计算液态混合物内能和内压的统计热力学理论

假定二元液态混合物分子间的相互作用势能可以表示成多体相互作用势能的和,分子间的力为短程力,相互作用势能只与分子间的相对距离有关.利用分布函数理论导出了二元液态混合物的过剩内能和内压的公式.二元液态混合物的过剩内能和内压可以表示成体积的幂级数形式,其中的系数可以用多体相互作用势和多体径向分布函数表出.讨论了单元液体的内压和过剩内能的表达式,在两种特殊情形下,过剩内能和内压的表达式分别与Egelstaff的微扰论结果及Frank的实验结果具有相同的形式.讨论了二元混合物内压和内能的两个特例,其一,在特殊情形下,给出了混合液体过剩内能的混合规则的一个证明.其二,给出的二元混合物的过剩内能和内压的表达式与Frank的实验结果具有相同的形式.

Statistical Thermodynamic Theory of Calculating the Inner Pressure and Inner Energy of the Liquid Mixture

The formulas of inner pressure and excess inner energy of the liquid mixture are derived using distribution function theory. During the derivation three characters of interaction potential energy of the liquid mixture are assumed. The first is that the interaction force between molecules is the short-range force. The second is that the many-body potential is only relying on the distances between the molecules. The third is that the potential energy of the liquid mixture can be written as the sum of a series of many-body potential . The inner pressure and inner energy of the liquid mixture can be expressed in the power series of the volume. The coefficients in the series are expressed in many-body potential and radial distribution functions and are only depend on temperature. The expression of the inner pressure and excess inner energy of pure liquid are discussed. The excess inner energy and inner pressure are agree with the result of Egelstaff′s perturbation theory and Frank′s experiment respectively in two special situations. Two special cases of the liquid mixture are discussed. One of them is that a method to prove the mixing law of the excess inner energy of the liquid mixture in special situation. The other is that the expressions of excess inner energy and the inner pressure have the same form with the result of Frank′s experiment.