Lecture Notes on CE Heat

8/12/2019 Lecture Notes on CE Heat

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____________________________________________________________________________________________________Y Y Chans physics learning materials CE Heat Page 1

LECTURE NOTES ON CE HEAT

1 TEMPERATURE, HEAT AND INTERNAL ENERGY

1.1 Temperature scale and thermometer

1.1.1 Terminology

Temperature: Measurement of degree of hotness or coldness.

Thermometer: An instrument for measuring temperature.

A substance which physical property is changed with temperature can be used to make a thermometer. Forexample: iron, mercury, etc.

Temperature scale: The temperature scale can be determined by choosing two fixed points:

A. Lower fixed point (ice point): The temperature at which pure ice melts under normal atmospheric

pressure.

B. Upper fixed point (steam point): The temperature at which pure water boils under normal atmospheric

pressure.

Then make calibration between the two fixed points.

In Celsius scale, the lower fixed point is defined as 0 and the upper fixed point is defined as 100, 100

divisions are divided between the two fixed points.

Thermal equilibrium: Two bodies in contact reaches the same temperature when the time is long enough.

1.1.2 Liquid-in-glass thermometer

Two common liquid-in-glass thermometers are (1) mercury thermometer and (2) alcohol thermometer.

Advantages of using liquid-in glass thermometer:

Relatively simple to operate

Accurate

Not expensive

Working range of mercury thermometer: -39C to 375C.Working range of alcohol thermometer: -115C to 78C.

Advantages for using a mercury thermometer over an alcohol thermometer

It does not wet the glass.

It conducts heat better.

It expands more uniformly.

For measuring human body temperature, a clinical thermometer is used.

1.1.3 Some other thermometers

Rotary thermometer

Resistance thermometer

Thermocouple thermometer

Infrared thermometer

1.2 Heat and internal energy

1.2.1 DefinitionsWhat is meant by hot and cold?

For two objects of the same material and same mass, a hot object contains more energythan a cold one.

What kind of energy does it contain more? It is the internal energy.

Internal energyis the total kinetic energyandpotential energyof all the molecules in that substance.


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Heatingis a process of energy transfer due to temperature difference between two bodies. It is not

something stored in an object.

Heatis the energy transfer by the process of heating.

It is wrongto say an object contains a lot of heat energy!

Example 1-2: Which one contains more internal energy?

(a) 1 kg of iron in 30C or 1 kg of iron in 60C?(b) 1 kg of iron in 30C or 2 kg of iron in 30C?

1.2.2 Ways of energy transfer

The internal energy of a body can be increased by

doing work, for example, hammering a piece of iron. Both the iron and the hammer are increase intemperature;

making two bodies of different temperature in contact, for example, putting a piece of iron into flame.

We cannot tell the difference whether the internal energy of an object is increased by heating or by work

done.

1.2.3 Unit for energy and work

In SI system, both the units for energy and work arejoule (J).

The rate of energy transfer or the rate of work done is power.

And power =energy transfer

time, or P

E

t=

The SI unit for power is watt (W).

Apparatus for measuring the change in internal energy

Joulemeter: To record the amount of (electrical) energy transfer

Low voltage power supply

Immersion heater

Foam cup (to reduce heat loss to surroundings and it absorbs very little heat)

Thermometer (to measure temperature change)From the experiment, it shows that

the amount of energy supplied is directly proportional to the temperature change if the mass is

constant; i.e. E where is the difference in temperature.

the amount of energy supplied is directly proportional to the mass of water if the temperature change is

constant. i.e. Em.

Therefore,

Em

That means the energy transferred by heating is directly proportional to the _________ and ___________.


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1.3 Heat capacity and specific heat capacity

Heat capacityis the amount of energy required to change the temperature in 1C of that substance.

The symbol for heat capacity is Cand the SI unit is J C-1

.

E = C

The heat capacity depends on the mass and material of the substance.

Specific heat capacityof a substance is the energy transferred by heating needed to raise the temperature

of 1 kg of that substance through 1C.Let cbe the symbol for s.h.c. of the substance

E= cm

SI unit for specific heat capacity is J kg-1

C-1

.

Specific heat capacity depends on material only.

The relation between heat capacity and specific heat capacity is

Heat capacity = mass specific heat capacity

Experiment 1: Measurement of specific heat capacity of water

Mass of water m: ____________ kg

Initial temperature 1 ____________ C

Final temperature 2 ____________ C

Difference in temperature.

____________CInitial joulemeter reading E1 ____________ J

Final joulemeter readingE2 ____________ J

Energy transferE ____________ J

s.h.c. of water c= _________ = ___________ J kg-1

C-1

Notice:

1. Even though the immersion heater is switched off, the temperature rises for a little while until itreaches the maximum value. We should take the maximum temperature to be the final temperature.

2. The reason for (1) is that just at the time when the immersion heater is switched off, the temperature ofthe heater is a little bit higher than the water. So heat is still transferred from the heater to the water.

Experiment 2: Measuring specific heat capacity of an aluminium block

Mass of aluminium block m ____________ kg

Initial temperature 1 ____________ CFinal temperature 2 ____________ C

Change in temperature ____________ C

Initial joulemeter readingE1 ____________ J

Final joulemeter readingE2 ____________ J

Energy transferredE ____________ J

Specific heat capacity of aluminium

c= ________________ = ____________ J kg -1C-1


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Precautions:

The aluminium block should be placed on apolystyrene tile to prevent energy loss to the table.

Some oil should be put into the hole to ensure agood contact between the thermometer and the

block.

Specific heat capacity of some substances:

Substance Specific heat capacity (J kg-1C-1)

water 4200

ice 2100

alcohol 2500

paraffin 2200

glass 670copper 390

lead 130

Example 1-2: 0.1 kg of water and 0.1 kg of lead are placed under sunlight. Which one will have a large

temperature rise? Explain your answer.

1.3.1 How can we know whether there is internal energy change in an object?

From the equationE= cm, for an object of same material (cconstant) with equal mass (mconstant), the

higher the temperature, the more internal energy absorbed. This is because a particle in high temperature

has more kinetic energy.

If two objects of same material and same mass are in the same temperature, we should consider their states

to compare the internal energy stored.

Example 1-3:What is the heat capacity of 0.2 kg of water.

Example 1-4: Find the energy needed to change 0.2 kg of water from 20C to 80C.


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1.3.2 Mixtures

When two bodies of different temperatures are placed in contact inside an insulated container, energy is

transferred from the body at high temperature to the body at low

temperature.

Therefore

Energy gained by body at low temperature = Energy lost by body at

high temperature.Finally, both bodies are in the same temperature.

Let

m1be mass of body at low temperature

c1be specific heat capacity of body at low temperature

1be lower temperature

m2be mass of body at high temperature

c2be s.h.c. of body at high temperature

2be high temperature

be the final temperature of the mixture

Energy gained by the cool bodyE1= m1c1 (- 1)

Energy lost by the hot bodyE2= m2c2(2- )

Assume there is no energy exchange with the surrounding, E1=E2m1c1 (- 1) = m2c2(2- )

Example 1-5: If 0.2 kg of water at 20C is added to 0.3 kg of water at 40C, find the final temperature of the

mixture. What assumption have you made in your calculation?

The above example is an application of theLaw of conservation of energy. That is, energy lost from one

body is equal to the energy gained in another body. No energy can be generated nor disappeared. In

practice, more or less there is some energy lost to or gained from the surroundings. The energy exchange

would be considerable if the temperature difference between the objects and the surroundings are

significantly large.


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Example 1-6: A piece of copper of mass 0.2 kg is heated by the flame of a Bunsen burner. It is then put into a

cup with 0.5 kg of water in it. The temperature of water rises from 20to 28C. Estimate the temperature

of the flame. Will the actual temperature of the flame higher or lower than the value you have calculated?

Give your reason. (s.h.c. of copper = 390 J kg-1C-1, s.h.c. of water = 4.2 10

3J kg-1C).

1.3.3 High specific heat capacity of water

Water has a high specific heat capacity (4200 J kg-1C-1) means it requires large amount of energy to

increase its temperature or it gives up a lot of energy with only small drop in temperature.

Importance of high specific heat capacity of water:

It is used as a coolant in engine. For the coolant used in car, some chemicals are added to prevent fromrusting and freezing.

Water is used for storing energy in a solar heater.

