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HEAT CAPACITY EXERCISES

1 The diagrams show equal masses of two liquids in identical beakers.

More heat is needed to raise the temperature of water than to raise the temperature
of paraffin (kerosene) by the same amount.
Why is this?
A the water has a greater density
B the water has a greater heat capacity
C the water has a lower boiling point
D the water has a smaller volume
2 The energy needed to melt 1 kg of a solid at its melting point defines its
A heat capacity
B specific heat capacity
C specific latent heat of fusion
D specific latent heat of vaporisation
3 Which statement is not true about a body when heated?
A the average speed of the molecules will increase.
B the temperature of the body will increase.
C the internal energy of the body will increase.
D the density of the body will increase.
4 A cup of coffee at 80 °C s left to cool to 30 °C. The heat capacity of the cup and
coffee is 2 kJ/°C.
How much heat is released during the cooling?
A 25 kJ
B 60 kJ
C 100 kJ
D 160 kJ
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5 When an object is heated its temperature changes.

Which ratio represents the change in temperature?
energy
A
mass × specific heat capacity

energy
B
mass × specific latent heat

mass × specific heat capacity

C
energy

mass × specific latent heat

D
energy

6 Which term describes the amount of heat energy needed to change 2 kg of water at
100 °C into steam at 100 °C?
A heat capacity
B latent heat
C specific heat capacity
D specific latent heat
7 What term describes the amount of heat energy needed to change the state of 1 kg
of a substance at a constant temperature?
A heat capacity
B latent heat
C specific heat capacity
D specific latent heat
8 A heater is used to supply 2000 J of energy to a liquid of mass 0.10 kg. The
temperature of the liquid rises by 5 °C.
What is the specific heat capacity of the liquid?
A 40 J / (kg°C)
B 200 J / (kg°C)
C 4000 J / (kg°C)
D 1 000 000 J / (kg°C)
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9 An immersion heater rated at 10 000 J/min is used to heat 2 kg of a liquid.

The graph shows how the temperature of the liquid varies with time.

What is the specific heat capacity of the liquid?

A 3.3 × 10 J/kg°C

B 8.33 × 102 J/kg°C

C 3.00 × 104 J/kg°C

D 5.00 × 104 J/kg°C

10 The table shows the masses and temperature rises of metal blocks that were heated
for 2 minutes each by a 50 W heater?
Which metal block has the smallest heat capacity?

metal block mass / g temperature rise /°C

A 500 20
B 150 18
C 250 25
D 100 30

11 A solid of mass 2.0 kg requires 2000 J of heat energy for its temperature to rise from
20 °C to 25 °C.
What is the heat capacity of the solid?
A 10 000 J/°C B 800 J/°C C 400 J/°C D 200 J/°C
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12 A 50 W immersion heater is used to heat a liquid from 20 °C to 35 °C in 300

seconds.
A 1000 J/°C B 750 J/°C C 429 J/°C D 273 J/°C
13 What is the amount of heat energy needed to melt a solid called?
A latent heat of fusion
B latent heat of vaporisation
C specific of fusion
D specific latent heat of vaporisation
14 A metal block of mass 2 kg requires 7800 J of energy to raise its temperature from
20 °C to 50 °C.
What is the specific heat capacity of the metal?
A 78 J/(kg°C) B 130 J/(kg°C) C 195 J/(kg°C) D 520 J/(kg°C)
15 A 100 W heater is used to heat a copper block of mass 2 kg for 40 s.
The specific heat capacity of copper is 400 J / kg °C.
What is the maximum temperature rise of the block?
A 0.125 °C B 0.2 °C C 5 °C D 8 °C
16 A solid requires 2000 J of thermal energy for its temperature to change from 20 °C to
25 °C. The specific heat capacity of the solid is 200 J / kg °C.
What is the mass of the solid?
A 2 kg B 10 kg C 12.5 kg D 50 kg
17 The heat capacity of an object is defined as the heat needed to
A heat up the object to a temperature of 1 °C
B heat up 1 kg of the object
C raise the temperature of the object by 1 °C
D raise the temperature of 1 kg of the object by 1 °C
18 A block of ice at 0 °C absorbs latent heat and changes to water.
Which of the changes will not take place during the process?
A its density increases
B its temperature increases
C the average energy of the molecules increases
D the forces between the molecules decrease
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19 A metal block of mass 2.0 kg has a specific heat capacity of 800 J / kg °C.
The block gains 2400 J 0f thermal energy.
What is the temperature rise of the block?
A 0.17 °C B 0.67 °C C 1.5 °C D 6.0 °C
20 Ice is used to cool 0.25 kg of water. The specific heat capacity of water is
4200 J / kg °C.
How much thermal energy must the ice gain from the water to reduce the
temperature of the water by 15 °C?
A 70 J B 1050 J C 15 750 J D 252 000 J

