Define the term specific heat capacity.
An ideal gas consisting of $N$ molecules, each with mass $m$, is enclosed in a sealed container of fixed volume $V$ and has pressure $p$.
State an expression for the thermodynamic temperature $T$ of the gas, in terms of $V$, $N$, $p$ and the Boltzmann constant $k$.
Show that the mean translational kinetic energy $E_{K}$ of one molecule of the gas is $E_{K} = \frac{3}{2}kT$.
Explain why the internal energy of the gas is equal to the total kinetic energy of its molecules.
In part (b), the gas receives thermal energy $Q$.
Explain, using 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 $c = \frac{3k}{2m}$.
The container in (b) is now changed to one with no fixed volume. The gas can therefore expand, so its pressure stays constant while thermal energy is supplied. Suggest, with a reason, how the specific heat capacity of the gas would compare with the value in (c)(ii).