A Thesis Submitted To The Department Of Physics In Partial Fulfillment Of The Requirements For The Degree Of Master Of Science In Physics (Statistical Physics

Abstract

In this work, we conduct a thermodynamic analysis and optimization of the Quan­ tum Spin Hall Effect (QSHE) heat engine. The analysis employs fermion gas as the working medium and utilizes a quantization method for the working medium. We calculate the maximum power output and the corresponding efficiency at this max­ imum power using A.C. Hernandez's optimization approach. In this approach, the maximum efficiency is set to the Carnot efficiency, while the minimum efficiency (ef­ ficiency at maximum power) is set to one-fifth of the Carnot efficiency.

We optimize the developed objective function with respect to the temperature differ­ ence between the heat reservoirs. Our findings indicate that the engine utilizes more than 60% of the maximum available power at very small temperature differences. However, at the maximum value of the optimized temperatures, the engine operates at less than 15% of its peak power. Additionally, the scale efficiency of the engine increases as the temperature difference increases. Therefore, compared to the maximum power operating mode, the optimal operat­ ing mode offers a significant advantage in terms of efficiency. Overall, our results demonstrate that the QSHE heat engine performs better than existing engines and approaches the Carnot efficienc