two fixed points are divided into a number of equal divisions called degree.

There are 3 commonly used temperature scales:

(a) Celsius scale

Lower fixed point (or ice point) is the temperature of pure melting ice at one standard temperature

and pressure (s.t.p.).

Upper fixed point (or steam point) is the temperature of pure boiling water at 1 s.t.p.

Temperature range is then divided into 100 equal divisions called degree Celsius, written as C. The

lower fixed point is 0C, and the upper fixed point is 100C.

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(b) Kelvin scale

The unit used is kelvin, written as K. The temperature interval of 1K is the same as that of 1C. 0K is

the lowest possible temperature of matter and is called absolute zero.

Kelvin scale and Celsius scale can be interconverted by:

Kelvin temperature = Celsius temperature + 273

(c) Fahrenheit scale

The unit used is degree Fahrenheit, written as F. It is most commonly used in the United States.

Kelvin scale and Celsius scale can be interconverted by:

Fahrenheit temperature =

Celsius temperature + 32

3. Thermometers

A. Types of thermometers

(a) Liquid-in-glass thermometer

It consists of a closed capillary tube with a glass bulb at one end. The bulb is filled with a

thermometric liquid which expands and contracts with temperature. It should expand or contract

linearly.

Wall of glass bulb is usually very thin to increase rate of heat transfer, and capillary tube is made

very narrow to improve sensitivity of the thermometer.

Mercury-in-glass thermometer Alcohol-in-glass thermometer

Working range ~30C to 400C -100C to 110C

Response to temperature change Quicker Slower

Appearance Silvery Colourless (usually with dye)

Concerns More costly, poisonous Flammable

(b) Clinical thermometer

It is designed to measure human body temperature. It only measures a small temperature range but is

quite sensitive. A conventional one has a constriction in the capillary tube near the bulb to prevent

the mercury column from falling back into the bulb.

A digital one uses an electronic device to measure temperature accurately within a short time.

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(c) Rotary thermometer

It consists of a bimetallic strip made of two different metal strips joined together side by side. Since

two different metals expand to different extents under heat, the strip bends.

The bimetallic strip is often wound to a spiral, which curls when heated and rotates a pointer attached

to its end. A large angle of deflection indicates a higher temperature.

It is robust and has a wide working temperature range from -50C to 300C. It is often used in large

freezers and ovens.

(d) Resistance thermometer

It consists of a coil of metal wire connected to an ammeter and a battery. As temperature increases,

the resistance of the metal increases, current passing through the coil drops, the reading of the

ammeter thus decreases.

It can accurately measure a wide range of temperature, but calibration should be done each time

before usage. It is widely used in industry to measure temperatures of ovens and engine parts.

(e) Thermistor thermometer

It works in a way similar to that of a resistance thermometer, but an electronic component called

thermistor is used instead of the coil of metal wire. When the temperature increases, the resistance

of the thermistor decreases, the reading of the ammeter thus increases.

It has a narrow working temperature range from -50C to 150C, but it is very sensitive. It is

commonly used in electrical appliances e.g. cookers for temperature control.

(f) Thermocouple thermometer

It consists of three pieces of wire in which two are of the same metal and the other one is different.

Two junctions are formed by twisting the ends of different metal wires together. One junction is kept

at a constant temperature (e.g. ice water at 0C) and the other is placed where the temperature to be

measured.

A larger temperature difference between the two junctions will cause a larger current to flow

through the circuit. After calibration, the reading of the ammeter can show the temperature

measured by the junction.

This type of thermometer measures a wide range of temperatures from -250C to 2300C, and its

response rate is fast. It is often used in industry to measure the temperatures of furnaces or in

geography to measure the temperatures of lava from volcanoes.

But, its calibration is not an easy task.

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(g) Infrared thermometer

Any object whose temperature is above absolute zero emits infrared radiation.

Objects emit more infrared radiation as the temperature rises. The infrared thermometer measures the

temperature of an object by measuring the infrared radiation emitted.

It is commonly used in measuring human body temperature. It is also used in measuring temperatures

up to 4000C in industry, and objects at a great distance. In addition, with the help of infrared

thermograph, we can also detect the temperature distribution of an object. Hotter regions will have a

red colour and colder regions will have a blue one.

(h) Liquid crystal thermometer

It consists of liquid crystals that change colour with temperature. It can measure temperature ranging

from 10C to 50C. It is used to measure human body temperature or water temperature in an

aquarium.

B. Calibration of thermometers

For thermometric properties that behave linearly, we have to mark two fixed points on the

thermometer first, and record the level of physical property (e.g. length of liquid column)

corresponding to the temperature we measure. The temperature can then be found by algebraic method

or graphical method.

For thermometric properties that do not behave linearly, we need to plot a calibration graph to

determine the temperature measured.

e.g. 1. A student calibrates an unmarked alcohol-in-glass thermometer and obtains the following:

length of alcohol column / cm

In pure melting ice 4

In pure boiling water 28

(a) The temperature now rises to 10C. Find the increase in length of the alcohol column.

(b) What is the temperature measured by the thermometer when the length of alcohol column is

16cm?

(c) If the thermometer is used to measure human body temperature, which is 36.5C, what will be the

length of alcohol column?

Solution

(a) As alcohol expands linearly with temperature,

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4. Heat and internal energy

Ways to increase internal energy

Power

5. Heat capacity

6. Specific heat capacity

Measurement of specific heat capacity

7. Mixture

Law of conservation of energy

8. Importance of high specific heat capacity of water

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CHAPTER 2

CHANGE OF STATE

1. States of matter

2. Cooling curve

3. Latent heat

As a measure of change of potential energy of molecules

4. Specific latent heat of fusion

Determination of specific latent heat of fusion of ice

5. Specific latent heat of vaporization

Determination of specific latent heat of vaporization of water

6. Evaporation and boiling

Factors affecting the rate of evaporation

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CHARTER 3

TRANSFER PROCESS

1. Conduction

2. Conductivity of heat

3. Molecular motion and conduction

Factors affecting the rate of conduction

4. Applications of conductors and insulators of heat

5. Convection

6. Examples of convection of heat

7. Radiation

8. Absorbers and emitters of radiation

9. Greenhouse and vacuum flask

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*CHAPTER 4

GAS LAW AND KINETIC THEORY

1. Pressure

Atmospheric pressure

Gas pressure

2. Boyle’s law

3. The pressure law

4. Charles’ law

5. General gas law

6. Ideal gas law

Mean separation between gas molecules at s.t.p.

7. Brownian motion

8. Assumptions in kinetic theory model

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9. Kinetic theory of gas (statistical mechanics)

10. Mean K.E. of a gas molecule

11. Some deductions from the kinetic theory

12. Maxwell-Boltzmann distribution for molecular speeds

13. Intermolecular forces**

14. van der Waals’ equation**

15. Departure from Boyle’s law for real gas at high pressure

16. Isotherm of real gas**