21 (a) What is meant by specific heat capacity?

heat energy supplied to a material of mass 1kg to change its temp by 1C

…………………………………………………………………………………………….

………………………………………………………………………………………… [1]

(b) A metal block is heated and then quickly transferred into 0.3 kg of water at
25 °C. The final temperature is 30 °C.
(i) What is the temperature change of the water?
30 - 25

5C
temperature =………………………… [1]

(ii) Calculate the heat energy gained by the water.

The specific heat capacity of water is 4200 J / kg °C.

Q = mxCxTc
0.3x4200x5

6300
heat = ……………………………………. J [2]
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22 (a) A hot metal block is immersed in a beaker containing 0.50 kg of cold water. The
temperature of the water rises by 20 °C.

Calculate the amount of heat energy gained by the water.

The specific heat capacity of water is 4200 J / kg °C.

Q = MxCxTc
0.5x4200x20

42000
heat = ……………………………………. J [2]
(b) Is the energy lost by the metal block equal to the energy gained by the water?
……………………………………………………………………………………………...
yes
Explain your answer.
energy is conserved or no energy loss
……………………………………………………………………………………………
………………………..……………………………………………………………..… [2]

23 Fig.23.1 shows the cross section of a drying pan for highly concentrated salt solution.

Fig.23.1
(a) (i) State two atmospheric conditions that increase evaporation from the salt
solution.
high temperature
……………………………………………………………………………………
lower humidity higher wind speed
……………………………………………………………………………………
(ii) Explain in terms of molecular motion why one of the above conditions
increases the rate of evaporation.
at high temp,molecules gain more energy move faster ,then leave the surface of the
……………………………………………………………………………………
liquid
……………………………………………………………………………………
(i) Suggest why the drying pan are made wide.
increase surface area to increase rate of evaporation
……………………………………………………………………………………
………………………………………………………………………………… [5]
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(b) A student wants to estimate the amount of solar (heat) energy absorbed by the
water.
The student measures the temperature of water at sunrise as 25 °C, and at noon
as 35 °C.
Calculate the energy needed to raise the temperature for 2000 kg of water
between sunrise and noon. (The specific heat capacity of water is 4200 J/kg °C.)

Q=MxCxTc
2000x4200x10

84000 000J
energy = …………………………….. [2]
(c) State two reasons why the sun has to provide more energy than you have
calculated in (b) to warm the water.
cater evap and loss
1. …………………………………………………………………………………………
…………………………………………………………………………………………
2. …………………………………………………………………………………………
…………………………………………………………….……………………….. [2]
(d) A plastic bottle is completely filled with 200 cm3 of water at 0 °C. The bottle is
closed and placed into a freezer. The density of water is 1.0 g/cm3.
(i) Calculate the mass of the water.

D=M/V 1x200

200g
mass = …………………………….
(ii) Calculate the heat given out by the water as it turns to ice at 0 °C. (The
specific latent heat of fusion of ice is 340 J/g).

Q=mLf
200x340

68000J
heat given out = ……………………………
(iii) Explain why the plastic bottle may burst as the water freezes.
water expands
……………………………………………………………………………………
…………………………………………………………………………………. [4]
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24 Fig.24.1 shows apparatus used to determine the specific heat capacity of copper.

