The efficiency of an irreversible cycle (Q913107)

It is proved here on a simple model that for a body whose boundary is subject to an absolute temperature \(\tau(t)\) and a pressure \(p(t)\) which are periodic in time the efficiency of an inversible cycle operating between the temperatures \(\text{Min}(\tau)\) and \(\text{Max}(\tau)\) cannot exceed \((1-\text{Min}(\tau)/\text{Max}(\tau))/(1+\Delta)\), where \(\Delta\) is a positive number which depends upon \(\tau\), \(p\), the size and the material properties of the body. This result must be composed with the efficiency of a reversible Carnot cycle \(1-\text{Min}(\tau)/\text{Max}(\tau)\).