In human body there is about 65% of water. More or less this helps us to maintain a constant body

temperature. The temperature change is small in coastal area. This is because a certain mass of water needs 5 times

more heat for its temperature to rise by 1C than does the same mass of soil.

2. CHANGE OF STATES

2.1 Cooling curve

A pure substance has a fixed melting point and boiling point. Change of state occurs at these temperatures.

The following experiment can obtain the melting point of octadecan-1-ol from its cooling curve:

First heat the octadecan-1-ol in a water bath until the temperature is 70C. At this temperature theoctadecan-1-ol is in liquid state.

Remove the flame and place a thermometer into the octadecan-1-ol.

Take the reading from the thermometer once per minute.

Plot the result on a graph and a cooling curve is obtained.Refer to the cooling curve:

PortionABis the octadecan-1-o1 in liquid state. The temperature is dropping because the octadecan-1-ol loses energy to surroundings.

AtBCthere is no temperature change in octadecan-1-ol but it continues to lose heat to surroundings

and is freezing. From the curve, we can find the melting point is 58C.

At CD, the temperature drops again. All octadecan-1-ol becomes solid.


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Heat transfer does not always result in changing temperature, sometimes the temperature is constant but its

state is changed. For example, when the ice at 0C absorbs heat, it melts and becomes water but

temperature may be still at 0C. Heat absorbed or released during change of state is called thelatent

heat.

2.2 Latent heat and potential energy

1. The temperature of a substance reflected the average kinetic energy of each particles of that substance.

2. When the latent heat is absorbed, the temperature is constant but the state is changed. This means theaverage kinetic energy of each particle does not change. However the potential energy of each particle

increases. Hence the internal energy of the substance increases.

2.3 Fusion and vaporization

The three states of matter are: solid, liquid and gas.

Fusion: Process that solid changes into liquid

Vaporization: Process that liquid changes into gas.

Condensation: Process that gas changes into liquid.

Solidification: Process that liquid changes into solid.

2.4 Specific latent heat

The specific latent heat of fusionLfis the heat required to change 1 kg of a substance from solid state to

liquid state or vice versa. The S.I unit of specific latent heat is J kg-1.

If an object of mass mabsorbed an amount of energyEto change from solid to liquid, then

E= mLf

The specific latent heat of fusion of ice is 3.36 105J kg-1.

The specific latent heat of vaporizationLvis heat required to change 1 kg of a substance from liquid state

to gaseous state. Latent heat is given out when steam is condensed to liquid.

If an object of mass mabsorbed an amount of energyEto change from liquid to gas, thenE= mLv.

The specific latent heat of vaporization of water is 2.26 106J kg

-1.

Example 2-1: Explain why the injury caused by 100C steam is more serious than that caused by boiling

water?

2.4.1 Measurement of specific latent heat of fusion of ice

Set up the experimental apparatus and the control apparatus. The only difference between them is thatthe experimental apparatus is connected to the power supply while the control apparatus is not.

The purpose of using the control apparatus is for comparison. When the immersion heat is turned on,the ice in the experimental apparatus is melted by the energy from the heater and the surroundings.

And in the control apparatus, the ice is melted by absorbing heat from surroundings only.

If E1be the initial joulemeter reading,E2be the final joulemeter reading,

m1be the mass of water collected in experimental apparatus,

m2be the mass of water collected in the controlled apparatus,

Then

Energy given out by the immersion heat isE=E2-E1

Mass of ice melted by the immersion heater m= m2- m1

The specific latent heat of fusion of ice is given by lE

mf =


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Precautions for the experiment:

1. Crushed and melting ice must be used. It is because the centres of the ice cubes would be very close tothe melting point.

2. Before the immersion heater is turned on, the rate of water dripping in both apparatus must be nearlythe same.

3. The immersion heater must be immersed deeply into the ice.

Example 2-2: If a student forgets to set up the control apparatus, will the value of specific latent of fusion be

larger or smaller?

2.4.2 Measurement of the specific latent heat of vaporization of water1. Set up the following apparatus as shown in the figure. Use a mains immersion heater, a kilowatt-hour

meter, a vacuum flask without lid, a beam balance.

2. Heat the water with the immersion heater till it is boiling. Take the readings of the kilowatt-hour meterE1and the balance m1at the same time.

3. Let the water continue to boil. After few minutes, some of water is vaporized and it escapes. Againmeasure the readings of the kilowatt-hour meterE2and the balance m2.

4. The latent heat given to the water isE=E2-E1and the mass of water vaporized is m= m1- m2

5. The specific latent heat of vaporization of water is given by LE

mv = .


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6. The possible errors in this experiment are:

Steam condensing on the top part of the heater drips back into the flask.

Some water may have bubbled out of the flask.

Energy is lost to the surroundings.

Example 2-3: For measuring the specific latent heat of vaporization of water, a student says, In order toreduce heat loss to surroundings, the water in the cup should be covered with a lid. Give comment to his

statement.

Example 2-4: An electric kettle with a heating element rated at 2.3.kW contains boiling water. What mass of

steam does it produce in 5 minutes?

Example 2-5: An aluminium can of mass 0.1 kg contains 0.2 kg of water at 15C. The can with water in it is

located in a refrigerator at -5C.

(a) Calculate the heat lost by the can as its temperature drops from 15C to -5C.

(s.h.c. of aluminium = 900 J kg-1

C-1

)

(b) Calculate the heat loss by water as its temperature drops from 15C to 0C.

(c) Calculate the heat loss by water as it freezes to ice at 0C.

(d) Calculate the heat loss by ice as it falls from 0C to -5C.(e) Determine the heat removed from water as its temperature drops from 15C to -5C.

(f) Determine the total amount of heat removed from the can and water as the temperature drops from

15C to -5C.

Example 2-6(1999): 0.1 kg of melting ice is added to 0.5 kg of water at 30C in a foam cup. Find the final

temperature of the mixture.

(Given: s.h.c. of water = 4200 J kg-1C-1, specific latent heat of fusion of ice = 3.4 10

5J kg-1)


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Example 2-7: A student sets up the apparatus shown in the figure to find out the specific latent heat of fusion

of ice. He leaves the heater off for 10 minutes and then turn on the heater for next 10 minutes.

A graph of the reading of the electronic balance against time is plotted in follow:

(a) Explain why the slope of the two straight lines are different.(b) The following readings on the joulemeter are recorded:

Initial reading = 15 000 J

Final reading = 25 000 J

Calculate the specific latent heat of fusion of ice.


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3. GAS LAWS

When a gas is heated, the pressureP, volume Vand temperature Twill change and these three quantities

are related to each other. In order to study the relations ofP, Vand T, we should keep one quantity

constant and see how the two other quantities vary.

3.1 Gas pressure and Bourdon gauge

The SI unit of pressure is N m-2or pascal (Pa). The normal atmosphere pressure is about 105Pa or100 kPa. The common apparatus used in laboratory for measuring pressure is the Bourdon gauge.

3.2 Pressure law

Trap the air in a flask and heat it in a water bath.

The flask is connected with a short rubber tubing to

a Bourdon gauge. Gradually increase the

temperature and take the readings from the

thermometer and the Bourdon gauge. Finally plot

the graph of pressure against the temperature.

Precautions:

The tubing should be as short as possiblebecause the temperature of air inside the tubing

is different from that inside the flask.

Stir the water so that the temperature aroundthe flask is homogeneous.

It is better to stop heating for taking each reading such that there is time allow the temperature andpressure to be steady.

A linear graph is obtained by plotting the gas pressure against its temperature. From the graph its is found

that:

the pressure increases as the temperature increases,

the extension of the graph intercepts the temperature axis at about -273C.

Experiments with different amounts and different types of gas show that the intercept remains at -273C.

Therefore a new temperature scale is necessary to introduce. This scale is called the Kelvin scale.

T= 273 + .

Tis the Kelvin temperature and its SI unit is kelvin (K). is the Celsius temperature.

By plotting the gas against the Kelvin temperature, the graph passes through the origin. From the

experiment, we conclude that

The pressure of a fixed mass of gas is directly proportional to its Kelvin temperature, providing that

the volume is fixed.

This is known as the pressure law.


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Expressing in equation,

p/T= constant or

p

T

p

T

1

1

2

2

=

Example 3-1: A flask contains gas at 0C. To what temperature must the flask be placed such that the pressure

of the gas inside is doubled? Assume the flask does not expand.

