Efficiency Analysis of a Stirling Power Cycle under Quantum Degeneracy Conditions

Abstract

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 (ηB and ηF respectively). Variations of them with the temperature ratio (τ = TL/TH) and specific volume ratio (rν = νH/νL) are examined. Efficiencies are compared with each other and that of the classical Stirling cycle (ηC). It is shown that ηF and ηB depend on both temperatures and specific volumes of the cycle although ηC depends on only the temperatures of the cycle. It is also seen that ηF < ηB < ηC. The quantities ΔηF = ηC - ηF and ΔηB = ηC - ηB go to zero at the classical gas conditions. Under degeneracy gas conditions, however, ΔηB is greater than zero and it has one maximum and one minimum value while TL decreases. On the other hand, ΔηF has no extremum point and increases continuously with decreasing TL · ηF and ηB decrease with increasing rν when νH is constant although they increase when νL is constant. Under the conditions that the working gas remains a completely degenerate Bose gas throughout the cycle, it is seen that ηB goes to 0.4 instead of unity when τ goes to zero.