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The second law of thermodynamics may be expressed in many specific ways, the most prominent classical statements being the statement by Rudolf Clausius (1854), the statement by Lord Kelvin (1851), and the statement in axiomatic thermodynamics by Constantin Carathéodory (1909). These statements cast the law in general physical terms citing the impossibility of certain processes. The Clausius and the Kelvin statements have been shown to be equivalent.

The second law of thermodynamics may be expressed in many specific ways, the most prominent classical statements being the statement by Rudolf Clausius (1854), the statement by Lord Kelvin (1851), and the statement in axiomatic thermodynamics by Constantin Carathéodory (1909). These statements cast the law in general physical terms citing the impossibility of certain processes. The Clausius and the Kelvin statements have been shown to be equivalent.

热力学第二定律可以用许多特定的方式来表达，最突出的经典陈述是 '''克劳修斯 Rudolf Clausius''' (1854)<font color = 'red'><s>陈述</s></font><font color = 'blue'>表述</font>，'''开尔文 Kelvin''' (1851)<font color = 'red'><s>陈述</s></font><font color = 'blue'>表述</font>，以及康斯坦丁·卡拉西奥多里 Constantin Carathéodory(1909)在'''<font color = '#ff8000'>公理化热力学axiomatic thermodynamics</font>'''中的<font color = 'red'><s>陈述</s></font><font color = 'blue'>表述</font>。这些<font color = 'red'><s>陈述</s></font><font color = 'blue'>表述</font>用一般的物理术语来描述定律，引用某些过程的不可能性。克劳修斯和开尔文表述被证明是等价的。

热力学第二定律可以用许多特定的方式来表达，最突出的经典陈述是 '''克劳修斯 Rudolf Clausius''' (1854)表述，'''开尔文 克劳修斯 Kelvin Clausius''' (1851)表述，以及康斯坦丁·卡拉西奥多里 Constantin Carathéodory(1909)在'''<font color = '#ff8000'>公理化热力学axiomatic thermodynamics</font>'''中的表述。这些表述用一般的物理术语来描述定律，引用某些过程的不可能性。克劳修斯和开尔文表述被证明是等价的。

热力学第二定律的历史起源是'''卡诺原理Carnot's principle'''。

热力学第二定律的历史起源是'''卡诺原理Carnot's principle'''。

它指的是'''<font color = '#ff8000'>卡诺热机Carnot heat engine</font>'''的一个循环，<font color = 'red'><s>它</s></font><font color = 'blue'>卡诺热机</font>以'''<font color = '#ff8000'>准静态quasi-static</font>'''的极限慢速运转，因此热<s>量</s>和功在子系统之间进行传递，子系统总是处于它们自己内部的热力学平衡状态。

它指的是'''<font color = '#ff8000'>卡诺热机Carnot heat engine</font>'''的一个循环，卡诺热机以'''<font color = '#ff8000'>准静态quasi-static</font>'''的极限慢速运转，因此热和功在子系统之间进行传递，子系统总是处于它们自己内部的热力学平衡状态。

卡诺热机是研究热机效率的工程师特别感兴趣的理想装置。

卡诺热机是研究热机效率的工程师特别感兴趣的理想装置。

当卡诺发现卡诺原理时，'''<font color = '#ff8000'>热量理论caloric theory of heat</font>'''还没有得到重视，热力学第一定律还没有得到承认，熵的概念还没有数学表达。

当卡诺发现卡诺原理时，'''<font color = '#ff8000'>热量理论caloric theory of heat</font>'''还没有得到重视，热力学第一定律还没有得到承认，熵的概念还没有数学表达。

The production of motive power is then due in steam engines not to an actual consumption of caloric, but to its transportation from a warm body to a cold body ...

The production of motive power is then due in steam engines not to an actual consumption of caloric, but to its transportation from a warm body to a cold body ...

