Optimizing the performance of a heat engine: A simulation study

We performed a simulation study of~a simple heat engine as it undergoes Carnot-type cyclic motion in a finite time over a wide range of piston speeds. There exists a specific piston speed at which the power delivered by the engine is maximum ($P_{max})$ and its corresponding efficiency is slightly larger than \textit{half~}of the Carnot efficiency (1/2 $\eta _{c})$. An optimization criterion leads to a trade-off between high power and high efficiency with respective values of 4/5 $P_{max}$ and 3/4 $\eta _{c}$. In addition, we found the time taken at the optimized state to be twice the time taken when operating at maximum power.