3.3 Charles law

Set up the apparatus shown in the figure. Confine the aircolumn inside a glass tube with a mercury thread. Immerse the

air column in a water bath and heat it. The mouth of the glass is

open at the top so that the pressure of the air column is equal to

the atmospheric pressure. Measure the length of air column with

a metric rule and the temperature with thermometer. Plot a

graph of the length of air column against the temperature.

Precautions:

The air column must be totally immersed into the waterbath.

Stir the water from time to time so that the temperature ofthe water is homogeneous.

Take readings after the temperature becomes steady.

Avoid the thermometer touching the bottom of the can.

Also a linear graph is obtained. Since the cross-sectional area of the glass tube is constant, so the length ofthe air column is directly proportional to the gas volume.


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From this experiment it is known that the volume of gas increases as the temperature rises. By changing

the amount of gas in the tube or increase the gas pressure (but keep constant), another linear graph is

obtained by the intercept on the temperature axis is also -273C.

Hence it is concluded that

The volume of a fixed amount of gas is directly proportional to its Kelvin temperature providing that

the pressure is constant. This is known as Charles law.

i.e. V/T= constant, orV

T

V

T

1

1

2

2

=

Example 3-2: An inflated balloon contains 310-3m3of air at 27C. It is put into a large tank of liquid

nitrogen at -198C. What is the new volume of the balloon?

3.4 Absolute temperature

Kelvin temperature is also known as absolute temperature. The conversion between Kelvin scale and

Celsius scale areT= + 273

From the pressure law and Charless law, when the Kelvin temperature is zero (0 K), the gas pressure and

the volume are zero. This temperature is known as absolute zero. This is the lowest temperature in the

universe.

3.5 Boyles law

Relation between the pressure and volume under constant

temperature can be investigated by setting up the apparatus

shown in the figure. The air is confined in a glass tube by

the oil reservoir. The pressure of the gas is increased by

pumping air in the space above the oil reservoir. Hence

more oil is pumped into the glass tube. It is assumed that the

gas pressure of the air column is the same as that the air

above the oil reservoir.

From the experiment it is found that the product of pressure

and volume is constant. A curve is obtained by plotting the

pressure against the volume. A straight line is obtained if

plotting the pressure against the reciprocal of the volume.

Express in equation,

PV

= constant1

, or

P1V1=P2V2


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3.6 General gas law

The relation between pressureP, volume Vand temperature (in Kelvin scale) Tcan be combined into one

equation, called the general gas law.

P V

T

P V

T

1 1

1

2 2

2

=

If volume is constant, i.e. V1= V2, we get the pressure lawP1/T1=P2/T2.If pressure is constant, i.e.P1=P2, we get the Charless law V1/T1= V2/T2.

If temperature is constant, i.e. T1= T2, we get the Boyles lawP1V1=P2V2.

Notice that by applying the general gas law:

the temperature must be in Kelvin scale,

the unit ofP1must be equal to that ofP2and V1be equal to that of V2,

the pressure must be small,

the temperature must be high.

Example 3.3: At a pressure of 1.00 atmosphere and a temperature of 27.0C a mass of gas has a volume of 200

cm3. What is its volume when the pressure is 1.50 atmosphere and the temperature 127C?

Example 3.4: The density of air at 0C and 105Pa is 1.0 kg m

-3. What is the mass of 5 litres of compressed air

in a cylinder at 107Pa and 27C? (1 m3= 103litres).


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4 KINETIC THEORY

4.1 Kinetic theory model to explain solids, liquids and gases

The kinetic theory is a scientific model which enables us to understand why matter in bulk behaves as it

does.

Solids: The molecules are close together and the attractive and repulsive forces between neighbouring

molecules are balanced. Each molecule vibrates to and fro about its own position. So solids have a

regular, repeating molecular structure and their shape is definite.Liquids: The molecules are usually slightly farther apart than in solids. As well as vibrating, they can at

the same time move rapidly over short distances, although they are never near each other for long enough

to get trapped in a regular structure. Therefore a liquid has no fixed shape and can flow.

Gases: The molecules are much farther apart than in solids or liquids. They have enough energy to move

in a very high speed (about 500 m s-1in room temperature for air). The molecular force acts only when the

molecules collide with other molecules or with the walls of the container.

4.2 Explanation of gas pressure and gas expansion.

Gas pressure: The pressure exerted by a gas is due to the molecules bombarding the walls of its container.

If the molecules hit the walls more violently or more frequently, the gas pressure increases.

Gas expansion: When a gas is heated, its temperature rises and the average speed of gas molecules

increases. Therefore the molecules require more space to move. When a gas is expanded the average

separation between the gas molecules increases.

4.3 Brownian motion

Brownian movement is significant evidence to the molecular motion. In 1827, the Scottish botanist, Robert

Brown discovered that fine pollen grains in water always move randomly. This is because the pollens are

collided by the water molecules. Therefore the pollens travel in zip-zap paths.

4.4 Postulates on kinetic theory of gases

1. A gas is composed of a large amount of tiny particles.2. The volume of particles is very small as compared to the volume of gas. That means there is a lot of

space between the gas molecules.

3. The particles are in random motion.

4. The force acting on the gas particles is negligible except when they collide each other or bombard ontothe walls of the container.5. The collision of the particles is perfectly elastic, that means there is no kinetic energy lost during

collision.

6. The time of contact during collision is negligible.

4.5 Gas laws and kinetic model

The relations between the pressure, volume and temperature of a gas can be

demonstrated by an apparatus called kinetic theory model machine. It consists of a

cylindrical tube with a movable piston and a vibrating base connecting to a rotating

motor. Some ball bearings are put between the piston and the base. Weights are

placed onto the piston.The characteristics are shown as following:

Pressure: shown by the weights on the piston.

Volume: shown by the separation between the piston and the base.

Temperature: shown by the speed of the rotation of motor.

Demonstration of kinetic theory model:

1. Increase the weights, separation between the piston and the base decreases.2. Increase the speed of motor, separation between the piston and the base

increases.

3. Increase the number of ball-bearings, separation between the piston and the baseincreases.


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4.6 Explanation of gas laws with kinetic theory

4.6.1 Explanation of Boyles law:

If the volume of a gas is decrease, the gas molecules are crowded together and hence hit the wall of the

container more frequently. So the average force acting on the wall increases and consequently the pressure

increases.

4.6.2 Explanation of pressure law:

As the temperature rises, the gas molecules move faster. If the volume is constant, the molecules hit thewall of the container more frequently and more violently. Therefore the pressure increases.

4.6.3 Explanation of Charles law:

As the temperature rises, the gas molecules hit the wall of the container more violently. In order to keep

the average force acting on the wall of the container constant such that it maintains a constant pressure, the

volume of the gas must be increase so that the gas molecules are widely spread out and hit the wall less

frequently.


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MC Exercise Heat 1: Heat and internal energy

1. The apparatus shown is used to find the specific heat

capacity of a liquid. Which of the following can

improve the accuracy of the experiment?

(1) Take the final temperature of the liquid

immediately after switching off the power supply.(2) Covering the cup with a lid.

(3) Stirring the liquid throughout the experiment.

A. (1) only B. (3) only

C. (1) and (2) only D. (2) and (3) only

2. 16500 J of energy is supplied to a metal block of mass 0.5 kg and its rise in temperature is 64C. The

specific heat capacity of the metal is

A16500 0 5

64

.J kg K -1 -1 . B

16500 64

0 5

.J kg K -1 -1 .

C16500

64 05 .J kg K -1 -1 . D

16500

64 273 05( ) .+ J kg K -1 -1 .

3. Equal masses of five different liquids are separately heated at the same rate. The initial temperatures of the

liquids are all 20C. The boiling point and the specific heat capacities of the liquid are shown below.

Which one of them will boil first?

Liquid Boiling point / C Specific heat capacity / J kg-1

K-1

A. P 50 1000

B. Q 60 530

C. R 70 850

D. S 80 1710

4. An immersion heater is used to heat a cup of water. It takes 10 minutes to bring the water from 20C to its

boiling point 100C. Find the time taken for the heater to vaporize the boiling water completely. (Given:

Specific heat capacity of water = 4200 J kg

-1

K

-1

, specific latent heat of vaporization of water = 2.268

10

6

J kg-1K-1.)

