Re-Optimisation of Otto Power Cycles Working with Ideal Quantum Gases

Abstract

To analyse the effect of quantum degeneracy of a working gas on the work optimisation of an ideal gas cycle, Otto power cycles working with ideal Bose and Fermi type quantum gases are considered. They are called Bose and Fermi Otto cycles respectively. Expressions for their net work outputs per cycle are derived by using the corrected ideal gas equation of state, which considers the quantum degeneracy of the working gas. For Bose and Fermi Otto cycles, the maximum net work output condition (MWOC) is re-derived. It is seen that this condition is different from that of the classical Otto cycle, which works with classical ideal gases. Therefore, expressions for maximum work output and efficiency at MWOC become different from their classical expressions. These new expressions are more general expressions which are valid under both classical and quantum ideal gas conditions. It is shown that maximum work output and efficiency at MWOC of a Bose Otto cycle can be higher than that of a classical Otto cycle. On the other hand, both quantities of the Fermi Otto cycle are always lower than their classical values.