Optimizing thermodynamic cycles with two finite-sized reservoirs
Hong Yuan1, Yu-Han Ma1, C P Sun1,2
1Graduate School of China Academy of Engineering Physics, Number 10 Xibeiwang East Road, Haidian District, Beijing 100193, China.
Physical Review. E
|March 16, 2022
Summary
This study explores nonequilibrium thermodynamics for heat engines with finite reservoirs. Optimal performance is achieved by balancing power and efficiency, with a universal efficiency at maximum power derived.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Physical Chemistry
Background:
- Studying heat engines operating between finite-sized reservoirs is crucial for understanding real-world thermodynamic systems.
- Nonequilibrium thermodynamics provides a framework for analyzing systems not in thermal equilibrium.
Purpose of the Study:
- To investigate the nonequilibrium thermodynamics of a heat engine coupled to finite heat reservoirs.
- To determine the relationship between power, efficiency, and reservoir properties.
- To derive optimal operating protocols for heat engines with finite reservoirs.
Main Methods:
- Analysis within the linear response regime.
- Derivation of power-efficiency tradeoffs based on reservoir heat capacities.
- Demonstration using an ideal gas heat engine model.
Main Results:
- A lower bound for reservoir temperature is established, inversely proportional to the final time (τ).
- A general power-efficiency tradeoff is identified, dependent on the heat capacity ratio (γ).
- A universal efficiency at maximum average power is obtained for any γ.
Conclusions:
- The findings offer a method for optimizing thermodynamic cycles with finite reservoirs.
- The derived universal efficiency provides a benchmark for practical heat engine design.
- The study contributes to the development of efficient energy conversion technologies.
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