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The first theory of the conversion of heat into mechanical work is due to Nicolas Léonard Sadi Carnot in 1824. He was the first to realize correctly that the efficiency of this conversion depends on the difference of temperature between an engine and its environment.
The first theory of the conversion of heat into mechanical work is due to Nicolas Léonard Sadi Carnot in 1824. He was the first to realize correctly that the efficiency of this conversion depends on the difference of temperature between an engine and its environment.
<font color = 'blue'>卡诺在1824年提出热</font><font color = 'red'><s>首先提出类热</s></font>转化为机械功的<font color = 'blue'>第一个</font>理论。他<font color = 'blue'>是第一个</font>正确认识到了转换效率取决于发动机和环境之间的温差<font color = 'blue'>的人</font>。
Recognizing the significance of James Prescott Joule's work on the conservation of energy, Rudolf Clausius was the first to formulate the second law during 1850, in this form: heat does not flow spontaneously from cold to hot bodies. While common knowledge now, this was contrary to the caloric theory of heat popular at the time, which considered heat as a fluid. From there he was able to infer the principle of Sadi Carnot and the definition of entropy (1865).
Recognizing the significance of James Prescott Joule's work on the conservation of energy, Rudolf Clausius was the first to formulate the second law during 1850, in this form: heat does not flow spontaneously from cold to hot bodies. While common knowledge now, this was contrary to the caloric theory of heat popular at the time, which considered heat as a fluid. From there he was able to infer the principle of Sadi Carnot and the definition of entropy (1865).
克劳修斯Rudolf Clausius 认识到詹姆斯•普雷斯科特•焦耳James Prescott Joule在能量守恒方面工作的重要性后，在1850年第一个提出了第二定律: 热不会自发地从冷物体流向热物体。虽然现在的常识是这样的，但是这与当时流行的热量理论相反，当时的热量理论认为热量是一种流体。从这些他能够推断出萨迪卡诺定律the principle of Sadi Carnot和熵的定义(1865年)。
'''<font color="#ff8000">克劳修斯Rudolf Clausius </font>'''认识到'''<font color="#ff8000">焦耳James Prescott Joule</font>'''在能量守恒方面工作的重要性后，在1850年<font color = 'red'><s>第一个提出了第二定律</s></font><font color = 'blue'>提出了第二定律的第一个公式，在这个公式中</font>: 热不会自发地从冷物体流向热物体。虽然<font color = 'red'><s>现在的常识是这样的</s></font><font color = 'blue'>现在这是常识</font>，但是这与当时流行的热理论相反，当时的热理论认为热是一种流体。从这些他推断出了'''<font color="#ff8000"> 萨迪卡诺定律the principle of Sadi Carnot</font>'''和熵的定义(1865年)。
Established during the 19th century, the Kelvin-Planck statement of the Second Law says, "It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work." This was shown to be equivalent to the statement of Clausius.
Established during the 19th century, the Kelvin-Planck statement of the Second Law says, "It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work." This was shown to be equivalent to the statement of Clausius.
<font color = 'red'><s>19世纪提出的开尔文-普朗克第二定律(Kelvin-Planck)表示：“任何循环运行的设备都不可能从单个蓄热体接收热量并产生净功。”这被证明相当于克劳修斯的陈述。</s></font><font color = 'blue'>19世纪提出的开尔文-普朗克第二陈述(Kelvin-Planck)表示：“任何循环运行的设备都不可能从单个热源接收热并产生净功。”这被证明与克劳修斯的陈述等价。</font>
The [[ergodic hypothesis]] is also important for the [[Boltzmann]] approach. It says that, over long periods of time, the time spent in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e. that all accessible microstates are equally probable over a long period of time. Equivalently, it says that time average and average over the statistical ensemble are the same.
The [[ergodic hypothesis]] is also important for the [[Boltzmann]] approach. It says that, over long periods of time, the time spent in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e. that all accessible microstates are equally probable over a long period of time. Equivalently, it says that time average and average over the statistical ensemble are the same.
The ergodic hypothesis is also important for the Boltzmann approach. It says that, over long periods of time, the time spent in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e. that all accessible microstates are equally probable over a long period of time. Equivalently, it says that time average and average over the statistical ensemble are the same.
The ergodic hypothesis is also important for the Boltzmann approach. <font color = 'green'>It says that, over long periods of time, the time spent in some region of the phase space of microstates with the same energy is proportional to the volume of this region, i.e. that all accessible microstates are equally probable over a long period of time.</font> Equivalently, it says that time average and average over the statistical ensemble are the same.
'''<font color="#ff8000">遍历假设ergodic hypothesis</font>'''对'''<font color="#ff8000">玻尔兹曼方法Boltzmann approach</font>'''也很重要。<font color = 'blue'>遍历假设认为</font>在很长一段时间内，在具有相同能量的微观态相空间的某些区域所花费的时间与这个区域的体积成正比，即在很长一段时间内，所有可访问的微观状态<font color = 'blue'>出现/成立</font>的可能性都是一样的。<font color = 'red'><s>同样的，</s></font><font color = 'blue'>等价于说，</font>它表明时间平均值和统计集合的平均值是相同的。
There is a traditional doctrine, starting with Clausius, that entropy can be understood in terms of molecular 'disorder' within a macroscopic system. This doctrine is obsolescent.
There is a traditional doctrine, starting with Clausius, that entropy can be understood in terms of molecular 'disorder' within a macroscopic system. This doctrine is obsolescent.
