Joule–Thomson coefficients of weakly interacting Fermi gases and Bose gases

The analytical expressions of the Joule–Thomson coefficient (JTC) for an imperfect Fermi gas and a Bose gas are derived by means of thermodynamic theory and “pseudopotential” method, respectively. It is discussed that the influence of the Joule–Thomson effect by repulsive interacting and attractive interacting. We find the following results: (1) For an ideal Fermi gas, the JTC is lower than zero owing to the equivalent repulsive potential arising from the quantum degeneracy at sufficiently low temperature; for repulsive interaction Fermi gases, the JTC is lower than zero at sufficiently low temperature; for attractive interaction Fermi gases, there is an inversion particle density at sufficiently low temperature, when the particle density is not only higher than the inversion density, but also lower than the boundary particle density of the criterion of the stability of the Fermi system, the JTC is higher than zero; when the particle density is lower than the inversion density, the JTC is lower than zero. (2) The JTC for an ideal Bose gas is the limit of the JTC of an imperfect Bose gas when S wave scattering length is zero; for repulsive interaction Bose gases, there is an inversion particle density at certain temperature, when the particle density is lower (higher) than the inversion density, the JTC is positive (negative); for attractive interaction Bose gases, the JTC is always positive.