A 54 minutes

B 60 minutes

C 67.5 minutes

D 77.5 minutes

5. Two bodies of the same volume have their specific heat capacities in the ratio 3:2 and their densities in the

ratio 2:1. What is the ratio of their heat capacities?

A. 1:3 B. 3:1 C. 1:1 D. 4:3

6. The heat capacity of an object depends on its

(1) material (2) mass (3) shape

A. (1) only B. (2) only C. (1) and (2) only D. (2) and (3) only


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7.

In the above diagram, the water is initially at room temperature. The electric heater is switched on for 300

seconds and then switched off. Which of the following graphs correctly describes the variation of the

reading of the thermometer?

A.

B.

C.

D.


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8. The graph shows the relationship between

temperature and time when 1 kg of a liquid is

heated by a 500 W immersion heater. Assuming no

loss of heat, what is the specific heat capacity of the

liquid?A 0.01 J kg-1K-1

B 250 J kg-1K-1

C 420 J kg-1K-1

D 2500 J kg-1K-1

9. A heater supplies energy to a liquid of mass 0.5 kg and specific heat capacity 4000 J kg-1K-1contained in a

vessel of negligible heat capacity. Assume that the heat exchange with the surroundings can be neglected.

If the temperature of the liquid rises from 10C to 70C in 100 s, the power of the heater is

A. 200 W B. 1200 W C. 1400 W D. 2080 W

10. Which of the following pairs of objects have different specific heat capacities?

A. 1 kg of water and 2 kg of water

B. 1 kg of liquid naphthalene and 1 kg of solid naphthalene

C. a rectangular block of aluminium of mass 1 kg and a cylindrical block of aluminium of mass 1 kg

D. 1 kg of oil in a glass container and 1 kg of oil in a metal container

Directions: Questions Nos. 11 - 15 consists of two statements. Decide whether each of the two statements is

true or false. If both are true, then decide whether or not the second statement is a correct explanation of

the first statement. Then select one option from A - D according to the following table:

1stStatement 2

ndStatement

A. True True 2

nd

statement is a correct explanation of the 1

st

statement.B. True True 2ndstatement is NOT a correct explanation of the 1ststatement.

C. True False

D. False True

11. The temperature of water in a long

insulated cylinder rises after vigorous

stirring.

Some of the mechanical energy of the

stirrer is transformed into heat energy.

12. The internal energy of a body always

increases when the body is heated.

The temperature of a body always

increases when the body is heated.

13. Two bodies of the same temperature

always have the same amount of internalenergy.

The internal energy of a body is the sum

of kinetic and potential energies of themolecules in the body.

14. The temperature of a pool of water

changes slowly even when the

temperature of the surroundings changes

rapidly.

Water has a high specific heat capacity.

15. When hot water is mixed thoroughly with

cold paraffin in a polystyrene cup, the

energy gained by the paraffin is equal to

the energy lost by the water.

When hot water is mixed thoroughly with

cold paraffin in a polystyrene cup, the

changes in temperature of the water and

paraffin are identical.


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16. Which of the following statements about heat is/are true?

(1) Heat is used to describe the total energy stored in a body.

(2) Heat is used to describe the energy transferred from one body to another as a result of a temperature

difference between them.

(3) A bodys internal energy is increased when it is heated.

A. (1) only B. (2) only C. (1) and (3) only

D. (2) and (3) only E. (1), (2) and (3)

17. Which of the following substances is a liquid at room temperature (about 20C)?

Substance Melting point/C Boiling point/C

A. P 25 444

B. Q -39 357

C. R 44 280

D. S -218 -183

18. An objectPhas a higher temperature than another object Q. Which of the following statement is/are

correct?

(1) The initial energy ofPmust be higher than that of Q.

(2) The specific heat capacity ofPmust be higher than that of Q.

(3) There will be a heat flow fromPto Qwhen they are in contact.


19. Which of the following statements about internal energy, heat and temperature is/are correct?

(1) The internal energy of a body is a measure of the total kinetic energy and potential energy of the

molecules in the body.

(2) Two bodies of the same temperature always have the same amount of internal energy.

(3) Heat is a measure of the energy transferred from one body to another as a result of temperature

difference between the two bodies.

A. (1) only B. (2) only C. (1) and (3) only

D. (2) and (3) only E. (1), (2) and (3)

20.

The above graph shows the variation of the temperature of a liquid with time when the liquid is heated by a

400 W heater. The mass of the liquid is 2 kg. Find the specific heat capacity of the liquid. Assume all the

energy given out by the heater is absorbed by the liquid.

A. 83 J kg-1

K-1

B. 480 J kg-1

K-1

C. 1200 J kg-1

K-1

D. 2400 J kg-1

K-1

E. 12000 J kg-1

K-1


21/44


22/44


MC Exercise Heat 2: Latent heat

1. An immersion heater of power 100 W is used to heat 0.3 kg of a liquid with specific heat capacity 2000 J

kg-1

K-1

. If the initial temperature of the liquid is 23C, find its temperature after 2 minutes. Assume all the

energy given out by the heater is absorbed by the liquid.

A. (0.3 2000 23)C B. (.

)0 3 2000 23 2

100

C

C. (.

)100 120 0 3

200023

+ C D. (

.)

100 120

0 3 200023

+ C

2.

The above apparatus is used to find the specific latent heat of fusion of ice. Which of the following is an

essential precaution to ensure an accurate result?

A. Crushed ice should be used.

B. The ice used should be just taken from the refrigerator so that its temperature is well below

0C.

C. The amount of ice used in funnelXshould be larger than that in Y.

D. The two funnels should be wrapped in insulating material.

3. A 400 W electric heater is used to heat 0.4

kg of a solid. The temperature-time graph

of the substance is shown above. The

specific latent heat of fusion of the

substance is

A. 64 kJ kg-1

.

B. 160 kJ kg-1.

C. 400 kJ kg-1

.

D. 500 kJ kg-1

.

4. A beaker of ether is placed in a dish of water. When air is bubbled through the ether, the water freezes

because

A. energy is required to force air through the ether.

B. ether absorbs energy from water during evaporation.

C. the specific heat capacity of air is very large.

D. the speed of the molecules of ether is increased by the process of bubbling.


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5.

The above apparatus is used to find the specific latent heat of vaporization of water. Which of the

following is NOT correct?

A. Cover the beaker with a lid.

B. Use a suitable heater to prevent boiling the water too vigorously.

C. Surround the beaker with some cotton.

D. Prevent the water drops which condense on the upper part of the heater from dropping back into the

beaker.

6. Two liquidsAandBare sealed in air. Their cooling curves are shown below:IfAandBhave the same mass, which of the following

statements is/are correct?

(1) Ahas a greater freezing point thanB.

(2) Ahas a greater specific latent heat of fusion thanB.

(3) LiquidAhas a greater specific heat capacity than liquidB.

A. (3) only

B. (1) and (2) only

C. (2) and (3) only

D. (1), (2) and (3)

7. A liquid placed inside an insulated vessel is kept boiling by a heating coil immersed in it. When the power

supplied to the coil is 42 W, the liquid boils away at a rate of 10-4kg s-1. What is the specific latent heat of

vaporization of the liquid?

A. 4.2 104J kg

-1B. 2.1 10

5J kg

-1C. 4.2 10

5J kg

-1

D. 2.1 106J kg-1 E. 4.2 10

6J kg-1

8. 0.1 g of steam at 100C is mixed with 0.10 g of ice at 0C. No heat is lost to the surroundings. Which of

the following describes the final mixture? (Specific heat capacity of water 4.2 kJ kg-1K-1, specific latent

heat of ice = 336 kJ kg-1, specific latent heat of steam = 2268 kJ kg-1 )

A. A mixture of ice and water at 0C

B. Water at 0C

C. Water at 50C

D. A mixture of water and steam at 100C

9. The following data show the thermal properties of five substancesP, Q,Rand S.substance melting point boiling point average specific

heat capacity in

J kg-1K-1

Specific latent

heat of fusion

in J kg-1

Specific latent

of vaporization

in J kg-1

P 40 K 280 K 800 2 104 30 104

Q 98 K 880 K 1 200 11 104 34 104

R 114 K 180 K 226 5 104 40 104

S 270 K 370 K 40 33 104 230 104

When 1 kg of each substance has its temperature increases from 250 K to 400 K, which one will absorb the

most heat?

A. P B. Q C. R D S


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10.

A 20 W heater is used to melt a solid. A graph of temperature against time tis plotted as shown above.

