Efficiency Analysis of a Stirling Power Cycle under Quantum Degeneracy Conditions

To examine the effect of quantum degeneracy on the cycle efficiency, Stirling power cycles working with ideal Bose and Fermi gases are thermodynamically analysed. These cycles are called Bose and Fermi cycles. Efficiency expressions of Bose and Fermi cycles are derived (η B and η F respectively). Variations of them with the temperature ratio (τ = T L / T H ) and specific volume ratio ( r ν = ν H /ν L ) are examined. Efficiencies are compared with each other and that of the classical Stirling cycle (η C ). It is shown that η F and η B depend on both temperatures and specific volumes of the cycle although η C depends on only the temperatures of the cycle. It is also seen that η F < η B < η C . The quantities Δη F = η C - η F and Δη B = η C - η B go to zero at the classical gas conditions. Under degeneracy gas conditions, however, Δη B is greater than zero and it has one maximum and one minimum value while T L decreases. On the other hand, Δη F has no extremum point and increases continuously with decreasing T L · η F and η B decrease with increasing r ν when ν H is constant although they increase when ν L is constant. Under the conditions that the working gas remains a completely degenerate Bose gas throughout the cycle, it is seen that η B goes to 0.4 instead of unity when τ goes to zero.