Kinetic Theory | CIE A Level Physics Structured Questions 2022

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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3d

3 marks

For the final step of the derivation of the kinetic theory of gases equation, state

(i)

the number of dimensions the molecules are moving in

[1]

(ii)

the volume of the cube in terms of its side length

[1]

(iii)

the equation for the density of the cube.

[1]

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1a

2 marks

A sealed container A has the shape of a rectangular prism and contains an ideal gas. The dimensions of the container are x, y and z as shown in Fig. 1.1.

15-2-1a-h-derivation-cube-hsq-cie-a-level

Fig. 1.1

The average force exerted by the gas on the bottom wall of the container is F
There are n moles of gas in the container
The temperature of the gas is T

Obtain an expression for the height of the container in terms of F, n and T.

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1b

3 marks

A second container B contains the same ideal gas.

The following information is known:

The pressure in B is a quarter of the pressure in A
The volume of B is five times the volume of A
Container B contains half the number of molecules as A
The temperature of container B is 800 K

Calculate the average translational kinetic energy of the molecules in the gas of container A.

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1c

2 marks

Calculate the value of the ratio of the r.m.s. speed of the particles in containers A and B.

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1a

2 marks

A cylinder contains 5.12 mol of an ideal gas at pressure 5.60 × 10⁵ Pa and volume 3.80 × 10^–2 m³.

Calculate the thermodynamic temperature of the gas.

temperature = ....................................................... K

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1b

4 marks

The average kinetic energy E_K of a molecule of the gas is given by the expression

$E_{K} = \frac{3}{2} k T$

where k is the Boltzmann constant and T is the thermodynamic temperature.

The gas is heated at constant pressure so that its temperature rises by 125 K.

(i)

Show that the new volume of the gas is 4.75 × 10^–2 m³ .

(ii)

Calculate the increase in internal energy of the gas. Explain your working.

increase in internal energy = .................................. J

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1c

4 marks

(i)

Use the information in (b)(i) to calculate the external work done during the expansion of the gas.

work done = ....................................................... J [2]

(ii)

Use the first law of thermodynamics to determine the total thermal energy transferred to the gas in (b). Explain your reasoning.

energy = ......................................... J [2]

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CIE A Level Physics

Topic Questions

15.2 Kinetic Theory