A diatomic ideal gas is heated at constant volume until the pressure is doubled and again heated at constant pressure until volume is doubled. The average molar heat capacity for whole process is -

Let initial pressure, volume, temperature be P₀, V₀, T₀ indicated by state A in P-V diagram. The gas is then isochorically taken to state 
B (2P₀ , V₀ , 2T₀) and then taken from state B to state C(2P₀ , 2V₀ , 4T₀) isobarically.

Total heat absorbed by 1 mole of gas
$\begin{array}{r}\mathrm{\Delta Q}={\mathrm{C}}_{\mathrm{V}}\left(2{\mathrm{P}}_0-{\mathrm{T}}_0\right)+{\mathrm{C}}_{\mathrm{P}}\left(4{\mathrm{T}}_0-2{\mathrm{T}}_0\right)\\ =\frac{5}{2}{\mathrm{RT}}_0+\frac{7}{2}\mathrm{R}\times 2{\mathrm{T}}_0=\frac{19}{2}{\mathrm{RT}}_0\end{array}$
Total change in temperature from state A to C is
$\mathrm{\Delta T}=3{\mathrm{T}}_0$ molar heat capacity $=\frac{\Delta Q}{\Delta T}=\frac{\frac{19}{2}R{T}_0}{3T_0}$
$=\frac{19}{6}R$