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Questions

Q1.

A weather balloon takes scientific equipment high into the atmosphere to monitor atmospheric
conditions.

A weather balloon is filled with hydrogen at a temperature of 22.5 °C and a pressure of 1.02 ×
105 Pa. The volume of the balloon is 7.50 m3.

The balloon rises through the atmosphere to a maximum height. At the maximum height, the
temperature of the hydrogen in the balloon is –48.0 °C and the pressure of the hydrogen in the
balloon is 8.40 × 104 Pa.

(a) Calculate the volume of the balloon at the maximum height.

(3)

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Volume of balloon = ...........................................................

(b) Calculate the decrease in the mean kinetic energy of a hydrogen molecule in the balloon as
the balloon rises to the maximum height.

(2)

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Decrease in mean kinetic energy = ...........................................................

(Total for question = 5 marks)

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Q2.

The 'escape velocity' is the minimum speed needed for an object to escape from the
gravitational field of a planet.

An object travelling at the escape velocity has a kinetic energy equal to the magnitude of its
gravitational potential energy at the surface of the planet.

(a) Show that the escape velocity v for a planet of mass M and radius r is given by the
expression

(2)

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(b) (i) Show that the escape velocity for a mass at the Earth's surface is about 1.1 × 104 m s–1.

mass of Earth = 5.98 × 1024 kg

radius of Earth = 6.36 × 106 m

(2)

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(ii) When the Earth formed, a large proportion of the gas in the Earth's atmosphere was
hydrogen.

Explain why hydrogen gas is no longer a large proportion of the gas in the
Earth's atmosphere. No further calculation is necessary.

at 20 °C,
= 1900 m s–1 for hydrogen

(2)
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(Total for question = 6 marks)

Q3.

Lead shot consists of small lead spheres.

Originally lead shot was made by dripping molten lead through a copper sieve from the top of a
'shot tower'. The lead cooled as it fell, before landing in water and producing solid lead spheres.
Figure 1 shows a shot tower, and figure 2 shows the process of making lead shot in a shot tower.

To avoid producing steam, the temperature of a lead sphere was below 100 °C as it reached the
cold water.

(a) (i) A lead sphere falls through a distance of 41.5 m.

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Show that it takes about 3 s for the lead sphere to fall through this distance.
Assume that resistive forces are negligible.

(2)

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(ii) The lead sphere has a radius of 1.2 mm. As it falls it cools from 615 K to 370 K.

The molten lead solidifies at 601 K.

Calculate the mean rate at which energy is transferred from the lead sphere to the surroundings.
You should assume that the specific heat capacities of liquid lead and solid lead are the same.

density of lead = 1.13 × 104 kg m–3

specific latent heat of lead = 2.47 × 104 J kg–1
specific heat capacity of lead = 130 J kg–1 K–1

(6)

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Mean rate of energy transfer from lead = ...........................................................

(b) A teacher demonstrates a mechanical method to determine the specific heat capacity of
lead. Some lead shot at room temperature is placed in a Perspex tube.
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The teacher turns the tube upside down, and the lead shot falls through a distance d.

The teacher repeats this N times and measures the final temperature of the lead shot.
The change in temperature Δθ of the lead shot is calculated.

The teacher uses the values of d, N and Δθ to determine a value for the specific heat capacity c
of the lead.

(i) Explain why the mass of lead shot in the tube should not affect the value of Δθ.

(2)

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(ii) Assess whether this method would produce an accurate value for c.

(2)

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(Total for question = 12 marks)

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Q4.

The spectrum of light emitted by the star Chi Lupi provides evidence of mercury atoms in the
outer layers of the star. The light emitted from the star is compared with light emitted from a
mercury lamp on Earth.

(a) The lamp contains 1.65 × 1019 mercury atoms in a volume of 1.50 × 10–5 m3. The pressure
of the mercury vapour is 4.25 × 104 Pa.

Calculate the mean kinetic energy of the mercury atoms.

(3)

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Mean kinetic energy of mercury atoms = ...........................................................

(b) One line in the spectrum of light from Chi Lupi has a wavelength of 576.933 nm.

The equivalent line in a mercury spectrum produced on Earth is 576.959 nm.

A student concluded from this data that Chi Lupi is moving towards the Earth, and that the
relative velocity of Chi Lupi is about 1400 m s–1.

Deduce whether the student's conclusions are correct.

(4)

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(c) The surface temperature of Chi Lupi is twice the surface temperature of the Sun.

