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

The Ericsson power cycles working with ideal Bose and Fermi monoatomic gase s are examined. They are conveniently called the Bose and Fermi cycles. Eff iciencies of Bose and Fermi cycles are derived (eta(B) and eta(F) respectiv ely). Variations of them with the temperature ratio (tau) and pressure rati o of the cycle are examined. A comparison of the efficiencies with each oth er and that of the classical Ericsson cycle (eta(Cl)) is made. In the degen erate gas state it is seen that eta(B) < eta(F) < eta(Cl), although eta(B) = eta(F) = eta(Cl) in the classical gas state. In a Bose cycle, it is shown that there is an optimum value for the lowest temperature (T-L) at which t he efficiency reaches its maximum value for a given pressure ratio. Further more, Bose-Einstein condensation restricts the value of T-L Of a Bose cycle for a given value of P-H. In a Fermi cycle, there is no an optimum value f or T-L. However, eta(F) goes to a finite value of less than unity when tau goes to zero.