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

Kinetic theory of gases — practice question

The pressure $p$ for an ideal gas with density $\rho$ is expressed by $p = \frac{1}{3}\rho\langle c^{2} \rangle$.
(a(i))[2]

State the definition of an ideal gas.

(a(ii))[1]

State what the symbol $\langle c^{2} \rangle$ means.

(b(i))[3]

A cylinder contains a fixed mass of gas at a temperature of $120\,^{\circ}\text{C}$. The gas volume is $6.8 \times 10^{-3}\,\text{m}^{3}$ when the pressure is $2.4 \times 10^{5}\,\text{Pa}$. Assuming ideal-gas behaviour, show that the number of atoms of gas in the cylinder is $3.0 \times 10^{23}$.

(b(ii))[2]

Each gas atom, treated as a sphere, has a radius of $3.2 \times 10^{-11}\,\text{m}$. Use the answer in (i) to estimate the true volume occupied by the gas atoms.

(b(iii))[2]

One assumption in the kinetic theory of gases concerns the volume of the atoms. State this assumption. Explain whether your answer in (ii) agrees with this assumption.

(iii)[2]

One assumption in the kinetic theory of gases concerns the volume of the atoms. State this assumption. Explain whether your answer in (ii) is in agreement with this assumption.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: The gas follows $\frac{pV}{T} = \text{constant}$

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