The motive power of heat is independent of the agents employed to realize it; its quantity is fixed solely by the temperatures of the bodies between which is effected, finally, the transfer of caloric.

The motive power of heat is independent of the agents employed to realize it; its quantity is fixed solely by the temperatures of the bodies between which is effected, finally, the transfer of caloric.

In modern terms, Carnot's principle may be stated more precisely:

In modern terms, Carnot's principle may be stated more precisely:

用现代术语<font color = 'red'><s>来说</s></font>，卡诺原理可能更为准确:

用现代术语，卡诺原理可能更为准确:

The efficiency of a quasi-static or reversible Carnot cycle depends only on the temperatures of the two heat reservoirs, and is the same, whatever the working substance. A Carnot engine operated in this way is the most efficient possible heat engine using those two temperatures.

The efficiency of a quasi-static or reversible Carnot cycle depends only on the temperatures of the two heat reservoirs, and is the same, whatever the working substance. A Carnot engine operated in this way is the most efficient possible heat engine using those two temperatures.

准静态卡诺循环或可逆卡诺循环的效率只取决于两种热源的温度，而且无论工作物质是什么，效率是相同的。<font color = 'red'><s>只有</s></font><font color = 'blue'>使用</font>两个热源与工作物质交换热源（一个高温热源温度<math>T_1</math>和一个低温热源温度<math>T_2</math>)的卡诺热机是最有效的热机。

准静态卡诺循环或可逆卡诺循环的效率只取决于两种热源的温度，而且无论工作物质是什么，效率是相同的。使用两个热源与工作物质交换热源（一个高温热源温度<math>T_1</math>和一个低温热源温度<math>T_2</math>)的卡诺热机是最有效的热机。

'''<font color="#32CD32">使用两个热源与工作物质交换热源（一个高温热源温度<math>T_1</math>和一个低温热源温度<math>T_2</math>)的卡诺热机是最有效的热机。 A Carnot engine operated in this way is the most efficient possible heat engine using those two temperatures.</font>'''  

'''<font color="#32CD32">使用两个热源与工作物质交换热源（一个高温热源温度<math>T_1</math>和一个低温热源温度<math>T_2</math>)的卡诺热机是最有效的热机。 A Carnot engine operated in this way is the most efficient possible heat engine using those two temperatures.</font>'''  

===Clausius statement克劳修斯表述===

===Clausius statement克劳修斯表述===

The German scientist Rudolf Clausius laid the foundation for the second law of thermodynamics in 1850 by examining the relation between heat transfer and work. His formulation of the second law, which was published in German in 1854, is known as the Clausius statement:

The German scientist Rudolf Clausius laid the foundation for the second law of thermodynamics in 1850 by examining the relation between heat transfer and work. His formulation of the second law, which was published in German in 1854, is known as the Clausius statement:

1850年，德国科学家'''鲁道夫·克劳修斯 Rudolf Clausius''' 通过研究热传递和功之间的关系，为热力学第二定律<font color = 'red'><s>实验室</s></font>奠定了基础。他在1854年用德语发表的论文中所提及的热力学第二定律定义被称为克劳修斯表述:

1850年，德国科学家'''鲁道夫·克劳修斯 Rudolf Clausius''' 通过研究热传递和功之间的关系，为热力学第二定律奠定了基础。他在1854年用德语发表的论文中所提及的热力学第二定律定义被称为克劳修斯表述:

<blockquote>Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.</blockquote>

<blockquote>Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time.</blockquote>

The statement by Clausius uses the concept of 'passage of heat'. As is usual in thermodynamic discussions, this means 'net transfer of energy as heat', and does not refer to contributory transfers one way and the other.

The statement by Clausius uses the concept of 'passage of heat'. As is usual in thermodynamic discussions, this means 'net transfer of energy as heat', and does not refer to contributory transfers one way and the other.

