In Q5.5 of Sethna 'Entropy, Order, Parameters and Complexity', we are presented with a pressure-volume diagram for a process on a monoatomic ideal gas consisting of the following steps:

"(a) cooling at constant volume by connecting to a heat bath at $T\_c$, (b) heating at constant pressure by connecting to heat bath at $T\_h$, (c) compressing at constant temperature while remaining to the bath at $T\_h$."

One is then expected to answer a series of T/F questions, for example:

"(T) (F) The work done per cycle has magnitude $|W | = P\_0 V\_0 |4 \text{log}(4) − 3|$."

As I understand it, we are expected to calculate work using standard methods, i.e. integrating the work one form $-PdV$ by pulling out the constant pressure or using the equation of state for the ideal gas. Indeed, by performing such a calculation my answer was marked correctly (I was set this question for a problem sheet).

My question is this. Given the process is clearly irreversible, as we have heat flowing from hot to cold for steps (a) and (b), how is such an integral supposed to even make sense? I thought we were only allowed to perform such calculations for reversible processes, for which the intermediate states are all equilibrium states.