(a(i))[1]
State what the symbol $N$ stands for.
(a(ii))[1]
State what is meant by the symbol $\langle c^{2} \rangle$.
(b)[2]
The quantity $pV$ is also represented by $pV = NkT$. Deduce an expression for the mean kinetic energy of a molecule of the ideal gas, in terms of the Boltzmann constant $k$ and the thermodynamic temperature $T$.
(c(i))[2]
A cylinder holds $1.0\ \text{mol}$ of an ideal gas. The cylinder volume stays fixed. Calculate the energy needed to increase the gas temperature by $1.0\ \text{kelvin}$.
(c(ii))[2]
The cylinder volume is now free to increase so that, on heating, the gas stays at constant pressure. Explain whether the energy needed to raise the gas temperature by $1.0\ \text{kelvin}$ is now different from your answer in (i).