克劳修斯的表述使用了“'''<font color = '#ff8000'>热通道Passage Of Heat</font>'''”的概念。<font color = 'red'><s>正如通常在热力学的讨论，这意味着“能量作为热的净转移” ，而不是另一种形式上的"分摊转账"或其他。</s></font><font color = 'blue'>

克劳修斯的表述使用了“'''<font color = '#ff8000'>热通道Passage Of Heat</font>'''”的概念。

在热力学的讨论中，通常这意味着“能量作为热的形式的净转移” ，而不是指其他方式的转移。</font>

在热力学的讨论中，通常这意味着“能量作为热的形式的净转移” ，而不是指其他方式的转移。

   --[[用户:趣木木|趣木木]]（[[用户讨论:趣木木|讨论]]）不太理解分摊转账contributory transfers

    

Heat cannot spontaneously flow from cold regions to hot regions without external work being performed on the system, which is evident from ordinary experience of refrigeration, for example. In a refrigerator, heat flows from cold to hot, but only when forced by an external agent, the refrigeration system.

Heat cannot spontaneously flow from cold regions to hot regions without external work being performed on the system, which is evident from ordinary experience of refrigeration, for example. In a refrigerator, heat flows from cold to hot, but only when forced by an external agent, the refrigeration system.

===Kelvin statements开尔文表述===

===Kelvin statements开尔文表述===

Lord Kelvin expressed the second law in several wordings.

Lord Kelvin expressed the second law in several wordings.

'''<font color = '#ff8000'>开尔文勋爵 Lord Kelvin</font>''' <font color = 'red'><s>用几个字表达</s></font><font color = 'blue'>表述</font>了热力学第二定律。

'''<font color = '#ff8000'>开尔文勋爵 Lord Kelvin</font>''' 表述了热力学第二定律。

It is impossible for a self-acting machine, unaided by any external agency, to convey heat from one body to another at a higher temperature.

It is impossible for a self-acting machine, unaided by any external agency, to convey heat from one body to another at a higher temperature.

<font color = 'red'><s>无法从单一热源取热使其完全转化为有用功而不对环境产生影响。</s></font><font color = 'blue'>不可能从单一热源取热使之完全转换为有用的功而不产生其他影响。</font>

不可能从单一热源取热使之完全转换为有用的功而不产生其他影响。

It is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects.

It is impossible, by means of inanimate material agency, to derive mechanical effect from any portion of matter by cooling it below the temperature of the coldest of the surrounding objects.

Suppose there is an engine violating the Kelvin statement: i.e., one that drains heat and converts it completely into work in a cyclic fashion without any other result. Now pair it with a reversed Carnot engine as shown by the figure. The efficiency of a normal heat engine is η and so the efficiency of the reversed heat engine is 1/η. The net and sole effect of the combined pair of engines is to transfer heat from <math>\Delta Q=Q\left(\frac{1}{\eta}-1\right)</math> the cooler reservoir to the hotter one, which violates the Clausius statement. (This is a consequence of the first law of thermodynamics, as for the total system's energy to remain the same, <math> \text{Input}+\text{Output}=0 \implies Q-\frac{Q}{\eta} = -Q_c </math>, so therefore <math> Q_c=Q\left( \frac{1}{\eta}-1\right) </math> ). Thus a violation of the Kelvin statement implies a violation of the Clausius statement, i.e. the Clausius statement implies the Kelvin statement. We can prove in a similar manner that the Kelvin statement implies the Clausius statement, and hence the two are equivalent.

