On the power cycles working with ideal quantum gases: I. The Ericsson cycle

摘要

The Ericsson power cycles working with ideal Bose and Fermi monoatomic gases are examined. They are conveniently called the Bose and Fermi cycles. Efficiencies of Bose and Fermi cycles are derived (ηB and ηF respectively). Variations of them with the temperature ratio (τ) and pressure ratio of the cycle are examined. A comparison of the efficiencies with each other and that of the classical Ericsson cycle (ηCl) is made. In the degenerate gas state it is seen that ηB < ηF < ηCl, although 250L荁 = ηF = ηCl in the classical gas state. In a Bose cycle, it is shown that there is an optimum value for the lowest temperature (TL) at which the efficiency reaches its maximum value for a given pressure ratio. Furthermore, Bose-Einstein condensation restricts the value of TL of a Bose cycle for a given value of PH. In a Fermi cycle, there is no an optimum value for TL. However, ηF goes to a finite value of less than unity when τ goes to zero.