Joule-Thomson expansion and heat engine efficiency of charged rotating black strings

TL;DR

Bakhtiarizadeh investigates Joule-Thomson throttling and heat engine efficiency for asymptotically AdS charged rotating black strings in the extended phase space. Using per-unit-horizon-length thermodynamics, he derives the JT coefficient $\mu$, the inversion temperature $T_i$, and the inversion/isenthalpic curves, and analyzes cooling/heating regions; for the heat engine, the Carnot efficiency $\eta_C$ and the rectangular-cycle efficiency $\eta_r$ are obtained and illustrated. The results show that charged rotating black strings exhibit cooling regions and a minimum $T_i$, analytically tractable in the uncharged limit with $T_i({\cal Q}=0)=\frac{2 \sqrt[6]{2}\,5^{5/6} \sqrt[3]{\mathcal{J}}\,P^{2/3}}{7^{2/3}}$ and $\mathcal{S}=\frac{\sqrt[6]{35/2}\,\sqrt{\pi}\,\mathcal{J}^{2/3}}{\sqrt{3}\,\sqrt[6]{P}}$, while the Carnot efficiency approaches unity as $S_2,P_1\to\infty$ and the rectangular efficiency tends to $0.375$ in the uncharged, non-rotating limit. These contributions extend black hole thermodynamics in the extended phase space to cylindrical horizons and provide benchmarks for future explorations of non-linear electrodynamics and non-spherical topologies.

Abstract

We perform the first study of the throttling process and heat engine efficiency of asymptotically Anti-de Sitter charged and rotating black strings in the extended phase space. For the throttling process, we calculate the Joule-Thomson coefficient and inversion temperature. We also depict the inversion and isenthalpic curves in the temperature-pressure plane, thereby identifying the corresponding cooling and heating regions. For the black string heat engine, we obtain analytical expressions for the efficiency of the Carnot and rectangular engine cycles and draw their diagrams in terms of some relevant thermodynamics variables.

Figures (8)

• Figure 1: The profile of heat capacity at constant pressure as a function of entropy at constant pressure $P=1$.
• Figure 2: The profile of JT coefficient as a function of entropy at constant pressure $P=1$.
• Figure 3: The inversion curves for ${\cal Q}=0$ and different values of ${\cal J}$.
• Figure 4: The isenthalpic and inversion curves for uncharged solutions and different valuse of ${\cal J}$ and ${\cal M}$.
• Figure 5: $P-{\cal V}$ diagram of thermodynamic cycles for the heat engine.