The radius of Chi Lupi is three times the radius of the Sun.

State where Chi Lupi would be located on the Hertzsprung-Russell diagram.

(1)

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(Total for question = 8 marks)

Q5.

Xenon gas is used as an anaesthetic. The gas is stored in cylinders, under pressure.
A cylinder with a volume of 6.0 × 10−2 m3 contains 7.5 × 1024 atoms of xenon.

(a) The gas in the cylinder is at a temperature of 20 °C.

Calculate the pressure exerted by the gas.

(3)

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Pressure exerted by gas = ...........................................................

(b) Gas is removed from the cylinder. The temperature of the gas decreases by 5.0 °C and the
new pressure of the gas
is 4.50 × 105 Pa.

Calculate the percentage of the original number of gas molecules remaining in the cylinder.

(2)

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Percentage = ...........................................................

(Total for question = 5 marks)

Q6.

A cylinder contains oxygen gas at a temperature of 25 °C and a pressure of 1.4 × 107 Pa.

Calculate the density of the oxygen gas in the cylinder.

mass of an oxygen molecule = 5.3 × 10–26 kg

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Density of oxygen gas = ...........................................................

(Total for question = 5 marks)

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Q7.

The water in a swimming pool at the Olympic Games should be at a temperature of 28.0 °C.

(a) A pool contains 2750 m3 of water at 16.5 °C.

Calculate the increase in internal energy ΔE of the water when it is heated to 28.0 °C.

density of water = 998 kg m–3

specific heat capacity of water = 4190 J kg–1 K–1

(3)

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ΔE = ...........................................................

(b) A heater is used to increase the temperature of the water.

State why the amount of energy supplied by the heater will be different from the value of ΔE
calculated in (a).

(1)

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(Total for question = 4 marks)

Q8.

A 'scuba tank' is used to store air at high pressure. A diver breathes underwater using air from
the scuba tank.

(a) A scuba tank contains air at a pressure of 1.28 × 107 Pa and a temperature of 17.5 °C.
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The scuba tank is left outside on a sunny day and the temperature of the air inside the scuba
tank increases to 42.5 °C. The volume of the scuba tank remains constant.

Calculate the increase in the pressure exerted by the air inside the scuba tank.

(4)

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Increase in pressure = ...........................................................

*(b) Explain why the pressure of the air inside the scuba tank increases as the temperature
increases. Your answer should refer to the motion of the air molecules.

(6)

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(Total for question = 10 marks)

Q9.

Natural gas produced from landfill consists of a mixture of methane and carbon dioxide gases.

(a) At a temperature of 20.0 °C and a pressure of 1.01 × 105 Pa the volume occupied
by 1 mole of carbon dioxide is 0.0241 m3.

Show that the number of molecules in 1 mole of carbon dioxide is about 6.0 × 1023

(3)

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(b) In a sample of natural gas, the r.m.s. velocity of the carbon dioxide molecules is 60.5 % of
the r.m.s. velocity of the methane molecules.

(3)

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(Total for question = 6 marks)

Q10.

In the book Charlie and the Chocolate Factory, a palace is made entirely from chocolate.
Soon after it was made the palace melted, due to energy transfer from the Sun.

The total volume of chocolate used for the palace was 1250 m3. The initial temperature of the
chocolate palace was
28.5 °C. Chocolate melts at a temperature of 36.0 °C.

The book states that the palace melted completely in less than a day.

Deduce whether this statement could be correct.

rate of energy transfer to the palace = 7.5 × 105 W

density of chocolate = 1325 kg m−3
specific latent heat of chocolate = 4.5 × 104 J kg−1
specific heat capacity of chocolate is 1.30 × 103 J kg−1 K−1

(6)

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(Total for question = 6 marks)

Q11.

According to the Football Association (FA) rules, the football used in a professional match should
have a circumference of between 68.0 cm and 70.0 cm. The pressure of the air in the football
must be between 60 kPa and 110 kPa above atmospheric pressure.

(a) A football was inflated with air at a temperature of 16.0 °C. When inflated, the circumference
of the football was 68.5 cm and it contained 2.50 × 1023 molecules of air.

Deduce whether this football met the FA rules.

atmospheric pressure = 105 kPa

(6)

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*(b) The pressure inside a football decreases as the temperature of the air inside falls. The
volume of the ball remains constant.

Explain why, in terms of the motion of the molecules.

(6)

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(Total for question = 12 marks)

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Q12.

