热力学中吉布斯熵的特色推导与理论计算

The Characteristic Derivation and Theoretical Calculation of Gibbs Entropy in Thermodynamics

摘要: 玻尔兹曼分布和吉布斯熵是统计物理的重要概念，在热力学教学过程中导出统计熵的方法较多，但抽象难理解。为了提供一种简短且易理解和掌握吉布斯熵的方法，首先从统计力学假设出发，推导出微观子系统的玻尔兹曼分布，再计算一些统计量的导数，通过对比经典的热力学方程，从而导出吉布斯统计熵表达式。其次，从微观到宏观两个视角，以Si和SiC材料为例，计算并讨论了不同压强、温度对吉布斯熵、自由能、德拜温度等的影响。

Abstract: Boltzmann distribution and Gibbs entropy are important concepts in statistical physics, and there are many methods for deriving statistical entropy in thermodynamic teaching process, but they are abstract and difficult to understand. In order to provide a concise and easy to understand method for mastering Gibbs entropy, a characteristic derivation is proposed from the fundamental postulate of statistical mechanics, deriving the Boltzmann distribution of microscopic subsystems, and then calculates the derivatives of some statistical variables. By comparing classical thermodynamic equations, the Gibbs statistical entropy expression is derived. In addition, from micro to macro viewpoints, taking Si and SiC materials as examples, the effects of different pressures and temperatures on Gibbs entropy, free energy and Debye temperature are calculated and discussed.