Past exam of the mathematics course of the University of Cambridge / 2017 / ii / Paper 3 / 34D / b / iii

On the straight sloping leg, $p=p_0(3-V/V_0)$ and $dp=-p_{0}dV/V_0$. Put $v=V/V_0$, which increases from $1$ to $2$. The reversible heat transfer isThus heat is absorbed for $1<v<15/8$ and emitted for $15/8<v<2$, with zero instantaneous heat at $v=15/8$. The switching point has $(p,V)=(9p_0/8,15V_0/8)$. In particular the net heat on this leg, $\frac{3}{2}{p}_0{V}_0$, is not the total positive heat on it.