Fig.24.1
(a) Complete Table 24.1 by naming and giving the functions of the devices M1, M2,
M3 and R.
Table 24.1
device name function

M1
ammeter current reading
M2
voltmeter voltage reading
M3 thermometer temperature reading
R varry voltage n current
variable resistor
[4]
(b) The copper block has a mass of 1.4 kg. The block is heated for 300 s and its
temperature increases from 25 °C to 50 °C.
The specific heat capacity of copper is 390 J / (kg°C).
(i) Calculate
1. the temperature rise of the block,
50 - 25
25C
temperature rise = ……………………………
2. the heat energy that causes this temperature rise.
Q=MxCxTc
1.4x390x25

13650J
heat energy = ……………………………
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(ii) The total heat energy supplied by the heater in 300 s is 18 000 J.
Calculate
(i) the amount of heat energy lost,

18 000- 13650

4350J
heat loss= ………………………………
(ii) the rate at which heat energy is lost.

P = Q/t
4350/300

14.5J/s
rate of heat loss= ………………………………
(iii) Suggest one way of reducing the heat loss from the block.

……………………………………………………………………………….…
insulation [7]

25 A student has 1 kg of cold water at 20 °C, and some hot water at 40 °C. She wants
to make water bath at 35 °C. Specific heat capacity of water is 4200 J/ (kg°C).
(a) Calculate the mass of cold water she must add.

Qloss=Qgained
1x4200x15 = m x 4200 x5

3kg
mass = ……………………………… [2]
(b) State the assumption you make in your answer to (a).
no heat loss
…………………………………………………………………………………………. [1]
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26 Fig.26.1 shows a bath tub with hot and cold water taps. The cold tap delivers 10 kg

of water at 20 °C. The hot tap delivers 5 kg water at 80 °C.

Fig.26.1

(a) Define absolute zero temperature.

temperature in kelvin scale
………………………………………………………………………………………………

…………………………………………………………………………………………. [1]

(b) State the value of the absolute zero temperature in degrees Celsius
-273C
value = ………………………………… [1]

(c) Calculate the final temperature of the water in the bath tub.
Qloss = Qgained
80 - f = 2f- 40
5x(80 - f) = 10x(f - 20)
120 = 3f

40C
temperature = ………………………………… [3]

27 A freezer contains 2kg of ice at -2 °C is defrosted within 30 minutes using hot water

at temperature of 80°C. The final temperature of the defrosted ice is 10°C. The

specific latent heat of fusion of ice is 340 000 J/ kg and the specific heat capacity of

ice is 2000 J/ (kg°C). The specific heat capacity of water is 4200 J/ (kg°C).

Calculate:

(a) the amount of heat energy needed to melt all the ice;
heat ice from -2 to 0 melting
Q= MxCxTc Q = mlf 8000+ 680000
2x2000x2 2x340 000
8000J 680 000J energy = 688
………………………………
000J [2]
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(b) the amount of heat energy needed to warm the water from 0°C to10°C;
Q= MxCxTc
2x 4200x10

energy = ………………………………
84000J [1]

(c) the mass of hot water; Qloss = Qgained

mcTc = Qgained
mx 4200x 70= 688000+84000

2.63kg
mass = ……………………………… [2]

(d) the rate at which heat was supplied by the hot water. P = Q/t
772 000/(30x60)

428.89J
rate = ……………………………… [2]

28 Lemonade is cooled by adding lumps of ice to it. 140 g of ice at a temperature of 0°C
cools 0.90 kg of lemonade from 26°C to 12°C. The specific latent heat of fusion of
ice is 330 000 J/ kg. The specific heat capacity of water is 4200 J/ (kg°C).
(a) Calculate the amount of energy
(i) gained by the ice in melting,

0.140x 330 000

energy = ………………………………… [1]

(ii) gained by the melted ice,

0.140x4200x12
energy = ………………………………… [1]
(iii) lost by the lemonade.
Qlost = Qgained

energy = ………………………………… [1]

(b) Determine the specific heat capacity of lemonade.

Q=0.9x14xC

specific heat capacity = ………………………………… [2]

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(c) The actual amount of heat lost by the lemonade is smaller than that calculated in
(a) (iii). Explain why.
………………………………………………………………………………………………
energy from environment
………………………………………………………………………………………….. [1]

29 (a) (i) Define absolute zero.

……………………………………………………………………………………….
temp in kelvin

…………………………………………………………………..………………. [1]

(ii) State the value of absolute zero in degrees Celsius.

