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

Kinetic theory of gases — practice question

The kinetic theory of gases rests on several simplifying assumptions. Gas molecules are treated as identical hard elastic spheres.
(a(i))[1]

State the assumption about ideal gas molecules that refers to the way they move.

(a(ii))[2]

State the assumption about ideal gas molecules that concerns their volume.

(b)[3]

A cube of volume $V$ contains $N$ molecules of an ideal gas. Each molecule has a velocity component $c_x$ normal to one side $S$ of the cube, as shown in Fig. 2.1. The pressure $p$ of the gas due to the component $c_x$ of velocity is given by the expression $pV = Nmc_x^2$, where $m$ is the mass of a molecule. Explain how the expression leads to the relation $pV = \frac{1}{3}Nm\langle c^2 \rangle$, where $\langle c^2 \rangle$ is the mean square speed of the molecules.

(c)[3]

An ideal gas has a root-mean-square (r.m.s.) speed of $520\,\text{m s}^{-1}$ at a temperature of $27\,^\circ\text{C}$. Calculate the r.m.s. speed of the molecules at a temperature of $100\,^\circ\text{C}$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Molecules move randomly or travel with constant velocity until a collision

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