Maximum efficiency of low-dissipation refrigerators at arbitrary cooling power

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Refrigeration Cycles

Background:

• Carnot-type refrigerators are fundamental in understanding thermodynamic cycles.
• Low-dissipation models are crucial for analyzing real-world efficiency limitations.
• Previous studies explored efficiency at maximum power, but optimal cycle duration under varying conditions requires further investigation.

Purpose of the Study:

• To analytically derive the maximum efficiency for Carnot-type low-dissipation refrigerators at a given cooling power.
• To determine the optimal cycle duration and its dependence on system parameters.
• To analyze the behavior of maximum efficiency concerning power output variations.

Main Methods:

• Analytical derivation of efficiency and optimal cycle duration.
• Parameter analysis to identify different qualitative behaviors of efficiency.
• Use of approximations for simplified analysis and demonstration of results.

Main Results:

• Maximum efficiency is achieved at a specific optimal cycle duration, dependent on irreversibility and bath temperatures.
• Efficiency exhibits a nonlinear increase with decreasing power for certain parameter ranges, and a linear increase for others.
• The transition between nonlinear and linear behavior is linked to the optimal power condition occurring at vanishing hot isotherm duration.

Conclusions:

• The study provides a comprehensive understanding of efficiency limits in low-dissipation refrigerators.
• Optimal cycle duration is a critical factor influenced by irreversibility and thermal bath conditions.
• Findings offer insights into designing more efficient refrigeration systems by managing irreversibility and cycle parameters.