If a 40 W heater is used, which graph (using the same scale) would be obtained?

11. A solid substance of mass 2 kg and specific heat capacity

1000 J kg-1

K-1

is heated uniformly by a constant heat source.

The temp-time graph of the substance is as shown above.

Assuming that no heat is lost, find from the graph the specific

latent heat of fusion of the substance.

A. 1 000 J kg-1

B. 20 000 J kg-1

C. 30 000 J kg

-1

D. 50 000 J kg-1

12. It is given that the specific latent heat of fusion of ice = 3.3 104J kg-1, the specific latent heat of

vaporization of water = 2.3 105J kg-1 and the specific heat capacity of water is 4200 J kg-1K-1. If 1 kg of

ice at 0C and 1 kg of steam at 100C are mixed in a well insulated vessel, the result will be

A. a mixture of ice and ice-cold water.

B a mixture of steam and boiling water.

C. water at 0C.

D. water at 50C.


25/44


Directions for questions 13-16, see page 19.

13. When a liquid is boiling, large amount of

energy are absorbed.

The average kinetic energy of its

molecules is increased during boiling.

14. When equal masses of ice (at 0C) and

steam (at 100C) are mixed, the product

is water at temperature higher than 50C.

The specific latent heat of fusion of ice is

larger than the specific latent heat of

vaporization of water.

15. The temperature of naphthalene remains

unchanged when it solidifies.

There is no heat loss in the naphthalene

when it solidifies.

16. Steam at 100C causes more severe burns

to the skin than boiling water at the same

temperature.

A large amount of latent heat of

vaporization is released when steam

condenses.

17.

The graph shows the cooling curve of liquid naphthalene. In which region has naphthalene completely

solidified?

A. P B. Q C. R D. S

18. Heat is needed to keep water boiling because energy is required to

(1) overcome the effect of atmospheric pressure.

(2) increase the kinetic energy of the water molecules.

(3) increase the potential energy of the water molecules.

A. (1) only B. (1) and (2) only C. (1) and (3) only D. (2) and (3) only

19. The figure shows an experiment to determine the specific

latent heat of fusion of ice. The result obtained is lower than

the expected one. The main reason could be

A. there is heat gain from the surroundings.

B. there is heat loss to the surroundings.

C. there is some water remaining in the funnel, not falling

into the beaker.D. the temperature of the ice is below 0C.

20. Arrange the following in ascending order.

E1= energy required to melt 1 kg of ice at 0C

E2= energy required to raise the temperature of 1 kg of copper by 1C

E3= energy required to vaporize 1 kg of water at 100C

E4= energy required to raise the temperature of 1 kg of water by 1C

A. E1


26/44


21. Five different solids, each of mass 1 kg, are heated by identical immersion heaters for 10 minutes. The

following graphs show their heating curves. Assuming no energy loss in heat, which solid has the greatest

specific latent heat of fusion?

A B

C D

For Questions 22 to 23. The following apparatus is used to find the specific latent heat of vapoization of a

liquid.

22. When the liquid boils, the reading of the balance is taken. After 200 s, the reading of the balance decreases

by 0.02 kg. The power output of the heater is 150 W. If 20% of the energy supplied is lost to the

surroundings, find the specific latent heat of vaporization of the liquid.

A. 120 J kg-1

B. 480 J kg-1

C. 3.0 105J kg

-1 D. 1.2 10

6J kg

-1

23. Which of the following can improve the accuracy of the experiment?

(1) Covering the beaker with a lid

(2) Completely immersing the heating coil in liquid

(3) Stirring the liquid throughout the experiment



27/44


24. Two solid substancesXand Yof equal mass are

separately heated by two identical heaters. The

above graph shows the variation of the

temperatures of the substances with time. Which

of the following statements is/are correct?

(1) The melting point ofXis higher than that of Y.(2) The specific heat capacity ofXis smaller than

that of Y.

(3) The specific latent heat of fusion ofXis

smaller than that of Y.


25. If an immersion heater takes 10 minutes to bring a cup of water to its boiling point of 100C from the room

temperature of 20C, what will be the time taken for the boiling water to vaporize completely?

(specific heat capacity of water = 4.2 kJ kg-1K-1, specific latent heat of steam = 2268 kJ kg-1)

A. 33.75 minutes B. 54.00 minutes C. 67.50 minutes D. 75.40 minutes

26.

A cooling curve for liquid naphthalene is shown above. From the graph, which of the followingstatement(s) is/are true?

(1) The melting point of the naphthalene is around 70C.

(2) In the period BC, only liquid naphthalene is present.

(3) In the period BC, no energy is given by naphthalene to the surroundings.


27. A block of melting ice with mass 0.02 kg is put into a polystyrene cup containing 0.3 kg of water with

initial temperature 20C. After the mixture is stirred well, the ice block melts completely and the final

temperature of the water becomes 14C. Which of the following equations can be used to find the specific

latent heat of fusion of ice,L?

(Given: Specific heat capacity of water = 4200 J kg-1K-1)

A. 0.3

4200

6 = 0.02L- 0.02

4200

6B. 0.3 4200 6 = 0.02L+ 0.03 4200 6

C. 0.3 4200 6 = (0.02L+ 0.02 4200) 14

D. 0.3 4200 6 = 0.02L+ 0.02 4200 14


28/44


28.

The above set-up can be used to find the specific latent heat of fusion of ice. Which of the following is not

an essential precaution to ensure an accurate result?

A. using crushed ice in the experiment

B. using melting ice in the experimentC. covering the funnels with lids

D. using the same amount of ice in both funnels

29.

The above apparatus is used to find the specific latent heat of vaporization of a liquid. Which of the

following can improve the accuracy of the experiment?

A. wrapping the beaker with cotton wool.

B. covering the beaker with a lid.

C. stirring the liquid throughout the experiment.

D. setting up a control experiment with the heater not connected to the power supply.

30. A cup of fruit juice is of mass 0.2 kg and temperature 70C. If the specific heat capacity of the fruit juice is

4000 J kg-1

K-1

, find the minimum amount of ice at 0C that should be added to the juice in order to lower

its temperature to 0C.

(Note: Specific latent heat of fusion of ice = 3.34 105J kg

-1.)

A. 0.17 kg B. 0.20 kg C. 0.37 kg D. 0.84 kg

31. A melting ice block of mass 0.05 kg is mixed withxkg of water at 0C in a well-insulated container. If

25 000 J of energy is supplied to the mixture, the mixture changes to water at 4C. Find the value ofx.

(Given: specific latent heat of fusion of ice = 3.34 105J kg-1,

specific heat capacity of water = 4200 J kg-1K-1)

A. 0.37 B. 0.44 C. 0.49 D. 1.44

32. A cup of liquid P and cup of liquid Q of equal mass are heated at the same rate. It is found that the

temperature ofPis rising at a rate faster than that of Q. Which of the following deductions is/are correct?

(1) Phas a lower specific latent heat of vaporization than Q.

(2) Phas a lower boiling point than Q.

(3) Phas a lower specific heat capacity than Q.A. (1) only B. (3) only C. (1) and (2) only D. (2) and (3) only


29/44


33.

The above apparatus is used to find the specific latent heat of vaporization of water lv. Which of the

following factors will cause the result obtained to be larger than the true value of lv?

(1) Some energy is lost to the surroundings.

(2) Some steam condenses and drips back into the beaker.

(3) Some boiling water inside the beaker splashes out of the beaker.


34.

The figure above shows the cooling curve of a substance which is initially in the liquid state. The

temperature of the substance remains unchanged during the periodPQ. Which of the following statements

about the substance during the periodPQis/are correct?

(1) The substance is notlosing any energy to the surroundings.

(2) Latent heat is absorbed by the substance.

(3) The average potential energy of the molecules of the substance is decreasing.


35. The melting point of copper is 1080C and its specific latent heat of fusion is 2.1 105J kg-1. How much

energy is needed to melt 0.5 kg of copper at its melting point?

A.21 10

0 5

5.

.

J B. 0.5 2.1 10

5J C.

2 1 10

0 5 1080

5.

.

J D.

