Kinetic Theory of Gases | CIE International A Level Physics Exam Questions 2025

1a

5 marks

The kinetic theory of gasses is based upon a number of assumptions.

Place ticks (✓) next to the correct assumptions in Table 1.1.

Table 1.1

Possible statements of the kinetic theory of gases	Place a tick (✓) here
The time of a collision is equal to the time between collisions
The molecules are mostly stationary but move upon collision with another molecule
Molecules of gas behave as identical, hard, perfectly elastic spheres
The volume of molecules is significant compared to the volume of the container
The time of a collision is negligible compared to the time between collisions
There are no forces of attraction or repulsion between the molecules
The molecules are in continuous random motion
The molecules all have mass, so are attracted towards each other
The volume of the molecules is negligible compared to the volume of the container

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1b

1 mark

Draw a circle around the correct symbol for the mean square speed of molecules in an ideal gas.

\sqrt{c}

\sqrt{<c>}

\sqrt{<c^{2}>}

c

<c^{2}>

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1c

1 mark

State the units for the mean square speed of the molecules in an ideal gas.

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1d

3 marks

Calculate the average root mean square speed of the particles travelling at the following velocities:

350 m s⁻¹ −356 m s⁻¹ 346 m s⁻¹ −351 m s⁻¹ 339 m s⁻¹

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3a

2 marks

This question is about the derivation of the kinetic theory of gases equation.

The derivation is based on a particle inside a cube, as shown in Fig. 1.1.

15-2-3a-e-derivation-cube-esq-cie-a-level

Fig. 1.1

Identify the following by adding the indicated letter to the correct arrow on the diagram:

(i)

The length

l

of the side of the cube

[1]

(ii)

The speed

c

of the molecule.

[1]

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3b

3 marks

Step two of the derivation of the kinetic theory of gases is explained by the statements in Table 1.1.

Place ticks (✓) next to the phrases that correctly explain step two.

Table 1.1

Some phrases about the derivation of the kinetic theory of gases	Place a tick (✓) here
c is the specific heat capacity of the particles of the gas
c is not the speed of light
Time between particle collisions with the container walls = $\frac{2 \times l e n g t h o f c u b e}{s p e e d o f m o l e c u l e}$
Time between particle collisions = $\frac{d i s t a n c e}{s p e e d}$
Time to travel length of cube = $l e n g t h o f c u b e \times s p e e d o f m o l e c u l e$

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3c

3 marks

Step four of the derivation of the kinetic theory of gases equation is explained in the sentences below.

Identify the correct words from the box to complete the sentences. You can use each word once, more than once or not at all.

velocity mean speed number amount area force exerted molecule

Pressure is defined as the force per unit __________. This is the pressure exerted by one __________. The __________ of one wall is $l^{2}$ .
The gas contains a large __________ of molecules. Each molecule has a different __________ and they all contribute to the pressure.
The __________ squared speed of c² is written with left and right-angled brackets <c²>.

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