Chapter 19, Problem 56P

In a diesel cycle, gas at volume V₁ and pressure p₁, undergoes adiabatic compression to a smaller volume V₂. It is then healed at constant pressure while it expands to volume V₃. The gas then expands adiabatically until it’s again at volume V₁, whereupon it cools, at constant volume, until it’s back to its initial state of p₁ and V₁. Show that the work done by the engine over one cycle can be written as $W=\frac{p_1{V}_1[r^{\text{γ-1}}(\alpha -1)\text{γ}-{\alpha }^{\text{γ}}+1]}{\text{γ}-1}$ Here r = V₁/V₂ is the compression ratio and α = V₃/V₂ is the so-called cutoff ratio.