0 5 21 10

1080

5. . J

Answers

1 D 11 D 21 C 31 B

2 A 12 B 22 D 32 B

3 C 13 C 23 B 33 C

4 B 14 A 24 D 34 B

5 A 15 C 25 C 35 B

6 D 16 A 26 A

7 C 17 D 27 D

8 D 18 C 28 C

9 D 19 A 29 A

10 C 20 D 30. A


30/44


MC Exercise HEAT 3: Gas Laws

1. A fixed mass of gas at 120C is heated at constant volume so that its pressure is tripled. Find the new

temperature of the gas.

A. 40C. B. 360C. C. 633C. D. 906C.

2. Which of the following graphs correctly shows the relation between the pressurePand volume Vof a fixed

mass of gas at constant temperature?

3. Which of the following graphs correctly shows the relation between the pressurePand the absolute

temperature Tof a fixed mass of gas at constant volume?

4. The pressure of a fixed mass of gas at 30C is 3 105Pa. What would be its pressure if the volume of the

gas is doubled and its temperature is increased to 60C?

A. 1.65 105Pa. B. 3.00 105Pa. C. 5.46 105Pa. D. 6.59 105Pa.

5. The absolute temperature of a fixed mass of gas is T. If the pressure and volume of the gas are bothdoubled, its absolute temperature becomes.

A.1

2T. B. T. C. 2T. D. 4T.

6. The above apparatus is used to study the relation between the volume

and temperature of a fixed mass of gas at constant pressure. Which of

the following is/are correct?

(1) Immersing the whole gas column in water.

(2) Sealing the capillary tube at both ends.

(3) Preventing the thermometer from touching the bottom of the

beaker.

A. (1) only B. (2) only

C. (1) and (3)only D. (2) and (3) only

7. An inexpansible vessel contains 1.2 kg of a gas at 300 K. What is the mass of gas expelled from the vessel

if it is heated from 300 K to 400 K under constant pressure?

A. 0.9 kg B. 0.75 kg

C. 0.6 kg D. 0.3 kg


31/44


8.

A column of gas is compressed slowly as shown in the figure above. Which of the following graphs

correctly shows the relation between the gas pressurePand the length of the gas column h?

9. Which of the following graphs correctly shows the variation of volume Vwith absolute temperature Tof afixed mass of gas at constant pressure?

10(91)

The above apparatus is used to study the relation between the temperature and the pressure of a fixed mass

of gas at constant volume. Which of the following is NOT correct?

A. Stir the water before taking a reading.

B. Connect the Bourdon gauge to the flask with a long tube.

C. Prevent the thermometer from touching the bottom of the beaker.

D. Ensure the flask is air-tight.

11. The pressure of a fixed mass of gas at 25C is 2 105N m

-2. What would its pressure be if the gas were

reduced to half its original volume and its temperature were increased to 95C?

A. 1.23 105N m-2 B. 2.47 105N m-2

C. 4.94 105N m

-2 D. 15.2 10

5N m

-2

12. A constant volume gas thermometer is considered a much more accurate thermometer than a mercury-in-

glass thermometer. Which of the following explain(s) this?


32/44


(1) Gas thermometers are more sensitive.

(2) The expansion of gases is more regular.

(3) Gas thermometers can be used over a wider range of temperature.

A. (1) only B. (3) only C. (2) and (3) only D. (1), (2) and (3)

13. A fixed mass of gas has its temperature changed from 127C to 27C at constant pressure. The ratio of the

new volume to the old volume isA. 27:127 B. 127:27 C. 3:4 D. 4:3

14. The initial pressure of a fixed mass of gas at 25C is 2 105N m-2. What would its pressure be if the gas

were reduced to half its original volume and its temperature were increased to 95C?

A. 1.23 105N m-2 B. 3.24 10

5N m-2 C. 4.94 105N m-2 D. 15.2 10

5N m-2

15.

In the experiment shown in the diagram, the value of the air inside the syringe is 25 cm3when the pressure

is 1.0 105N m-2. What is the volume of the air when the pressure is 0.5 105N m-2?

(Assume that the mass of the air in the syringe remains constant.)

A. 30 cm3 B. 50 cm3 C. 70 cm3 D. 100 cm3

16. When observed through a microscope, smoke particles in a smoke cell are seen to be in continuous random

motion. This is mainly due to

A. convection.

B. air current.

C. the motion of atoms in the smoke particles.

D. the motion of air molecules.

17. If the pressure of a fixed mass of initial volume Vis doubled and its absolute temperature halved, its

volume becomes

A.1

4V B. V C. 2V D. 4V

18. Which of the following graphs correctly shows the relation between the pressure (P) and the volume (V) of

a fixed mass of gas under constant temperature?

19. A cylinder contains a gas at a pressure of 105Nm-2and temperature 20C. It is compressed to half of its

original volume and the temperature increases to 55C. What is the final pressure of the gas?

A. 0.56 105Nm-2 B. 0.73 105Nm-2 C. 1.79 105Nm-2 D. 2.24 105Nm-2


33/44


20. The following graph shows the result obtained when an experiment performed to study Boyles Law. What

do the axes of the graph represent ?

yaxis xaxis

A. Volume Temperature

B. Volume

1

Temperature

C. Pressure Volume

D. Pressure1

Volume

21. The volume of a fixed mass of gas is V. If the pressure of the gas is doubled and its absolute temperature is

reduced to half of the initial value, the volume of the gas becomes

A.1

4V B.

1

2V C. V D. 2V

22.

The above apparatus is used to study the relationship between the pressure and volume of a fixed mass of

gas at constant temperature. Which of the following can improve the accuracy of the experiment ?

(1) Pressing the piston quickly (2) Using a large syringe

(3) Using a short length of rubber tubing

A. (3) only B. (1) and (2) only C. (2) and (3) only D. (1), (2) and (3)

23. A cylinder contains a fixed mass of gas at a pressure of 105N m-2and a temperature of 27C. The cylinder

is compressed to half of its original volume and the pressure increases to

3 105N m-2. Find the final temperature of the gas.

A. 40.5 C B. 177 C C. 313.5C D. 450C

24. The curve Cin the graph shows theP-Vrelation of a fixed mass of ideal

gas at a certain temperature. PointXdenotes the initial state of the gas.

The state of the gas is now changed along the path shown fromXto Y,then from YtoZ, and finally fromZback toXalong the curve C. Which

of the following statements is/are correct?

(1) The temperature of the gas remains unchanged in the transition from

Xto Y.

(2) The temperature of the gas decreases in the transition from YtoZ.

(3) The temperature of the gas remains unchanged in the transition from

ZtoX.

A. (3) only B. (1) and (2) only

C. (2) and (3) only D. (1), (2) and (3)


34/44


25. The above apparatus is used to study the

relation between the pressure and the

temperature of a fixed mass of gas at

constant volume. Which of the following

can improve the accuracy of the

experiment?(1) using a larger flask

(2) using a shorter length of rubber

tubing to connect the gauge and the

flask

(3) setting up a control experiment with

the burner removed.

A. (3) only

B. (1) and (2) only

C. (2) and (3) only

D. (1), (2) and (3)

26. The above graph shows the V-Trelation of a fixed mass of idealgas. PointXdenotes the initial state of the gas. The gas changes

its state fromXto Y, then from YtoZand finally fromZback toX

along the path shown. Which of the following statements about

the pressure of the gas is/are correct?

(1) The pressure remains unchanged in the transition fromXto Y.

(2) The pressure increases in the transition from YtoZ.

(3) The pressure decreases in the transition fromZtoX.

A. (3) only B. (1) and (2) only

C. (2) and (3) only D. (1), (2) and (3)

Answers1 D 11 C 21 A

2 C 12 D 22 C

3 C 13 C 23 B

4 A 14 C 24 C

5 D 15 B 25 B

6 C 16 D 26 D

7 D 17 A

8 B 18 B

9 C 19 D

10 B 20 D


35/44


M.C. Exercise HEAT 4: Kinetic Theory of Gases

1. The above diagram shows a mechanical model of a gas. The weight of the disc and the power of the motor

can give a measure of two different properties of the gas. What

are these two properties?

Weight of the disc Power of the motor

A. Pressure VolumeB. Pressure Temperature

C. Volume Pressure

D. Volume Temperature

2. Energy is supplied to a fixed mass of gas which is kept at a

constant volume. Which of the following statements is INCORRECT?

A. The average speed of the gas molecules increases.

B. The average spacing between the gas molecules increases.

C. The gas molecules hit the container wall more frequently.

D. The temperature of the gas increases.

3. The above diagram shows a mechanical model of a gas. Which of thefollowing processes can be used to demonstrate the variation of the

pressure with the volume of a fixed mass of gas under constant

temperature?

