Effect of Spatial Dimension and External Potential on Joule–Thomson Coefficients of Ideal Bose Gases

Abstract

Based on the form of the n-dimensional generic power-law potential, the state equation and the heat capacity, the analytical expressions of the Joule–Thomson coefficient (JTC) for an ideal Bose gas are derived in n-dimensional potential. The effect of the spatial dimension and the external potential on the JTC are discussed, respectively. These results show that: (i) For the free ideal Bose gas, when n/s ≤ 2 (n is the spatial dimension, s is the momentum index in the relation between the energy and the momentum), and T → TC (TC is the critical temperature), the JTC can obviously improve by means of changing the throttle valve's shape and decreasing the spatial dimension of gases. (ii) For the inhomogeneous external potential, the discriminant Δ = [1 – ∏[ni = 1(kT/ϖi)1/tiΓ(1/ti + 1)] (k is the Boltzmann Constant, T is the thermodynamic temperature, ϖi is the external field's energy), is obtained. The potential makes the JTC increase when Δ > 0, on the contrary, it makes the JTC decrease when Δ < 0. (iii) In the homogenous strong external potential, the JTC gets the maximum on the condition of kT/ϖi < 1.