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 （3TC） for an ideal Bose gas are derived in n-...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 （3TC） 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 △= [1 - y∏^ni=1（kT/εi）^1/tiГ（1/ti＋1）] （k is the Boltzmann Constant, T is the thermodynamic temperature, ε is the external field＇s energy）, is obtained. The potential makes the JTC increase when △ 〉 0, on the contrary, it makes the JTC decrease when A 〈△. （iii） In the homogenous strong external potential, the JTC gets the maximum on the condition of kTεi〈〈1.展开更多
Based on the analysis of the Boltzmann＇s distribution in an infinitely high temperature found degeneration of the thermodynamic system in a purely informational with independently of each particle on its energy level...Based on the analysis of the Boltzmann＇s distribution in an infinitely high temperature found degeneration of the thermodynamic system in a purely informational with independently of each particle on its energy level, thus providing them full visibility of and the ability to calculate the maximum entropy in the Boltzmann formula S∞ = R·InNA = 455.251 J/（mol.K）. This value, when expressed in terms of fundamental constants, is itself a physical and chemical constants and mole monatomic ideal gas is unsurpassed in any studied temperature range. For complex substances this limit increases in direct proportion to their atomic. The existence of two limits entropy change--lower, equal to zero according to the third law of thermodynamics, and the top, equal to S∞, makes possible the explicit expression of the temperature dependence of the entropy in the form of an exponentialS=S∞exp[-5030.31p 2/5 /（M3/5T）]（5/2）r e/s∞. rather than in the form of a logarithmic dependence of the infinite by the approximateformula Sakura-Tetrode with which this the dependence is almost identical in the studied temperature range （100-10,000 K）, but not absurd negative entropy in the extrapolation formula Sakura-Tetrode absolute zero to the region and especially in the area of T → ∞where it turns S →∞.展开更多
基金Supported by Natural Science Foundation of Shaanxi Province under Grant No. 2007A02the Science Foundation of Baoji University of Science and Arts of China under Grant No. ZK0914
文摘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 （3TC） 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 △= [1 - y∏^ni=1（kT/εi）^1/tiГ（1/ti＋1）] （k is the Boltzmann Constant, T is the thermodynamic temperature, ε is the external field＇s energy）, is obtained. The potential makes the JTC increase when △ 〉 0, on the contrary, it makes the JTC decrease when A 〈△. （iii） In the homogenous strong external potential, the JTC gets the maximum on the condition of kTεi〈〈1.
文摘Based on the analysis of the Boltzmann＇s distribution in an infinitely high temperature found degeneration of the thermodynamic system in a purely informational with independently of each particle on its energy level, thus providing them full visibility of and the ability to calculate the maximum entropy in the Boltzmann formula S∞ = R·InNA = 455.251 J/（mol.K）. This value, when expressed in terms of fundamental constants, is itself a physical and chemical constants and mole monatomic ideal gas is unsurpassed in any studied temperature range. For complex substances this limit increases in direct proportion to their atomic. The existence of two limits entropy change--lower, equal to zero according to the third law of thermodynamics, and the top, equal to S∞, makes possible the explicit expression of the temperature dependence of the entropy in the form of an exponentialS=S∞exp[-5030.31p 2/5 /（M3/5T）]（5/2）r e/s∞. rather than in the form of a logarithmic dependence of the infinite by the approximateformula Sakura-Tetrode with which this the dependence is almost identical in the studied temperature range （100-10,000 K）, but not absurd negative entropy in the extrapolation formula Sakura-Tetrode absolute zero to the region and especially in the area of T → ∞where it turns S →∞.