-273C
…………………………………………………………………..………………. [1]

(b) Fig.28.1 shows a 0.40 kg iron bolt being cooled by immersing it in 8.0 kg of

water at 25 °C. The specific heat capacity of iron is 450 J/(kg°C) and that of

water is 4200 J/(kg°C). The initial temperature of the iron bolt is 800 °C.

Fig.28.1

Determine the final temperature of the water.

Qloss=Qgain
0.4x450x(800-f)=8x4200x(f-25)

final temperature = …………………………………… [3]

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30 Fig.29.1 shows a 2 000 W electric kettle connected to the mains being used to boil
some water. The kettle is placed on an electronic balance and the balance reads
350.0 g.

Fig.29.1
(a) The specific latent heat of vaporisation of water is 336 J/ g.
Explain the meaning of this statement.

………………………………………………………………………………………………
336j of heat supplied to a mass of 1g to change from liquid to gas

………………………………………………………………………………………….. [1]

(b) After boiling the water for a while, the balance displays a reading of 330.0 g.
Determine
(i) the mass of the water vaporised,

350 - 330 = 20g

mass = ……………………………… [2]

(ii) the amount of heat energy used to vaporise the water,

Q=mlv
20 x 336=

heat energy = ……………………………… [2]

(iii) the time taken to vaporise the water.

P=Q/t

time = ……………………………… [2]

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31 Fig.30.1 shows an energy resource.

Fig.30.1
1000 kg of cold water at 20 °C is pumped down to the hot rock.
The water boils at 100 °C and 100 kg of water turns into steam.
(a) State the name of the energy resource in Fig.45.1.
geothermal
………………………………………………………………………………………….. [1]
(b) Calculate
(i) The energy needed to heat all the water from 20 °C to100 °C,
The specific heat capacity of water is 4200 J / (kg °C)

Q = MxCxTc
= 1000x4200x80

33600 0000J
energy = ………………………….. [2]
(ii) The energy needed to change 100 kg of water to steam.
The specific heat of vaporisation of water is 2.3 х 106 J / kg.

Q=mlv
100x2300000

230000000J
energy = ………………………….. [2]
(c) Suggest one environmental impact of the source of energy in Fig.45.1.
……………………………………………………………………………………………..
underground habitat disturbed or destroyed
…………………………………………………………………………………………. [1]

32 (a) Define the term specific neat capacity.

heat supplied to a material of mass 1kg to change its temp by 1C
……………………………………………………………………………………………

……………………………………………….………………………………………. [1]
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(b) An iron ball of mass 0.030 kg is transferred from boiling water at 100 °C to

0.120 kg of cold water at 24 °C. The final temperature of the water is 26 °C.

The specific heat capacity of water is 4200 J / (kg °C).

Assume that the thermal energy lost by the iron ball is equal to the thermal

energy gained by the water and that no evaporation occurs,

Calculate

(i) the temperature decrease of the iron ball,

100-26= 74C

temperature decrease = ……………………. [1]

(ii) thermal energy gained by the cold water,

Q = MxCxTc

0.120 x 4200 x 2

1008J
thermal energy = ………………………………… [2]

(iii) the specific heat capacity of the ball.

1008=0.030x74xC

454.05J
specific heat capacity = ……………………… [2]

(iv) Explain why the actual amount of thermal energy lost by the iron ball is

more than the actual amount of thermal energy gained by water.

……………………………………………………………………………………
some energy lost

………………………………………………………………………………... [1]

33 (a) Define the term neat capacity.

heat supplied to a material to change its temperature by 1C
……………………………………………………………………………………………

……………………………………………….………………………………………. [1]
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(b) An electric heater supplies 1.2 kW to heat some ice.

The ice, initially at 0 °C, melts and changes to water at 100 °C in a time of

30 minutes.

Calculate

(i) the amount of thermal energy supplied to the ice and water in30 minutes,

Q=Pxt
1200 x (30x60)

2160 000J
thermal energy = ……………………. [2]

(ii) the mass of the heated ice.

The specific heat of fusion of ice is 330 J / g.

The specific heat capacity of water is 4.2 J / g °C.

Qgained = Qloss

2160 000= m(330 + 4.2x100)

2880g
mass = ……………………. [2]

(c) Explain why the electrical energy input to the heater is not equal to the energy

supplied to the ice and water.

energy loss to surrounding
……………………………………………………………………………………………

………………………………………………………………………………………… [1]