Suppose there is an engine violating the Kelvin statement: i.e., one that drains heat and converts it completely into work in a cyclic fashion without any other result. Now pair it with a reversed Carnot engine as shown by the figure. The efficiency of a normal heat engine is η and so the efficiency of the reversed heat engine is 1/η. The net and sole effect of the combined pair of engines is to transfer heat from <math>\Delta Q=Q\left(\frac{1}{\eta}-1\right)</math> the cooler reservoir to the hotter one, which violates the Clausius statement. (This is a consequence of the first law of thermodynamics, as for the total system's energy to remain the same, <math> \text{Input}+\text{Output}=0 \implies Q-\frac{Q}{\eta} = -Q_c </math>, so therefore <math> Q_c=Q\left( \frac{1}{\eta}-1\right) </math> ). Thus a violation of the Kelvin statement implies a violation of the Clausius statement, i.e. the Clausius statement implies the Kelvin statement. We can prove in a similar manner that the Kelvin statement implies the Clausius statement, and hence the two are equivalent.

假设有一个热机违反了开尔文定理: 也就是说，这个热机以循环的方式吸收热<s>量</s>并将其<font color = 'blue'>完全</font>转化为功，而<font color = 'blue'>且</font>不产生任何影响。现<font color = 'blue'>在将其</font>与反向卡诺<font color = 'red'><s>发动</s></font>机<font color = 'red'><s>相对应</s></font><font color = 'blue'>比较</font>，如图所示。

假设有一个热机违反了开尔文定理: 也就是说，这个热机以循环的方式吸收热并将其完全转化为功，而且不产生任何影响。现在将其与反向卡诺机相比较，如图所示。

普通热机的效率为η，反向热机的效率为1/η。这对<font color = 'red'><s>热机的联合作用为</s></font><font color = 'blue'>联合热机的净效应和唯一效应是</font><math>\Delta Q=Q\left(\frac{1}{\eta}-1\right)</math> 将热<s>量</s>从较冷热源<font color = 'blue'>转移</font>到较热热源，这违反了克劳修斯表述。（这是能量守恒定律的结果，因为系统的总能量保持不变<math> \text{Input}+\text{Output}=0 \implies Q-\frac{Q}{\eta} = -Q_c </math>，所以<math> Q_c=Q\left( \frac{1}{\eta}-1\right) </math>。）因此，违反开尔文表述意味着违反克劳修斯表述，即克劳修斯表述暗示了开尔文表述。我们可以用类似的方式证明开尔文表述暗示了克劳修斯表述，因此两者是等价的。

普通热机的效率为η，反向热机的效率为1/η。这对联合热机的净效应和唯一效应是</font><math>\Delta Q=Q\left(\frac{1}{\eta}-1\right)</math> 将热从较冷热源转移到较热热源，这违反了克劳修斯表述。（这是能量守恒定律的结果，因为系统的总能量保持不变<math> \text{Input}+\text{Output}=0 \implies Q-\frac{Q}{\eta} = -Q_c </math>，所以<math> Q_c=Q\left( \frac{1}{\eta}-1\right) </math>。）因此，违反开尔文表述意味着违反克劳修斯表述，即克劳修斯表述暗示了开尔文表述。我们可以用类似的方式证明开尔文表述暗示了克劳修斯表述，因此两者是等价的。

===Planck's proposition普朗克<font color = 'red'><s>假设</s></font><font color = 'blue'>命题</font>===

===Planck's proposition普朗克命题===

It is impossible to construct an engine which will work in a complete cycle, and produce no effect except the raising of a weight and cooling of a heat reservoir.

It is impossible to construct an engine which will work in a complete cycle, and produce no effect except the raising of a weight and cooling of a heat reservoir.

'''<font color="#32CD32">写成广泛性质（质量，体积，熵……）的函数时，第二定律被证明等价于弱凸函数内能 U。The second law has been shown to be equivalent to the internal energy U being a weakly convex function, when written as a function of extensive properties (mass, volume, entropy, ...).</font>'''

'''<font color="#32CD32">写成广泛性质（质量，体积，熵……）的函数时，第二定律被证明等价于弱凸函数内能 U。The second law has been shown to be equivalent to the internal energy U being a weakly convex function, when written as a function of extensive properties (mass, volume, entropy, ...).</font>'''

==Corollaries 推论==

==Corollaries 推论==