Efficiency at maximum power output of linear irreversible Carnot-like heat engines

Abstract

The efficiency at maximum power output of linear irreversible Carnot-like heat engines is investigated based on the assumption that the rate of irreversible entropy production of working substance in each "isothermal" process is a quadratic form of heat exchange rate between the working substance and the reservoir. It is found that the maximum power output corresponds to minimizing the irreversible entropy production in two "isothermal" processes of the Carnot-like cycle, and that the efficiency at maximum power output has the form as ${\eta }_{mP}={\eta }_C/(2-\gamma {\eta }_C)$ where ${\eta }_C$ is the Carnot efficiency while $\gamma$ depends on the heat transfer coefficients between the working substance and two reservoirs. The value of ${\eta }_{mP}$ is bounded between ${\eta }_{-}\equiv {\eta }_C/2$ and ${\eta }_{+}\equiv {\eta }_C/(2-{\eta }_C)$. These results are consistent with those obtained by Chen and Yan [J. Chem. Phys. \textbf{90}, 3740 (1989)] based on the endoreversible assumption, those obtained by Esposito \textit{et al.} [Phys. Rev. Lett. \textbf{105}, 150603 (2010)] based on the low-dissipation assumption, and those obtained by Schmiedl and Seifert [EPL \textbf{81}, 20003 (2008)] for stochastic heat engines which in fact also satisfy the low-dissipation assumption. Additionally, we find that the endoreversible assumption happens to hold for Carnot-like heat engines operating at the maximum power output based on our fundamental assumption, and that the Carnot-like heat engines that we focused does not strictly satisfy the low-dissipation assumption, which implies that the low-dissipation assumption or our fundamental assumption is a sufficient but non-necessary condition for the validity of ${\eta }_{mP}={\eta }_C/(2-\gamma {\eta }_C)$ as well as the existence of two bounds ${\eta }_{-}\equiv {\eta }_C/2$ and ${\eta }_{+}\equiv {\eta }_C/(2-{\eta }_C)$.

6 journal pages

References in corpus (6)

• Efficiency at maximum power: An analytically solvable model for stochastic heat engines
• Efficiency at maximum power of low dissipation Carnot engines
• Optimal finite-time processes in stochastic thermodynamics
• Efficiency at maximum power of Feynman's ratchet as a heat engine
• Efficiency at maximum power of minimally nonlinear irreversible heat engines
• Maximum-power quantum-mechanical Carnot engine

Cited by in corpus (40)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Coefficient of performance at maximum figure of merit and its bounds for low-dissipation Carnot-like refrigerators
• Stochastic heat engine with the consideration of inertial effects and shortcuts to adiabaticity
• Efficiency at maximum power output of quantum heat engines under finite-time operation
• Coefficient of performance under optimized figure of merit in minimally nonlinear irreversible refrigerator
• Experimental validation of the $1/\tau$ -scaling entropy generation in finite-time thermodynamics with dry air
• Universal features in the efficiency of ultra hot quantum Otto engines
• Efficiency at maximum power output of an irreversible Carnot-like cycle with internally dissipative friction
• Coefficient of performance for a low-dissipation Carnot-like refrigerator with nonadiabatic dissipation
• Heat devices in nonlinear irreversible thermodynamics
• Bounds of efficiency at maximum power for linear, superlinear and sublinear irreversible Carnot-like heat engines
• Efficiency of a thermodynamic motor at maximum power
• Weighted reciprocal of temperature, weighted thermal flux, and their applications in finite-time thermodynamics
• Efficiency at maximum power of a quantum Otto engine: Both within finite-time and irreversible thermodynamics
• Geodesic path for the minimal energy cost in shortcuts to isothermality
• Connection between maximum-work and maximum-power thermal cycles
• Universality of energy conversion efficiency for optimal tight-coupling heat engines and refrigerators
• Geometric Heat Engines Featuring Power that Grows with Efficiency
• Efficiency at maximum power for classical particle transport
• Abstract models for heat engines
• Optimizing Thermodynamic Cycles with Two Finite-Sized Reservoirs
• Thermodynamics at the microscale: from effective heating to the Brownian Carnot engine
• Network analysis of the performance of organic photovoltaic cells: The open circuit voltage and the zero current efficiency
• Bounds of Efficiency at Maximum Power for Normal-, Sub- and Super-Dissipative Carnot-Like Heat Engines
• Coefficient of performance under maximum $\chi$ criterion in a two-level atomic system as a refrigerator
• Feynman-Smoluchowski engine at high temperatures and the role of constraints
• General relations between the power, efficiency and dissipation for the irreversible heat engines in the nonlinear response regime
• Expected Behavior of Quantum Thermodynamic Machines with Prior Information
• Coefficient of performance at maximum χ-criterion for Feynman ratchet as a refrigerator
• Optimizing Brownian heat engine with shortcut strategy
• Near-equilibrium universality and bounds on efficiency in quasi-static regime with finite source and sink
• Efficiency at maximum power of thermochemical engines with near-independent particles
• Hidden symmetries and nonlinear constitutive relations for tight-coupling heat engines
• Global linear-irreversible principle for optimization in finite-time thermodynamics
• Self-consistency of optimizing finite-time Carnot engines with the low-dissipation model
• Retainability of canonical distributions for a Brownian particle controlled by a time-dependent harmonic potential
• Bounds and phase diagram of efficiency at maximum power for tight-coupling molecular motors
• Geodesic path for the optimal nonequilibrium transition: Momentum-independent protocol
• Maximum power Stirling-like heat engine with a harmonically confined Brownian particle
• Unified approach to power-efficiency trade-off relations of generic thermal machines