Adv-thermodynamics-5化工热力学书.pptVIP

分布函数理论基础 引言 分布函数及其统计力学基础 分布函数的统计力学基础 流体的化学位: * * 定义一个函数 为流体的径向分布函数，物理意义是：与一指定分子相距r处，流体分子的局部密度与平均密度之比 The h-body correlation function Some basic points: in the absence of external potential, the n-body distribution function are independent of the choice of origin. The distribution function is isotropic In a uniform fluid with no external forces, all distribution functions are translational invariant. The properties of distribution functions Recursion relation Normalization relation The ideal gas limit Limit of large separation Other correlation function 1. Total correlation function: 2. Background correlation function: Revisiting the meaning of g (r) Given a molecule in the differential volume dr1 at a position r1, the probability of finding any one of the N-1 remaining molecules in dr2 at r2 is, By a variable transformation, the probability that a specific molecule is We let the given molecule move over the entire volume. Integration of the above equation This equation gives the probability that a second molecule is to be found in a differential volume at a position from the central molecule For g(2) independent of orientation, we could form a spherical shell of thickness dr at a distance r from the central molecule This expression gives the number of molecules in the spherical shell of thickness dr at a distance r from the central molecule. Integration over a coordination distance L gives the so-called coordination number N(L) counts the number of molecule inside a sphere of radius L surrounding the central molecule. Namely, it is a counter of neighbor. 径向分布函数与流体热力学性质 1. 流体的能量 已知在正则系综中,系统的能量可用下式表示 其中正则配分函数可表示为 对于N个单原子分子构成的经典流体,假定流体的势能等于各分子对势能之和 上式就是能量与径向分布函数的关系,也称为能量方程 流体的压力 在正则系综中 引入分布函数: 与Virial状态方程相比, Virial系数为 We denote the Helmholtz free energy of an N-body system as, For system with larger N, we can approximate the derivate by a difference 流体化学位 * * * * *