(a(i))[1]
State the meaning of the symbol $\langle c^2 \rangle$.
(a(ii))[3]
Use the expression to show that the mean kinetic energy $E_K$ of a gas molecule is given by $E_K = \frac{3}{2}kT$, where $k$ is the Boltzmann constant and $T$ is the thermodynamic temperature.
(b(i))[3]
An ideal gas containing $1.0\,\text{mol}$ of molecules is heated at constant volume. Use the result in (a)(ii) to show that the thermal energy needed to raise the temperature of the gas by $1.0\,\text{K}$ is $\frac{3}{2}R$, where $R$ is the molar gas constant.
(b(ii))[2]
Nitrogen can be treated as an ideal gas. Its molar mass is $28\,\text{g mol}^{-1}$. Use the answer in (b)(i) to calculate the specific heat capacity, in $\text{J kg}^{-1}\text{K}^{-1}$, at constant volume for nitrogen.