Answer the question with a cross in the box you think is correct . If you change your
mind about an answer, put a line through the box and then mark your new answer
with a cross .

The pressure law states that, if certain conditions are met, the pressure exerted by an ideal gas
is proportional to the temperature of the gas.

Which of the following conditions is not correct?

A The absolute temperature must be used.

B The molecules in the gas must be identical.

C The number of molecules in the gas must stay constant.

D The volume of the gas must stay constant.

(Total for question = 1 mark)

Q13.

Cocoa powder, milk and hot water are mixed together to produce a 'hot chocolate' drink. The
mass of the drink is 275 g, and its initial temperature is 71.5 °C.

Ice at 0.0 °C is added to the drink to reduce its temperature. Research indicates that the
maximum serving temperature of any hot drink should be 58.0 °C.

Deduce whether 4.0 g of ice would be enough to bring the temperature below 58.0 °C.

specific latent heat of ice = 3.34 × 105 J kg–1

specific heat capacity of 'hot chocolate' = 3750 J kg–1 °C–1
specific heat capacity of water = 4190 J kg–1 °C–1

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(Total for question = 5 marks)

Q14.

* Wax is heated until the temperature is above the melting point of the wax. The hot wax is
poured into a bowl and allowed to cool.

The graph shows how the temperature of the wax varies with time as it cools.

Describe how the internal energy of the wax changes as the wax cools.

You should refer to the energy of the wax molecules as the liquid wax cools and becomes solid,
and the solid wax cools.

Times X and Y have been included to help you refer to the graph.

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(Total for question = 6 marks)

Q15.

A student learns that the energy required to heat water for a bath can be 10 times the energy
required to heat water for a shower.

The student uses a shower for 9 minutes. The water comes out of the shower at 38 °C at a flow
rate of 1.8 × 10–5 m3 s–1.

The student usually fills the bath with 160 kg of water at 32 °C.

Deduce whether the bath uses 10 times more energy than using the shower.

initial temperature of water = 15 °C

density of water = 1.00 × 103 kg m–3
specific heat capacity of water = 4.18 × 103 J kg–1 K–1

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(Total for question = 5 marks)

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Q16.

The school apparatus shown is used to demonstrate a gas law.

Air is trapped in a glass tube of uniform cross-sectional area. A pump forces oil into the base of
the glass tube. This forces the air into a smaller volume. The pressure of the trapped air is
displayed on the pressure gauge.

(a) The pressure of the trapped air increases when the air is forced into a smaller volume.

Explain why, using ideas of molecular motion.

(4)

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(b) The apparatus is used in a laboratory where the temperature is 293 K.

When the air occupies a volume of 2.43 × 10−3 m3 the reading on the pressure gauge is 1.05 ×
105 Pa.

Calculate the number of molecules of air trapped in the glass tube.

(2)

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Number of molecules of air = ...........................................................

(Total for question = 6 marks)

Q17.

Answer the question with a cross in the box you think is correct . If you change your
mind about an answer, put a line through the box and then mark your new answer
with a cross .

Helium gas in a closed cylinder is heated until the pressure exerted by the helium is four times
the original pressure. The volume occupied by the helium stays constant.

The mean square speed of the helium molecules before heating is . The mean square speed
of the helium molecules after heating is .

What is the ratio

A 1

B 2

C 4

D 8
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(Total for question = 1 mark)

Q18.

Ice cubes can be made in an ice cube tray. One type of ice cube tray is shown.

Each compartment in the ice cube tray has dimensions 2.5 cm by 2.5 cm by 3.5 cm, as shown.

(a) Show that the mass of water needed to fill one compartment is about 0.02kg.

density of water = 1.00 × 103 kg m−3

(3)

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(b) All 6 compartments in the ice cube tray are filled with water to a depth of 3.5 cm.

The ice cube tray is placed in a freezer.

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The initial temperature of the water is 22.5°C.

It takes 12 minutes for all the water to become ice at 0°C.

The manufacturer of the freezer states that the freezer can transfer energy at a rate of 110 W.

Evaluate whether energy is transferred from the water in the tray at a rate of 110 W.

specific heat capacity of water = 4180 J kg−1 K−1

specific latent heat of fusion of water = 3.34 × 105 J kg−1

(4)

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(Total for question = 7 marks)

Q19.

Answer the question with a cross in the box you think is correct . If you change your
mind about an answer, put a line through the box and then mark your new answer
with a cross .

Boyle's law states that, under certain conditions, the pressure exerted by a gas is inversely
proportional to the volume occupied by the gas.

