Optimizing Thermodynamic Cycles with Two Finite-Sized Reservoirs

TL;DR

This paper analyzes the thermodynamics of heat engines between finite reservoirs, deriving bounds on temperature, efficiency, and power, and proposing optimal operation protocols for real-world applications.

Contribution

It introduces a universal efficiency at maximum power for finite-sized reservoirs and demonstrates an optimal protocol for ideal gas engines.

Findings

Bound on final reservoir temperature based on entropy production

Universal efficiency at maximum power for arbitrary heat capacity ratio

Optimal operation protocol for ideal gas heat engine

Abstract

We study the non-equilibrium thermodynamics of a heat engine operating between two finite-sized reservoirs with well-defined temperatures. Within the linear response regime, it is found that the uniform temperature of the two reservoirs at final time $\tau$ is bounded from below by the entropy production $\sigma_{\mathrm{min}}\propto1/\tau$. We discover a general power-efficiency trade-off depending on the ratio of heat capacities ($\gamma$) of the reservoirs for the engine. And a universal efficiency at maximum average power of the engine for arbitrary $\gamma$ is obtained. For practical purposes, the operation protocol of an ideal gas heat engine to achieve the optimal performance associated with $\sigma_{\mathrm{min}}$ is demonstrated. Our findings can be used to develop an general optimization scenario for thermodynamic cycles with finite-sized reservoirs in real-world circumstances.