Physics 9702 · AS & A Level · Internal energy

Internal energy — practice question

An ideal gas is enclosed in a cylinder by a movable frictionless piston, as shown in Fig. 2.1. At the start, the gas occupies a volume of $1.8 \times 10^{-3}\,\text{m}^3$ at a pressure of $3.3 \times 10^{5}\,\text{Pa}$ and a temperature of $310\,\text{K}$.
(a)[2]

Show that the cylinder contains $1.4 \times 10^{23}$ gas molecules.

(b)[3]

Use kinetic theory to explain why, when the piston is moved so that the gas expands, the temperature of the gas falls.

(c(i))[3]

The gas expands until its volume is $2.4 \times 10^{-3}\,\text{m}^3$ while the pressure is $2.3 \times 10^{5}\,\text{Pa}$ and the temperature is $288\,\text{K}$, as shown in Fig. 2.2. The average translational kinetic energy $E_K$ of one molecule of an ideal gas is given by $E_K = \frac{3}{2}kT$, where $k$ is the Boltzmann constant and $T$ is the thermodynamic temperature. Calculate the increase in internal energy $\Delta U$ of the gas during the expansion.

(c(ii))[2]

The work done by the gas during the expansion is $76\,\text{J}$. Use your answer in (i) to explain whether thermal energy is transferred to or from the gas as the expansion takes place.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Application of $pV = NkT$ or $pV = nRT$

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