Which of the following conditions is not necessary?

A The gas must be ideal.

B The mean kinetic energy of the molecules must stay constant.

C The molecules in the gas must be identical.

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D The number of molecules in the gas must stay constant.

(Total for question = 1 mark)

Q20.

Select one answer from A to D and put a cross in the box . If you change your mind
about an answer, put a line through the box and then mark your new answer with
a cross .

In an experiment to determine the specific latent heat of vaporisation of water LV, a student used
an electrical heater to boil water in a beaker.
–1
The experimental data gave LV = 2.20 MJ kg–1. The textbook value of LV is 2.26 MJ kg .

Which of the following could be an explanation for this difference in the values of LV?

A Some energy is transferred to the surroundings.

B The heater power was underestimated.

C The student did not stir the water.

D The heater is inefficient.

(Total for question = 1 mark)

Q21.

Answer the question with a cross in the box you think is correct . If you change your
mind about an answer, put a line through the box and then mark your new answer
with a cross .

A fixed mass of a gas occupies a constant volume. The temperature of the gas is increased.

Which of the following is not true?

A The internal energy of the gas increases.

B The mean kinetic energy of the molecules increases.

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C The mean momentum of the molecules increases.

D The pressure exerted by the gas increases.

(Total for question = 1 mark)

Q22.

Select one answer from A to D and put a cross in the box . If you change your mind
about an answer, put a line through the box and then mark your new answer with
a cross .

A fixed mass of an ideal gas has a volume V and exerts a pressure p. The absolute temperature
of the gas is T. When the gas is heated, the new pressure is 4p.

Which row of the table gives correct values of the new volume and the new temperature?

(Total for question = 1 mark)

Q23.

Answer the question with a cross in the box you think is correct . If you change your
mind about an answer, put a line through the box and then mark your new answer
with a cross .

Two gas cylinders have the same volume. One cylinder contains nitrogen gas. The other cylinder
contains oxygen gas.
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Both gases are at the same temperature and pressure.

Which of the following statements is not correct?

A Each cylinder contains the same number of molecules.

B The average molecular kinetic energy is the same for each gas.

C The density of gas is the same in each cylinder.

D The internal energy is the same for each gas.

(Total for question = 1 mark)

Q24.

A mixture of oxygen gas and nitrogen gas is kept at room temperature. Oxygen molecules are
more massive than nitrogen molecules.

Which of the following is correct?

A The mean velocity of the oxygen molecules is greater than the mean velocity of the
nitrogen molecules.

B The mean speed of the oxygen molecules is the same as the mean speed of the nitrogen
molecules.

C The mean kinetic energy of the oxygen molecules is greater than the mean kinetic
energy of the nitrogen molecules.

D The mean kinetic energy of the oxygen molecules is the same as the mean kinetic
energy of the nitrogen molecules.

(Total for question = 1 mark)

Q25.

An airbag is a safety feature used in cars.

Nitrogen gas is released into an airbag. The airbag inflates to a volume of 7.08 × 10−2 m3. The
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pressure of gas in the inflated airbag is 1.24 × 105 Pa.

(a) Show that the number of molecules of nitrogen gas released into the airbag is about 2 ×
1024.

temperature of gas in airbag = 25°C

(3)

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(b) Nitrogen gas escapes from small holes in the inflated airbag. The pressure decreases to 3.45
× 104 Pa.

Calculate the number of nitrogen molecules that escape from the airbag.

The volume and temperature remain constant.

(2)

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Number of nitrogen molecules that escape = ...........................................................

(Total for question = 5 marks)

Q26.

Answer the question with a cross in the box you think is correct . If you change
your mind about an answer, put a line through the box and then mark your new
answer with a cross .

A closed container holds a mixture of two gases at a constant temperature. Each molecule of gas
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X has a mass four times that of each molecule of gas Y.

What is the ratio

?

(Total for question = 1 mark)

Q27.

A portable electric heater with a power of 280 W is used to boil water for a hot drink.
The heater is placed into a cup of water.

There is 165 g of water in the cup. The initial temperature of the water is 12.5 °C.
Assume that all the energy from the heater is transferred to the water.

(a) The heater is used in London, where the boiling point of water is 100.0 °C.

Show that the time taken for the water to reach a temperature of 100.0 °C is about 220 s.

specific heat capacity of water = 4190 J kg−1 K−1

(3)

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(b) The same heater is used in La Paz, the world's highest capital city, where the boiling point of
water is 87.7 °C.

