Efficiency analysis of a stirling power cycle under quantum degeneracy conditions

To examine the effect of quantum degeneracy on the cycle efficiency, Stirli ng power cycles working with ideal Bose and Fermi gases are thermodynamical ly analysed. These cycles are called Bose and Fermi cycles. Efficiency expr essions of Bose and Fermi cycles are derived (eta (B) and eta (F) respectiv ely). Variations of them with the temperature ratio (tau = T-L/T-H) and spe cific volume ratio (r(v) = v(H)/v(L)) are examined. Efficiencies are compar ed with each other and that of the classical Stirling cycle (eta (C)) It is shown that eta (F) and eta (B) depend on both temperatures and specific vo lumes of the cycle although eta (C) depends on only the temperatures of the cycle. It is also seen that eta (F) < eta (B) < eta (C). The quantities De lta eta (F) = eta (C) - eta (F) and Delta eta (B) = eta (C) - eta (B) go to zero at the classical gas conditions. Under degeneracy gas conditions, how ever, Delta eta (B) is greater than zero and it has one maximum and one min imum value while TL decreases. On the other hand, Delta eta (F) has no extr emum point and increases continuously with decreasing T-L. eta (F) and eta (B) decrease with increasing r(v) when v(H) is constant although they incre ase when v(L) is constant. Under the conditions that the working gas remain s a completely degenerate Bose gas throughout the cycle, it is seen that et a (B) goes to 0.4 instead of unity when tau goes to zero.