Charged AdS black hole heat engines

TL;DR

This paper analyzes the efficiency of heat engines based on charged AdS black holes, revealing how temperature, charge, and spacetime dimensions influence their performance and potential as power sources.

Contribution

It provides an exact formula for black hole engine efficiency using a Rankine cycle and explores the effects of various parameters on performance, including higher dimensions.

Findings

Efficiency increases with high temperature $T_{1}$ and spacetime dimensions.

Work and efficiency decrease with black hole charge $q$ at fixed low temperature.

Higher-dimensional black holes can serve as more efficient power sources.

Abstract

We study the heat engine by a $d$-dimensional charged anti-de Sitter black hole by making a comparison between the small-large black hole phase transition and the liquid-vapour phase transition of water. With the help of the first law and equal-area law, we obtain an exact formula for the efficiency of a black hole engine modeled with a Rankine cycle with or without a back pressure mechanism. When the low temperature is fixed, both the heat and work decreases with the high temperature $T_{1}$. And the efficiency increases with $T_{1}$, while decreases with the charge $q$. For a Rankine cycle with a back pressure mechanism, we find that both the maximum work and efficiency can be approached at the high temperature $T_{1}$. In the reduced parameter space, it also confirms the similar result. Moreover, we observe that the work and efficiency of the black hole heat engine rapidly increase with the number of spacetime dimensions. Thus higher-dimensional charged anti-de Sitter black hole can act as a more efficient power plant producing the mechanical work, and might be a possible source of the power gamma rays and ultrahigh-energy cosmic rays.