Why is a macroscopic thermoelectric engine less efficient than a compressor-based heat engine? (Q2854129)

In [Phys. Rev. Lett. 95, 190602 (2005; \url{doi:10.1103/PhysRevLett.95.190602})], \textit{C. Van den Broeck} introduced a linear irreversible heat engine described by the Onsager relation. Its efficiency at maximum power can reach the Curzon-Ahlborn efficiency under the strong-coupling condition. Further studies reveal that a compressor-based heat engine is approximately a strongly coupled linear irreversible heat engine. In this paper, we demonstrate that a macroscopic thermoelectric engine is a moderately or weakly coupled linear irreversible heat engine. This explains why a macroscopic thermoelectric engine is less efficient than a compressor-based heat engine for same relative temperature differences of heat reservoirs. As is well known, the upper bound of the efficiency of a heat engine is the Carnot efficiency \(\eta _{\text{Carnot}} =1-{T_{1} / T_{h} }\). Here, \(T_{1} \) and \(T_{h} \), are the temperatures of the two heat reservoirs (\(T_{1} <T_{h} \)). Nevertheless, the Carnot engine has zero power output since it must work infinitely slowly. Because of irreversible effects, the real heat engines work at finite rates and hence have finite power outputs. \textit{F. L. Curzon} and \textit{B. Ahlborn} [``Efficiency of a Carnot engine at maximum power output'', Am. J. Phys. 43, No. 1, 22 (1975; \url{doi:10.1119/1.10023})] first incorporated irreversible effects into the Carnot cycle. Using Fourier's law and the endoreversible approximation, they obtained the efficiency at maximum power as NEWLINE\[NEWLINE\eta _{\text{CA}} =1-\sqrt{\frac{T_{1} }{T_{h} } } =\frac{1}{2} \frac{T_{h} -T_{1} }{T_{h} } +\frac{1}{8} \left(\frac{T_{h} -T_{1} }{T_{h} } \right)^{2} +O(T_{h} -T_{1} )^{3} . NEWLINE\]NEWLINEThey found that the Curzon-Ahlborn efficiency \textit{tjca} is in good agreement with the observed efficiencies of some real heat engines. The author demonstrates that a macroscopic thermoelectric engine is a moderately or weakly coupled linear irreversible heat engine. This explains why the efficiency of a macroscopic thermoelectric engine is always lower than that of a compressor-based heat engine.