Show that the cylinder contains $1.4 \times 10^{23}$ gas molecules.
Using kinetic theory, explain why moving the piston so that the gas expands causes the gas temperature to decrease.
The gas expands so that its volume rises to $2.4 \times 10^{-3}\,\text{m}^3$ at a pressure of $2.3 \times 10^{5}\,\text{Pa}$ and a temperature of $288\,\text{K}$, as shown in Fig. 2.2. The mean translational kinetic energy $E_{K}$ of a 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.
The work done by the gas during the expansion is $76\,\text{J}$. Use your answer in part (i) to explain whether thermal energy is transferred to or from the gas during the expansion.