Define the meaning of specific heat capacity.
A sealed container with fixed volume $V$ holds an ideal gas at pressure $p$, containing $N$ molecules, each of mass $m$.
State an expression, in terms of $V$, $N$, $p$ and the Boltzmann constant $k$, for the thermodynamic temperature $T$ of the gas.
Show that the mean translational kinetic energy $E_K$ of a molecule of the gas is given by $E_K = \frac{3}{2}kT$.
Explain why the internal energy of the gas is equal to the total kinetic energy of the molecules.
The gas in (b) receives thermal energy $Q$. Explain, with reference to the first law of thermodynamics, why the increase in internal energy of the gas is $Q$.
Use the expression in (b)(ii) together with the information in (c)(i) to show that the specific heat capacity $c$ of the gas is given by $c = \frac{3k}{2m}$.
The container in (b) is now replaced by one without a fixed volume. Instead, the gas is allowed to expand, so that the pressure of the gas stays constant as thermal energy is supplied. Suggest, with a reason, how the specific heat capacity of the gas would now compare with the value in (c)(ii).