The mass and initial temperature of the water are the same as in (a), and the heater is used for
the same time.
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Calculate the mass of water converted to water vapour as the water boils.

latent heat of vaporisation of water = 2.29 × 106 J kg−1

(3)

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Mass of water converted to water vapour = ...........................................................

(Total for question = 6 marks)

Q28.

Answer the question with a cross in the box you think is correct . If you change
your mind about an answer, put a line through the box and then mark your new
answer with a cross .

A negative temperature coefficient thermistor and a resistor are connected as shown.

The temperature of the thermistor decreases.

Select the row of the table that shows how the readings on the meters change.
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(Total for question = 1 mark)

Q29.

Microwave ovens use microwave radiation at a frequency of 2.45 GHz to cook food. The
absorption of microwave energy by water in the food causes a heating effect.

(a) The graph shows how the energy absorbed by a water molecule depends on the frequency
of the radiation.

A website suggests that water molecules absorb energy because the microwaves produced by
the oven cause the water molecules to resonate.

Comment on this suggestion.

(2)

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(b) The microwave radiation causes the water molecules to rotate.

(i) Explain how this cooks the food.

(3)

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(ii) Suggest why the transfer of energy from the microwaves may be less efficient for ice than
for liquid water.

(2)

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(c) 325 g of water at 25.0 °C is heated at full power in a microwave oven. After 225 s the
temperature of the water is 85.0 °C.

power of microwave oven = 650 W

specific heat capacity of water = 4190 J kg−1 K−1

(i) The manufacturer claims that the microwave oven has an efficiency of 90%.

Assess the validity of this claim.

(3)

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(ii) The 325 g of hot water at 85.0 °C is poured into a polystyrene beaker containing 62.5 g of
ice at 0.0 °C.

Calculate the final temperature of the mixture of water and melted ice.

latent heat of fusion of ice = 3.33 × 105 J kg−1

(4)

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Final temperature of mixture = ...........................................................

(Total for question = 14 marks)

Q30.

Answer the question with a cross in the box you think is correct . If you change
your mind about an answer, put a line through the box and then mark your new
answer with a cross .

A solid is heated and it melts at a constant temperature.

Which row of the table shows how the kinetic energy and the potential energy of the molecules
change as the solid melts?
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(Total for question = 1 mark)

Q31.

A mass of 250 g is hung from a spring as shown. The spring extends by 16.5 cm when the mass
is added to the spring.

The mass is then displaced a further 3.5 cm vertically downwards and released.
The mass oscillates with simple harmonic motion.

(a) State the conditions for a mass to undergo simple harmonic motion.

(2)

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(b) Calculate the maximum kinetic energy of the oscillating mass.

(5)

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Maximum kinetic energy = ...........................................................

(c) The graph shows how the displacement of the oscillating mass varies over two cycles.

Add to the graph to show how the kinetic energy of the mass varies over the same time interval.

(2)

(d) The mass is submerged in water as shown.

The mass is set into oscillation as before.

Explain how the water would affect the amplitude of oscillation of the mass.

(3)

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(Total for question = 12 marks)

Q32.

A kettle was used to heat 855 g of water to boiling point. The initial temperature of the water
was 21.5 °C and it took 115 s to heat the water to 100 °C.

The kettle is left switched on for 175 s after the water has reached 100 °C.

Calculate the mass of water that was boiled away.

specific heat capacity of water = 4190 J kg−1 K−1

specific latent heat of vaporisation of water = 2.26 × 106 J kg−1

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Mass of water that was boiled away = ...........................................................

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(Total for question = 4 marks)

Q33.

Answer the question with a cross in the box you think is correct . If you change your
mind about an answer, put a line through the box and then mark your new answer
with a cross .

A student measured the temperature of 0.015 kg of wax as it cooled and changed state from a
liquid to a solid.

Energy was transferred from the wax to the surroundings at a rate of 25 W.

The temperature of the wax varied with time t, as shown.

Which of the following expressions gives a value for the specific latent heat capacity of the wax?

(Total for question = 1 mark)

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Q34.

Answer the question with a cross in the box you think is correct . If you change your
mind about an answer, put a line through the box and then mark your new answer
with a cross .

A cylinder contains a mixture of gas X and gas Y. The mean kinetic energy of the molecules of
gas X is EX and the mean kinetic energy of the molecules of gas Y is EY.

The molecules of gas X have twice the mass of the molecules of gas Y.

Which of the following equations is correct?

(Total for question = 1 mark)

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