c
\(Heat\,given\,to\,system = {\left( {n{C_V}\Delta T} \right)_{A \to B}} + {\left( {n{C_P}\Delta T} \right)_{B \to C}}\)

\( = {\left[ {\frac{3}{2}\left( {nR\Delta T} \right)} \right]_{A \to B}} + {\left[ {\frac{5}{2}\left( {nR\Delta T} \right)} \right]_{B \to C}}\)

\( = {\left[ {\frac{3}{2} \times {V_0}\Delta P} \right]_{A \to B}} + \left[ {\frac{5}{2} \times 2{P_0} \times {V_0}} \right]\)

\( = \frac{{13}}{2}{P_0}{V_0}\)