PARTTWOStatisticalPhysicsChapterIIIStatisticDistrib.pptVIP

PART TWO Statistical Physics Chapter III:Statistic Distributions for ideal gases 32 Statistics Regularities. Distributions, Most Probable Distributions 统计调节。分布，最大概率分布 The main objective of statistical physics: 1 to establish the behavior laws 行为 for macroscopic quantities of a substance. 2 to offer a theoretical substantiation 证实 of thermodynamic laws on the basis of atomic and molecular ideas. Basic Methods Condition : a system consisting of a large number N of molecules 由微观极大数目的粒子构成 . Classical: using Newton’s classical mechanics 经典力学 to describe the state of the system； Quantum: using quantum-mechanical description, the ideal of wave mechanics. Newton’s classical mechanics 经典力学 Ignoring: intramolecular 分子内 structure， to visualize a molecule as a point or particle. The equation of Newton’s motion for each of the N particles. 困 难 与 解 决 方 法 数学计算上的求和的难度，使其几乎不可能。因为系统的粒子数达到1025m-3。 即使知道了粒子的路径和运动方程，也未必能提供以系统作为一个整体有用的信息。 In a system consisting of a great number of particles new purely statistical or probability laws take effect that are foreign to 不适合于 a system containing a small number of particles. 解决的思路 如果不考虑粒子运动的路径，即忽略坐标，只考虑动量或能量。当考虑动量时，为分子运动论，在此不讨论。 当考虑能量时，先用一个简单的模型分析。 每个分子的能量虽然各不相同，若假设如下图 Statistical Method Assumption: It is possible to measure rapidly the energy of each molecule of a gas. The results of such measurement are present graphically in the Figure. Energy Distribution Function and “ Boxes” The relative number of molecules in the range l?0~ l+1 ?0 is denoted by n l : Cell A box which energy l?0~ l+m ?0, m?0 is the length of a box, which varies little. Actually, all the histograms 矩形高度 will be close to some averaged histogram and large deviations from it will be rare. Microstate 微观（运动）状态 To describe the state of a gas at some moment of time: Microstate Classical mechanics: “coordinates 坐标 and velocity” 设粒子的坐标与势能相关，而动能与速度相关： 微观（运动）状态的性质 某一时刻，整个系统的N个粒子构成了一个“微观状态”，如前述的能量-粒子柱形图为能量分布图，或“状态分布”图。下一个时刻，N个粒子的能量 坐标及动量 发生了变化，微观状态也发生了变化。 一个气体分子平移