A cycle is proposed as a development of the Lenoir cycle, in which the working fluid is expanded isentropically from its peak pressure down to a point where its temperature is equal to \(T_{1}\), the initial temperature. The gas is then compressed isothermally back to the initial pressure. Prove that the thermal efficiency of the cycle is given by

\[\eta_{\mathrm{th}}=1-\frac{T_{1}}{T_{2}-T_{1}} \ln \frac{T_{2}}{T_{1}}\]

where \(T_{2}\) is the maximum temperature achieved in the cycle.

Calculate the thermal efficiency of the cycle if the initial pressure is \(10 \mathrm{bar}\) and the maximum pressure is 35 bar. Compare this to the Carnot efficiency achievable between the temperature limits and explain why this cycle would not be used in practice.

[49.9\%; 71.4\%]