A Deeper Look at the Sadly Cannot Thermodynamic Cycle

The “Sadly Cannot” (SC) thermodynamic cycle was introduced by Willis and Kirwan in a paper that appeared in the January 1980 issue of this journal.¹ Comprising but two steps, it appears remarkably simple. First, an ideal monatomic gas is expanded from initial state (P₀, V₀) to final state (P₁, V₁) along a path that is a straight line of negative slope in the PV plane, but with (P₀, V₀) and (P₁, V₁) chosen to be connected by an adiabat: P₀V₀^γ = P₁V₁^γ, where we set γ = 5/3. The return path is the adiabat, along which there can be no heat energy exchange. The cycle is sketched (not to scale) in Fig. 1. As with all such cycles, all...