2016/02/29 by Xiaoguang Luo, Nian Liu, Teng Qiu
Chemistry · Engineering · Mathematics · Physics and Astronomy · #Advanced Thermodynamic Systems and Engines #Advanced Thermodynamics and Statistical Mechanics #Boltzmann constant #Bounded function #Carnot cycle #Chemistry #Coupling (piping) #Heat engine #Materials science #Mathematical analysis #Mathematics #Maximum power principle #Particle (ecology) #Particle number #Physics #Power (physics) #Thermal Radiation and Cooling Technologies #Thermodynamics #Upper and lower bounds #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.93.032125
published as Phys. Rev. E 93, 032125 (2016) · 12 pages, 4 figures
openalex publication_date 2016/03/15 · arxiv created 2016/05/15 · arxiv updated 2016/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Two-reservoir thermochemical engines are established by using near-independent particles (including Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein particles) as the working substance. Particle and heat fluxes can be formed based on the temperature and chemical potential gradients between two different reservoirs. A rectangular-type energy filter with width \mathrm\ensuremathΓ is introduced for each engine to weaken the coupling between the particle and heat fluxes. The efficiency at maximum power of each particle system decreases monotonously from an upper bound \ensuremathη+ to a lower bound \ensuremathη^\ensuremath- when \mathrm\ensuremathΓ increases from 0 to \ensuremath∞. It is found that the \ensuremathη+ values for all three systems are bounded by \ensuremathηC/2\ensuremath≤\ensuremathη+\ensuremath≤\ensuremathηC/(2\ensuremath-\ensuremathηC) due to strong coupling, where \ensuremathηC is the Carnot efficiency. For the Bose-Einstein system, it is found that the upper bound is approximated by the Curzon-Ahlborn efficiency: \ensuremathηCA=1\ensuremath-√1\ensuremath-\ensuremathηC. When \mathrm\ensuremathΓ\ensuremath→\ensuremath∞, the intrinsic maximum powers are proportional to the square of the temperature difference of the two reservoirs for all three systems, and the corresponding lower bounds of efficiency at maximum power can be simplified in the same form of \ensuremathη^\ensuremath-=\ensuremathηC/[1+a0(2\ensuremath-\ensuremathηC)].