5.9 For a gas obeying van der Waals’ equation

(i) obtain the isobaric coefficient of thermal expansion α;

(ii) show that the energy E satisfies

(iii) show that the molar heat capacity at constant volume is a function of the temperature only;

(iv) obtain the difference of the molar heat capacities at constant pressure and at constant volume: (CP–CV);

(v) obtain the change in entropy dS of the gas for infinitesimal changes in volume dV and in temperature dT;

(vi) obtain the Joule–Thomson coefficient (∂T/∂P)H;
(vii) obtain the equation of the inversion curve as a function of volume and temperature.