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Journal of Chongqing University of Arts and Sciences

Parameters Changing Analysis of Bose Gas with Throttling Process

Zhou Sheng-en

Published Jan 1, 2008• 0 citations

Abstract

Considering the changes of internal energy caused by weak degeneracy and interaction between molecules,the internal energy of weak degenerate non-ideal Bose gas,partition function and equation of state were brought out.Using the results and relevant thermodynamic relations,Joule-Thomson coefficient was deduced.The results show that the Joule-Thomson coefficient of weak degenerate non-ideal Bose gas system is influenced by weak degeneracy and interaction between molecules.If it's a repulsive system,after throttling process,not only the change direction of the system temperature is influenced by weak degeneracy and interaction between molecular,but also the critical state of the temperature changing direction is influenced by them.If it's an attractive system,after throttling process,change of the system temperature has a limit,it's impossible to reach this limit temperature by throttling process.

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•Sep 5, 2013•0 citations

Considering the changes of internal energy caused by weak degeneracy and interaction between molecules,the internal energy of weak degenerate non-ideal Bose gas,partition function and equation of state were brought out.Using the results and relevant thermodynamic relations,Joule-Thomson coefficient was deduced.The results show that the Joule-Thomson coefficient of weak degenerate non-ideal Bose gas system is influenced by weak degeneracy and interaction between molecules.If it's a repulsive system,after throttling process,not only the change direction of the system temperature is influenced by weak degeneracy and interaction between molecular,but also the critical state of the temperature changing direction is influenced by them.If it's an attractive system,after throttling process,change of the system temperature has a limit,it's impossible to reach this limit temperature by throttling process.

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 → T C (T C 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 – ∏[ n i = 1 (kT/ϖ i ) 1/t i Γ(1/t i + 1)] (k is the Boltzmann Constant, T is the thermodynamic temperature, ϖ i 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/ϖ i < 1.

The Joule–Thomson effect reflects the interaction among constituent particles of macroscopic system. For classical ideal gas, the corresponding Joule–Thomson coefficient is vanishing while it is non-zero for ideal quantum gas due to the quantum degeneracy. In recent years, much attention is paid to the unitary Fermi gas with infinite two-body scattering length. According to universal analysis, the thermodynamical law of unitary Fermi gas is similar to that of non-interacting ideal gas, which can be explored by the virial theorem P = 2 E /3 V . Based on previous works, we further study the unitary Fermi gas properties. The effective chemical potential is introduced to characterize the nonlinear levels crossing effects in a strongly interacting medium. The changing behavior of the rescaled Joule–Thomson coefficient according to temperature manifests a quite different behavior from that for ideal Fermi gas.

Using the free energy and the equation of state for an imperfect Bose gas, the analytical expression between the critical temperature and the length of dispersion wave and the pressure for the imperfect Bose gas is derived. The unusual properties of the specific heat at constant pressure and the expansion coefficient at constant pressure and isothermal compressibility by the attractive force for the imperfect Bose gas are revealed. The instability arising from the attractive force is pointed out, and the temperature criterion and particle density criterion of instability is given for the imperfect Bose gas under the action of attraction.

We study the thermodynamics of Bose-Einstein condensation in a weakly interacting quasi-homogeneous atomic gas, prepared in an optical-box trap. We characterise the critical point for condensation and observe saturation of the thermal component in a partially condensed cloud, in agreement with Einstein's textbook picture of a purely statistical phase transition. Finally, we observe the quantum Joule-Thomson effect, namely isoenthalpic cooling of an (essentially) ideal gas. In our experiments this cooling occurs spontaneously, due to energy-independent collisions with the background gas in the vacuum chamber. We extract a Joule-Thomson coefficient

\mu_{\rm JT} > 10^9

K/bar, about ten orders of magnitude larger than observed in classical gases.