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

Kinetic theory of gases — practice question

An ideal gas may be described by the equation of state $pVA = NBT$, in which $p$ denotes the gas pressure, $V$ its volume, $A$ the Avogadro constant, $B$ another constant, and $N$ the number of molecules in the gas.
(a(i))[1]

State what the symbol $T$ means in the equation.

(a(ii))[1]

Identify what the constant $B$ represents.

(b)

For an ideal gas, the product $pV$ is also written as $pV = \frac{1}{3} N m \langle c^2 \rangle$.

(b(i))[2]

State what the symbols $m$ and $\langle c^2 \rangle$ mean in this equation.

(b(ii))[2]

Use the equations in (a) and (b) to derive an expression, in terms of $A$, $B$ and $T$, for the mean kinetic energy $E_{K}$ of one molecule of the gas.

(c)[2]

On Fig. 4.1, sketch how the root-mean-square (r.m.s.) speed of the molecules of an ideal gas varies with $T$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: the thermodynamic temperature

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