能态方程多种形式的证明

On Some Proof Forms of Energy State Equation

能态方程是热力学中一个重要的基本方程,它给出了在温度保持不变时内能随体积的变化率与物态方程偏导数之间的关系,本文利用全微分和复合函数的性质、雅克比行列式、循环关系、特性函数、经典统计方法等对能态方程进行了多种形式的证明。

Energy state equation is an important basic equation in Thermodynamics, which gives the relation between equation of state and the derivative of internal energy with respect to volume at constant temperature. The energy state equation is testified by various forms such asutilizing total differential, composite function, Jacobian transformation and circular relation, characteristic function and classical statistical physics and so on.