Low-temperature behaviour of an ideal Bose gas and some forbidden thermodynamic cycles

Abstract

Based on the equation of state of an ideal Bose gas, the heat capacities at constant volume and constant pressure of the Bose system are derived and used to analyse the low-temperature behaviour of the Bose system. It is expounded that some important thermodynamic processes such as a constant pressure and an adiabatic process cannot be carried out from the region of T > Tc to that of T < Tc, where Tc is the critical temperature of Bose–Einstein condensation of the Bose system. Consequently, some typical thermodynamic cycles such as the Carnot cycle, Brayton cycle, Otto cycle, Ericsson cycle, Diesel cycle and Atkinson cycle cannot be operated across the critical temperature Tc of Bose–Einstein condensation of an ideal Bose gas.