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## Application of the Thermodynamic Equations in Calculating the Thermodynamic Functions

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Abstract

The thermodynamic equation includes basic thermodynamic equations, the thermodynamic state equations, and Gibbs-Helmholtz equations. In this paper, we derived the other thermodynamic state equations which are rarely mentioned in physical chemistry teaching materials. At the same time, we emphasized the systematic characteristics and the completeness of the thermodynamic theory. Furthermore, the application of surface chemistry was concluded from the first Gibbs-Helmholtz equations. Finally, we emphasized the relations between the characteristic variables and the reaction conditions.

Keywords： Maxwell′s relations ; Characteristic variable ; Basic thermodynamic equation ; Thermodynamic state equation ; Gibbs-Helmholtz equation

ZHU Yuan-Ju. Application of the Thermodynamic Equations in Calculating the Thermodynamic Functions. University Chemistry[J], 2017, 32(5): 81-88 doi:10.3866/PKU.DXHX201610031

## 4 热力学焓态方程在一般变化中的应用

【例】试求水从25 ℃、0.1 MPa变化到45 ℃、50 MPa的焓变。

【解】从物理化学手册查到水的有关数据为：

Cp≈ 75.30 J∙K－1∙mol－1V ≈ 18.0 × 10－6 m3∙mol－1α ≈ 3.5 × 10－4 K－1

ΔH = 75.30 × 20 + 18.0 × 10－6 × (1 － 20 × 3.5 × 10－4) × 50 × 106 J∙mol－1 = 2.406 × 103 J∙mol－1

### 5.1 吉布斯-亥姆霍兹第一方程的导出

$\begin{gathered} {\left( {\frac{{\partial A}}{{\partial T}}} \right)_V} =-S \hfill \\ {\left( {\frac{{\partial A}}{{\partial V}}} \right)_T} =-p \hfill \\ \end{gathered}$

### 6.2 等压化学反应中吉布斯自由能随温度的变化

Gibbs自由能实质上就是化学亲和势，是化学反应的推动力，因而主要用于研究化学反应系统。在讨论化学反应问题时，常常需要由某一温度下的反应自由能∆rG(T1)计算另一温度下的反应自由能∆rG(T2)，即有：

Cp(B)为纯物质的热容量，物质的热容量一般只是温度的函数，下式是对气体、液体或固体普遍适用的关系式：

### 6.3 吉布斯自由能G(T, p)的一般计算公式

G-H方程可得等压p0条件下的G函数：

${p_0} = {p^\theta }$，得：

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