Physics 9702 · AS & A Level · Kinetic theory of gases

Kinetic theory of gases — practice question

(a)[2]

One assumption in the kinetic theory of gases is that gas molecules act like hard, elastic identical spheres. State two further assumptions of the kinetic theory of gases.

(b)

From the kinetic theory of gases, it follows that the pressure $p$ multiplied by the volume $V$ of an ideal gas is described by $pV = \frac{1}{3}Nm\langle c^2 \rangle$, where $m$ denotes the mass of one gas molecule.

(b(i)1)[1]

State the meaning of the symbol $N$.

(b(i)2)[1]

State the meaning of the symbol $\langle c^2 \rangle$.

(b(ii))[2]

Use the expression in (b)(ii) to deduce that the mean kinetic energy $\langle E_K \rangle$ of a gas molecule at temperature $T$ is given by $\langle E_K \rangle = \frac{3}{2}kT$, where $k$ is a constant.

(c(i))[2]

State what is meant by the internal energy of a substance.

(c(ii))[2]

Use the equation in (b)(ii) to explain that, for an ideal gas, the change in internal energy $\Delta U$ is given by $\Delta U \propto \Delta T$, where $\Delta T$ is the temperature change of the gas.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Molecules are in random (rapid) motion

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