Joule–Thomson coefficients of quantum ideal-gases

Abstract

The temperature drop of a gas divided by its pressure drop under constant enthalpy conditions is called the Joule–Thomson coefficient (JTC) of the gas. The JTC of an ideal gas is equal to zero since its enthalpy depends on only temperature. On the other hand, this is only true for classical ideal gas which obeys the classical ideal gas equation of state, pV=mRT. Under sufficiently low-temperature or high-pressure conditions, the quantum nature of gas particles becomes important and an ideal gas behaves like a quantum ideal gas instead of a classical one. In such a case, enthalpy becomes dependent on both temperature and pressure. Therefore, JTC of a quantum ideal gas is not equal to zero. In this work, the contribution of purely quantum nature of gas particles on JTC is examined. JTCs of monatomic Bose and Fermi type quantum ideal gases are derived. Their variations with temperature are examined for different pressure values. It is shown that JTC of a Bose gas is always greater than zero. Minimum value of temperature is limited by the Bose–Einstein condensation phenomena under the constant enthalpy condition. On the other hand, it is seen that JTC of a Fermi gas is always lower than zero and there is not any limitation on its temperature. For high temperature values, JTCs of Bose and Fermi gases go to zero since the quantum nature of gas particles becomes negligible. Moreover, variation of temperature versus pressure under the constant enthalpy condition is also examined. Consequently, it is understood that the quantum nature of a Bose-type gas contributes to the positive values of JTC while the quantum nature of a Fermi type gas contributes to the negative values of JTC. Therefore, a Bose-type gas is more suitable for cryogenic refrigeration systems.