A. Varying the weight of the disc

B. Varying the power of the motor

C. Varying the number of ball bearings in the cylinder

D. Adding a larger polystyrene ball into the cylinder

4. If the volume of a fixed mass of gas is reduced at constant

temperature, the pressure of the gas increases. Which of the following correctly account(s) for the increase

in pressure?

(1) The gas molecules hit the container wall more frequently.(2) The average spacing between the gas molecules increases.

(3) The average speed of the gas molecules increases.


5. Which of the following can increase the average kinetic energy of the molecules of a fixed mass of gas?

(1) Heating the gas at constant volume

(2) Increasing the volume of the gas at constant pressure

(3) Reducing the volume of the gas at constant temperature


6. Which of the following statements concerning the Brownian motion of smoke particles in air is/are correct?

(1) The Brownian motion is caused by collision between smoke particles.

(2) The air molecules are moving randomly in all directions.(3) The mass of air molecules is almost the same as that of smoke particles.

A (1) only B (2) only C (1) and (3) D (2) and (3) only

7. Some gas is sealed inside a container of fixed volume. If the gas is heated, which of the following

statements is/are true?

(1) The pressure of the gas increases.

(2) The kinetic energy of the gas molecules increases.

(3) The density of the gas increases.



36/44


8. When a gas is heated under constant volume, which of the following will increase?

(1) The average speed of the gas molecules.

(2) The average number of collisions per second of the gas molecules on the wall of the gas container.

(3) The average distance between the gas molecules.


Directions for Question 9 10, see page 19.

9. A gas exerts a pressure on the walls of

the vessel which contains it.

The molecules of a gas change their

momentum when they rebound from the

walls of the vessels.

10. The pressure of a fixed mass of gas in a

closed container will increase if it is

heated.

The momentum of gas molecules

increases with temperature.

11. When a constant mass of gas is compressed inside a vessel at constant temperature, the pressure of the gas

increases. This is because

(1) the average distance between the molecules decreases.(2) the frequency of the gas molecules hitting the walls of the container increases.

(3) the average speed of the gas molecules increases.


12. The pressure exerted by a gas in a container would increase if

(1) the average speed of the gas molecules were increased.

(2) the number of gas molecules were increased.

(3) the volume of the container were increased.


13. When a constant mass of gas is heated at constant volume inside a vessel, the pressure of the gas increases.

The main reason included that(1) the average speed of the gas molecules increases.

(2) the frequency of the gas molecules hitting the walls increases.

(3) the average spacing between the gas molecules increases.


14. A fixed mass of gas is heated at a constant pressure. Which of the following statements is/are correct?

(1) The average speed of the gas molecules increases.

(2) The average spacing between the gas molecules increases.

(3) The number of gas molecules increases.


15. Which of the following descriptions concerning the gas molecules is correct when a fixed mass of gas is

compressed and also heated at the same time ?Average spacing between

the gas molecules

Average speed of the

gas molecules

A. remains unchanged increases

B. remains unchanged remains unchanged

C. decreases decreases

D. decreases increases

16. Which of the following can increase the average kinetic energy of the molecules of a fixed mass of gas?

(1) increasing the volume of the gas at constant pressure

(2) increasing the pressure of the gas at constant volume

(3) increasing the pressure of the gas at constant temperature



37/44


17.

The above diagram shows a mechanical model of a gas. The ball bearings are set into motion by a motor-

driven vibrating platform. Which of the following statements is/are correct if the operating voltage of the

motor is increased?

(1) The disc rises to a higher level.

(2) The average speed of the ball bearings increases.

(3) The average spacing between the ball bearings increases.

A. (3) only B. (1) and (2) only C. (1) and (3) only D. (1), (2) and (3)

18.

Figure (a) shows a mechanical model of a gas and Figure (b) shows theP-Vrelation of a fixed mass of

ideal gas at a certain temperature. If the operating voltage of the motor in the model is increased, which of

the following denotes a corresponding transition in theP-Vgraph (pointXrepresents the initial state of the

gas)?

A. XA B. XB C. XC D. XD

Answers

1 B 11 B

2 B 12 C

3 A 13 C

4 A 14 C

5 C 15 D

6 B 16 C

7 C 17 D8 B 18 B

9 A

10 A


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Long Questions Heat 1: Heat and internal energy

1(92)

A student uses the experiment set-up shown in Figure 1 to find the specific heat capacity of a metal. The

cylindrical metal block is heated by an immersion heater of unknown power. The following results are

obtained:

Mass of metal block = 1 kg

Initial temperature of metal block = 29C

Final temperature of metal block = 41C

Energy supplied by the heater = 12300 J

(a) Describe, with the help of a diagram, a method to measure the energy supplied by the heater.

(b) Calculate the specific heat capacity of the metal.

(c) The value obtained in (b) is found to be higher than the actual specific heat capacity of the metal.

Suggest a reason for this and explain your answer briefly.

(d) Suggest TWO improvements on the set-up to increase the accuracy of the experiment.

(e) Is the above method suitable for finding the specific heat capacity of wood? Explain briefly.

2(91)

Figure 2 shows the apparatus of an experiment to study the absorption of solar energy by gases. Identical

flasksAandBare filled with carbon dioxide and air respectively. They are placed under sunlight and their

temperature are taken at 3-minute intervals. The results are as follows:

Time/minutes 0 3 6 9 12 15 18

Temperature

inA/C28.0 38.4 44.0 46.2 47.8 48.8 48.8

Temperature

inB/C

28.0 37.8 41.8 43.7 45.2 46.0 46.0

(a) Using a scale that 2 cm represents 5C and 2 cm represents 3 minutes, plot the temperature-time graphs

for carbon dioxide and air on the same graph paper.

(b) Why does each of the gases reach a steady temperature?

(c) The mass of carbon dioxide in flaskAis 0.00196 kg and the mass of air in flask Bis 0.00125 kg. The

specific heat capacities of carbon dioxide and air are 640 J kg-1

C-1

and 740 J kg-1

C-1

respectively.

Which flask of gas gains more energy to reach its steady temperature? Show your calculations.

(d) Each year the amount of carbon dioxide in the atmosphere is increased by billions of tons.

(i) Suggest a possible effect on the mean temperature of the earth.

(ii) Suggest two methods to reduce the amount of carbon dioxide in the atmosphere.


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3(86)

Figure 3 shows the apparatus which may be used to measure the specific heat capacity of water.

(a) Draw a simple diagram to show how the apparatus can be set up for the experiment.

(b) The following are readings taken in the experiments:

The rating of the heater = 12 V 40 W

Mass of water used = 200 gInitial temperature of the water = 25.1C

Final temperature of the water = 53.2C

Time taken to heat up the water = 10 minutes

(i) Given that the water is well-stirred throughout the experiment, calculate the specific heat capacity

of water as measured from the experiment.

(ii) Given two reasons why a polystyrene cup should be used in the experiment.

(iii) Why should the water be stirred throughout the experiment?

(c) Describe, with the aid of a diagram, a method to check whether the power output of the heater is

40 W. Show how the actual power output of the heater can be calculated.

4(00)

An electric heater has two settings: low and high. The power output of the heater is 1400 W at the

low setting and 2200 W at the jigh setting. The heater is used to cook an egg. The egg is first put into a

pot containing 1 kg of water and the heater is operated at the high setting. (See Figure 4.) The

temperature of the water is recorded every 30 s and the following are obtained:Time t/ s 0 30 60 90 120 150 180 210 240

Temperature /C 27 32 44 57 69 81 92 98 100

(a) Use a scale of 1 cm to 5C and 1 cm to 15 s, plot a graph of against t on graph paper.

(b) (i) Find the energy supplied by the heater from t= 0 to t= 240 s.

(ii) Find the energy absorbed by the water from t= 0 to t= 240 s

(Note: Specific heat capacity of water = 4200 J kg-1K-1.)

(iii) State tworeasons to account for the difference between your answers in (i) and (ii).

(c) After the water boils, the heater is turned to the low setting and the water still boils afterwards. A

student argues that this will lengthen the time required to cook the egg. Do you agree? Explain your

answer.

(d) If less water is used in the above cooking process, on the graph in (a), draw the graph of against tyou

expect to obtain.


40/44


Long Questions Heat 2: Change of states

1(97).

