Year: 2022
Type: article
Abstract: We study the ratio between the variances of work output and heat input, ${\ensuremath{\eta}}^{(2)}$, for a class of four-stroke heat engines, which covers various typical cycles. Recent studies on the upper and lower bounds of ${\ensuremath{\eta}}^{(2)}$ are based on the quasistatic limit and the linear response regime, respectively. We extend these relations to the finite-time regime within the endoreversible approximation. We consider the ratio ${\ensuremath{\eta}}_{\text{MP}}^{(2)}$ at maximum power and find that the square of the Curzon-Ahlborn efficiency, ${\ensuremath{\eta}}_{\mathrm{CA}}^{2}$, gives a good estimate of ${\ensuremath{\eta}}_{\text{MP}}^{(2)}$ for the class of heat engines considered, i.e., ${\ensuremath{\eta}}_{\text{MP}}^{(2)}\ensuremath{\simeq}{\ensuremath{\eta}}_{\mathrm{CA}}^{2}$. This resembles the situation where the Curzon-Ahlborn efficiency gives a good estimate of the efficiency at maximum power for various kinds of finite-time heat engines. Taking an overdamped Brownian particle in a harmonic potential as an example, we can realize such endoreversible small heat engines and give an expression of the cumulants of work output and heat input. The approximate relation ${\ensuremath{\eta}}_{\text{MP}}^{(2)}\ensuremath{\simeq}{\ensuremath{\eta}}_{\mathrm{CA}}^{2}$ is verified by numerical simulations. This relation also suggests a trade-off between the efficiency and the stability of finite-time heat engines at maximum power.
Source: Physical Review Research
Institution: Zhejiang University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,625
OpenAlex ID: W4310142175