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