A polytropic process for an ideal gas in one in which pressure and volume are related by = const., where n is a constant. It is a generalization of the special processes considered earlier. Thus n = 0 defines an isobaric process, n = cp/cv an adiabatic process, n = 1 an isothermal process, and n = 8 an isochoric process. Suppose 1 kg of dry air at 280 K and 100 kPa undergoes a polytropic expansion in which the pressure falls to 70kPa and the potential temperature increases by 10 K. Solve for

(a) the value of n;

(b) the change in internal energy of the air;

(c) the work done by the air;

(d) the heat absorbed by the air.