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## Discussion on Spontaneous Process of Thermodynamics and Its Criteria

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Abstract

Current criteria for spontaneity are used with the confined conditions. The various definitions of spontaneous change show the lack of universality. Here, the first law of thermodynamics was put in the total entropy criterion without any constraints. Then another form of entropy criterion was obtained and discussed. The nature of energy change in thermodynamics processes was summarized based on the characteristics of spontaneous process. As a result, the universal definition of spontaneous process was put forward. The original total entropy criterion can distinguish between the reversible and irreversible processes, but not the spontaneous and non-spontaneous processes. Another form of the entropy criterion, i.e., the exergy criterion for the arbitrary process in the closed system, was proposed. This criterion can distinguish between the spontaneous and non-spontaneous processes. Through the theoretical derivation and the actual examples, we found that the exergy criterion is equivalent to the total entropy criterion. The exergy criterion can be returned to all kinds of direction criteria when using the corresponding limited conditions. In the paper, the spontaneity criteria for the processes with variable temperature or pressure were also given, which have not appeared in the current textbooks. In summary, the universal definition and the exergy criterion can solve the problems arisen from the confusing conception and explanation related to spontaneous processes.

Keywords： Closed system ; Arbitrary process ; Spontaneous change ; Non-spontaneous change ; Exergy ; Criteria for spontaneity

GUO Zi-Cheng, LI Jun-Xin, REN Jie. Discussion on Spontaneous Process of Thermodynamics and Its Criteria. University Chemistry[J], 2016, 31(7): 83-90 doi:10.3866/PKU.DXHX201509017

$\Delta {{S}_{\text{iso}}}=\Delta {{S}_{\text{sys}}}+\Delta {{S}_{\text{sur}}}\ge \left( \begin{matrix} >自发\\ =平衡\\\end{matrix} \right)$

$\Delta {{A}_{T,V,{W}'=0}}\le 0\left( \begin{matrix} ＜自发\\ =平衡\\\end{matrix} \right)$

$\Delta {{A}_{T,P,{W}'=0}}\le 0\left( \begin{matrix} ＜自发\\ =平衡\\\end{matrix} \right)$

### 1.1 由顾名思义引发

“在自然条件下发生的过程就是自发过程”。这样的定义简单易懂，很容易被初学者接受，但后来人们发现它并不十分准确[15]。例如绿色植物在阳光下的光合作用，就是在自然条件下发生的，是个复杂的过程，很难从单纯的热力学角度来解释它是一个自发过程，因为过程中有光能的参与，光能被认为是非体积功的一种形式。

“自发过程的特征”是不可逆，所以“一切不可逆过程都是自发过程”。这样的概念在很多物理化学学习者的头脑中存在过。由于很多热力学教材在介绍热力学第二定律时从来都不明确提及非自发过程，因此这样的问题由来已久，已经困扰人们多年，不过近几年人们已经有了共识[16]：自发过程一定是不可逆过程，不可逆过程不一定都是自发过程，因为还有非自发过程。因此有文献[19]将不可逆过程称作“能发生过程”。能发生过程就是自然发生的或人为帮助发生的一切实际过程。

### 2.2 总熵判据的另一种形式

$\text{d}U+{{p}_{\text{sur}}}\text{d}V-{{T}_{\text{sur}}}\text{d}S\le \delta {W}'\left( \begin{matrix} ＜不可逆，能发生\\ =可逆，平衡\\\end{matrix} \right)$

(i)系统无非体积功，即δW' = 0时有：dU + psurdV-TsurdS ＜ 0，若过程中系统没有得到环境的帮助，系统能发生的过程一定是自发过程。有做功能力是自发过程的特征之一，若系统还能向环境做出非体积功，即δW' ＜ 0时也应该包含在自发过程之中。综合两者说明，在无非体积功和系统能向环境做出非体积功时，系统能发生的过程一定都是自发过程。因此得自发过程判据为：

$\text{d}U+{{p}_{\text{sur}}}\text{d}V-{{T}_{\text{sur}}}\text{d}S ＜0\left(自发,条件是\delta {W}'\le 0 \right)$

(ii)当过程中环境向系统提供可用能量，并满足δW' > dU + psurdV-TsurdS时发生非自发过程，非自发过程方向与自发过程方向相反，dU + psurdV-TsurdS > 0，综合两者得非自发过程判据为：

$\delta {W}'>\text{d}U+{{p}_{\text{sur}}}\text{d}V-{{T}_{\text{sur}}}\text{d}S>0\left(非自发\right)$

$\left. \begin{matrix} \text{d}U+{{p}_{\text{sur}}}\text{d}V-{{T}_{\text{sur}}}\text{d}S \\ \text{d}U+{{p}_{\text{sur}}}\text{d}V-{{T}_{\text{sur}}}\text{d}S-\delta {{{{W}'}}_{r}} \\\end{matrix} \right\}=0\left(平衡\right)$

### 3.1 在变温过程中的应用

1)变温恒压时，psur = p，dU + pdV = dH

2)变温恒容时，dV = 0，

3)对于均相无组成变化的封闭系统，将dU = TdS-pdV代入判据中得：

## 参考文献 原文顺序 文献年度倒序 文中引用次数倒序 被引期刊影响因子

Atkins ; P;de Paula ; J Physical Chemistry, 9th ed;W H Freeman and Company:New York, 2010.

Bard,A.J.;Faulkner,L.R.Electrochemical Methods,2nd ed.;John Wiley&Sons Inc.:Hoboken NJ,2001.

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