boltzmann endue(赋予) the entropy an statistical meaning 宏观的熵 .ppt

The meaning of g For instance, the spin of a particle is s, the projection of the spin in any direction have 2s+1 different values(-s, -s+1, … s-1,s). In this case g = 2s+1. The light quantum, photon, has not spin, but has two vibrational directions, g = 2. The photon is Boson. The electron, the Fermion, g = 2s+1 = 2. Three distributions The important distinction(差异)。 For the boson and fermion, a can be solved by the comparison with the experiment results of Cv. The discussion of Maxwell-Boltzmann distribution The situation is quite different for the Maxwell-Boltzmann distribution. The chemical potential and the cell volume are presented in the same form: exp(?/T)/a. But two others Distinction The energy depends on ? and, consequently, (从而) on a。For the exact statistical Fermi-Dirac and Bose-Einstein distribution, the volume of a cell is not arbitrary: exactly by laws of nature and by experiment. Impossible in the case of small occupation numbers, because of the phase volume of a cell acquires arbitrary value. 在此情况下，可以考虑用经典分布替代量子分布。在什么情况下可以替代，标准如何？ The criterion of validity of the Maxwell-Boltzmann distribution In the case of mono-atomic ideal gas 能量依赖于动量，细分球形动量空间得到： 已知Maxwell-Boltzmann 分布的有效性为： 对于一个单原子气体，一个元胞的体积为a = h3,(Planck’s constant), and g = 1 The criterion of validity of the Maxwell-Boltzmann distribution is The criterion are low density, high temperature, and large molecular masses m. 简并条件 The reverse criterion The MB distribution is inapplicable; The gas obeys the BE or FD distribution. The gas is then said to be “degenerate”(简并) Eq.(37.9) is known as the “degeneracy criterion” For a gas: at low temperatures shows “quantum” and at high temperatures shows “classical”. Examples For the ordinary atoms, N/V~1019cm-3, m ~ ( 10-23 to 10-24 )g, T10-1K as quantum. For ordinary gases, the normal MB distribution is a good approximation down to rather low temperatures. 随着低温技术的提高，最近几年统计物理学的主要研究内容是极低温下气体所表现出的量子效应“玻色凝聚”。 由于电子的质量仅为10-27g, 临界温度高达104K。 2)