A student uses the apparatus shown in Figure 1 to perform an experiment to measure the specific latent heat

of fusion of ice. He uses a joulemeter to measure the energy required to melt a certain amount of ice.

(a) Draw a diagram to show how the apparatus can be set up for the experiment.

(b) The following data are obtained in the experiment:

Initial joulemeter reading = 28 000 J

Final joulemeter reading = 40 000 J

Mass of water collected in the beaker = 0.045 kgCalculate the specific latent heat of fusion of ice.

(c) Why should the ice used in the experiment be crushed?

(d) A teacher comments that the result of this experiment is not accurate. She points out that a control

experiment is required in order to improve the accuracy of the experiment.

(i) Describe how the control experiment can be set up and explain its function.

(ii) After setting up the control experiment, the student repeats the above experiment. Would you

expect the specific latent heat of fusion obtained to be higher or lower than that obtained in (b)?

Explain your answer.

2(93)

A student performs an experiment to find the specific latent heat of vaporization of water. A beaker

containing water is placed on an electronic balance. The water is heated by a 100 W immersion heater,

which is immersed in the water such that it does not touch the beaker, as shown in Figure 2.

(a) It is found that there is a slight decrease in the mass of water in the beaker before the water boils.Explain briefly in terms of molecular motion.

(b) When the water boils, the reading of the balance is taken. After 240 s, the reading of the balance is

taken again. The following results are obtained:

Initial reading of the balance = 525.4 g

Final reading of the balance = 515.2 g

Calculate (i) the energy supplied by the heater in 240 s,

(ii) the specific latent heat of vaporization of water.

(c) The value obtained in (b) (ii) is found to be higher than the actual specific latent heat of vaporization of

water. Suggest a reason for this and explain briefly.

(d) If the student covers the beaker with a lid, how would the result of the experiment be affected?

Explain briefly.

(e) Suggest TWO improvements on the set-up to increase the accuracy of the experiment.


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3(90)

Figure 3 shows the cooling curve of a substance changing from liquid to solid state.

(a) Given a boiling tube half filled with this substance in its solid state, describe, with the help of a

diagram, an experiment to obtain the cooling curve of the substance.(b) Read from the above cooling curve the melting point of the substance.

(c) Explain why the temperature remains constant as the substance solidifies at its melting point, even

though heat is lost to the surroundings.

(d) If the mass of substance used is 0.05 kg and the rate of heat loss to the surroundings at its melting point

is 25 W, find the specific latent heat of fusion of the substance.

(e) Describe the arrangement and motion of the molecules of the substance in the

(i) solid state, and (ii) liquid state.

4(85) Figure 4 shows an experimental set-up to determine the specific latent heat of fusion of ice. The ice

used is crushed and melting. In the left hand side,A, the electrical energy consumed by the heater is

measured by a joulemeter. The water from the melted ice was collected in a beaker. In the right hand side,

B, shows a control experiment ofAset up without electricity supply to the heater.

(a) What is the purpose of the control experiment inB?

(b) Why should the ice used in the experiment be

(i) crushed, and (ii) melting?

(c) Calculate the specific latent heat of fusion of ice from the following experiment data:

Initial joulemeter reading = 39 428 J.

Final joulemeter reading = 50 328 J

Mass of water collected inA = 0.04 kg

Mass of water collected inB = 0.01 kg

(d) Would you expect the latent heat of fusion of ice obtained to be higher than, equal to or lower than the

result you obtain in (c), if the experiment were repeated.

(i) neglecting the control experiment? (ii) using ice at -5C?Explain briefly in each case.


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Long Questions HEAT 3: Gas Laws and kinetic theory of gases

1(94)

A student uses the set-up shown in Figure 1 to study the relationship between the pressure and volume of a

fixed mass of gas at constant temperature. The piston is pushed in or pulled out to vary the volume of gas

and the corresponding pressure is measured by the Bourdon gauge.

(a) The following results are obtained in the experiment:

PressureP/kPa 80 100 120 140 160

Volume V/m3 2.60 10-4 2.10 10

-4 1.75 10-4 1.50 10

-4 1.31 10-4

Plot a graph ofPagainst1

V

on graph paper, withPranging from 0 to 160 kPa and1

V

ranging from 0

to 8000 m-3

. What physical law is the student attempting to verify?

(b) Should the rubber tubing be long or short? Explain briefly.

State TWO other precautions that should be taken to improve the accuracy of the experiment.

(c) Explain, in terms of the kinetic theory of gases, the increase in the pressure of the gas when the volume

decreases at a constant temperature.

(d)

The student uses another set of apparatus as shown in Figure 2 to measure the volume of a container.

Initially the readings of the syringe and the gauge are 1.8 10-4m3and 100 kPa respectively. The

piston is then completely pushed in and the reading of the gauge becomes 210 kPa. Assuming that

temperature remains unchanged, calculate the volume of the container.


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2(89)

Figure 2 shows an experiment done by a student to find the variation of pressure of air inside a flask withtemperature. The pressure Yand the temperature tare measured by Bourdon gauge and a thermometer

respectively.

(a) The following data are recorded in the experiment:

t/C 20 35 45 60 78 90 100

Y/ kN m-2 107 112.5 116 121.5 128 132.5 136

Using a scale that 4 cm represents 10 kN m-2

and 2 cm represents 10C, plot a graph of Yagainst t

ranging from 0C to 100C.

(b) Find the equation relating the pressure and temperature from the graph in (a).

(c) The flask is then transferred into a trough of oil and the gauge reading is 118 kN m-2

. What is the

temperature of the oil?

(d) Give THREEsuggestions to improve the experimental setup as shown in Figure 2.

(e) Based on the kinetic theory of gases, explain briefly why the pressure increases as the temperaturedoes.

3(88) Figure 3 shows a mechanical model of a gas. A large number

of bearings are set in motion by a vibrating platform. The ball

bearings represents gas molecules.

(a) Which property of the gas (pressure, volume or temperature)

would

(i) the weight of the disc

(ii) the voltage of the d.c. supply.

Represent in this model?

(b) For a fixed amount of gas, when temperature is kept constant,

its pressure increases as the volume decreases. Describe how

this behaviour of gas can be demonstrated using the model.Describe the change in the average speed of the ball bearings

and the frequency of bombardment on the walls in this

demonstration.

(c) In a real situation, gas molecules could keep on moving by

themselves without an external energy supply but in this model

energy has to be supplied to the ball bearings continuously by the vibrating platform. Briefly describe

and explain this difference.

(d) A large polystyrene ball is now placed into the cylinder. Briefly describe and explain the motion of the

polystyrene ball.


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4(87) A mercury thread is trapped in a uniform bored capillary tube which is used in an experiment to verify

Charles law (see Figure 4). The following data are recorded:

Temperature /C 20 30 40 50 60 70 80

Length of air columnL/mm 136 140 146 152 156 160 166

(a) Draw a diagram to show an experimental set-up and describe briefly the

procedure to obtain the above data.(b) Name any TWOprecautions in this experiment.

(c) Plot a graph ofLagainst with ranging from -300C to 100C.

(d) What is the absolute zero as obtained from this experiment?

(e) What is the relationship amongL, and the absolute zero in (d)?

(f) How does the pressure of the trapped air in the tube change with temperature?

5(99)

David uses the set-up shown in Figure 5 to study the relationship between the pressurepand temperature

of a fixed mass of gas inside a flaskA.

The following results are obtained:

Temperature / C 20 36 50 64 80 98

PressureP/ kPa 102 109 111 115 124 129

(a) Using a scale of 1 cm to 10 kPa and 1 cm to 10C, plot a graph ofPagainst on the graph paper, with

P ranging from 0 to 200 kPa and ranging from 0 to 100C.

(b) From the graph in (a), David concludes that

The pressure (in kPa) of the gas is directly proportional to its temperature (in C).

Comment on Davids conclusion.

(c) State two precautions that should be taken to improve the accuracy of the experiment.(d) Based on the kinetic theory, explain why the pressure of gas increases with temperature at a constant

volume.

(e) David uses a larger flaskBto replace flaskAand repeats the experiment. The volume of the flaskBis

twice that ofA. Assume that the masses of the gas in both flasks are the same.

(i) Estimate the gas pressure in flaskB at 0C.

(ii) On the same graph in (a), draw the graph ofPagainst you expect to obtain in this experiment.

Lecture Notes on CE Heat

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