Past exam of the physics B course of the University of Cambridge / 2017 / Paper 2 / Section C / C10 / Diesel-cycle geometry / Solution

Label the initial state 1, the end of compression 2, the end of constant-pressure heating 3, and the end of adiabatic expansion 4. The volume sequence is $V_1\to V_2\to V_3\to V_1\to V_1$, with $V_2<V_3<V_1$. The Diesel cycle has a compression adiabat $1\to 2$, a horizontal constant-pressure heat-input segment $2\to 3$, an expansion adiabat $3\to 4$, and a vertical constant-volume cooling segment $4\to 1$.

For an ideal gas, a reversible adiabat obeys $p{V}^{\gamma }=\mathrm{constant}$, so it falls more steeply than an isotherm. The expansion adiabat lies above the compression adiabat at equal volume between $V_3$ and $V_1$, giving a clockwise cycle with positive work output.