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

Kinetic theory of gases — practice question

An ideal gas has volume $V$ and pressure $p$. For this gas, the product $pV$ is described by $pV = \frac{1}{3}Nm\langle c^2 \rangle$, where $m$ denotes the mass of one molecule of the gas.
(a(i))[1]

State the meaning of the symbol $N$.

(a(ii))[1]

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

(b(i).1)[3]

A gas cylinder of volume $2.1 \times 10^4\,\text{cm}^3$ contains helium-4 gas at pressure $6.1 \times 10^5\,\text{Pa}$ and temperature $12^\circ\text{C}$. Helium-4 may be assumed to be an ideal gas. Determine, for the helium gas, the amount, in mol.

(b(i).2)[2]

Determine, for the helium gas, the number of atoms.

(b(ii))[3]

Calculate the root-mean-square (r.m.s.) speed for the helium atoms.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: count of molecules

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