克劳修斯还提出了一种传统的学说，他认为熵可以被理解为宏观系统中的'''<font color = '#ff8000'>分子“无序”molecular 'disorder'</font>'''，但这种学说已经过时了。
===Account given by Clausius===
===Account given by Clausius===
In 1856, the German physicist Rudolf Clausius stated what he called the "second fundamental theorem in the mechanical theory of heat" in the following form:
In 1856, the German physicist Rudolf Clausius stated what he called the "second fundamental theorem in the mechanical theory of heat" in the following form:
1856年，德国物理学家'''<font color = '#ff8000'>鲁道夫 • 克劳修斯Rudolf Clausius </font>'''阐述了他所谓的“热力学理论中的第二个基本定理second fundamental theorem in the mechanical theory of heat” ，其形式如下:
<math>\int \frac{\delta Q}{T} = -N</math>
<math>\int \frac{\delta Q}{T} = -N</math>
- n / math
<math>\int \frac{\delta Q}{T} = -N</math>
where Q is heat, T is temperature and N is the "equivalence-value" of all uncompensated transformations involved in a cyclical process. Later, in 1865, Clausius would come to define "equivalence-value" as entropy. On the heels of this definition, that same year, the most famous version of the second law was read in a presentation at the Philosophical Society of Zurich on April 24, in which, in the end of his presentation, Clausius concludes:
where Q is heat, T is temperature and N is the "equivalence-value" of all uncompensated transformations involved in a cyclical process. Later, in 1865, Clausius would come to define "equivalence-value" as entropy. On the heels of this definition, that same year, the most famous version of the second law was read in a presentation at the Philosophical Society of Zurich on April 24, in which, in the end of his presentation, Clausius concludes:
其中 q 是热，t 是温度，n 是一个循环过程中所有未补偿的相变的“等价值”。后来在1865年，克劳修斯将“等价值”定义为熵。也就是在同一年，第二定律最著名的版本在4月24日苏黎世哲学学会的一次演讲中被宣读，在演讲的最后克劳修斯总结道:
其中 Q 是热，T 是温度，N 是一个循环过程中所有<font color = 'red'><s>未补偿</s></font><font color = 'blue'>非补偿</font>的相变的“等价值”。后来在1865年，克劳修斯将“等价值”定义为熵。<font color = 'red'><s>也就是在</s></font><font color = 'blue'>基于这个理论，</font>同一年，第二定律最著名的版本在4月24日苏黎世哲学学会的一次演讲中被<font color = 'red'><s>宣读</s></font><font color = 'blue'>提出</font>，在演讲的最后克劳修斯总结道:
This statement is the best-known phrasing of the second law. Because of the looseness of its language, e.g. universe, as well as lack of specific conditions, e.g. open, closed, or isolated, many people take this simple statement to mean that the second law of thermodynamics applies virtually to every subject imaginable. This is not true; this statement is only a simplified version of a more extended and precise description.
This statement is the best-known phrasing of the second law. Because of the looseness of its language, e.g. universe, as well as lack of specific conditions, e.g. open, closed, or isolated, many people take this simple statement to mean that the second law of thermodynamics applies virtually to every subject imaginable. This is not true; this statement is only a simplified version of a more extended and precise description.
这句话是第二定律最著名的<font color = 'red'><s>措辞</s></font><font color = 'blue'>陈述</font>。由于其语言松散<font color = 'blue'>模糊</font>，如“宇宙universe”，<font color = 'red'><s>与缺乏具体的条件相同</s></font><font color = 'blue'>和缺乏具体的条件</font>，如“开放open”，“封闭closed”，或“孤立isolated”，许多人认为这一简单的陈述意味着热力学第二定律几乎适用于每一个可以想象的<font color = 'red'><s>学科</s></font><font color = 'blue'><主题/font>。这不是真的；这句话只是一个更广泛和更精确的描述的简化版本。
In terms of time variation, the mathematical statement of the second law for an isolated system undergoing an arbitrary transformation is:
In terms of time variation, the mathematical statement of the second law for an isolated system undergoing an arbitrary transformation is:
就时间变化而言，<font color = 'blue'>一个</font>经历任意变换的孤立系统<font color = 'blue'>的</font>第二定律的数学表述是:
<math>\frac{dS}{dt} \ge 0</math>
<math>\frac{dS}{dt} \ge 0</math>
0 / math
<math>\frac{dS}{dt} \ge 0</math>
where
where
这里''S'' 是系统的熵
The equality sign applies after equilibration. An alternative way of formulating of the second law for isolated systems is:
The equality sign applies after equilibration. An alternative way of formulating of the second law for isolated systems is:
平衡后用等号。另一种表述孤立系统第二定律的方法是：
<math>\frac{dS}{dt} = \dot S_{i}</math> with <math> \dot S_{i} \ge 0</math>
<math>\frac{dS}{dt} = \dot S_{i}</math> with <math> \dot S_{i} \ge 0</math>
<math>\frac{dS}{dt} = \dot S_{i}</math> with <math> \dot S_{i} \ge 0</math>
==here==
with <math> \dot S_{i}</math> the sum of the rate of [[entropy production]] by all processes inside the system. The advantage of this formulation is that it shows the effect of the entropy production. The rate of entropy production is a very important concept since it determines (limits) the efficiency of thermal machines. Multiplied with ambient temperature <math>T_{a}</math> it gives the so-called dissipated energy <math> P_{diss}=T_{a}\dot S_{i}</math>.
with <math> \dot S_{i}</math> the sum of the rate of [[entropy production]] by all processes inside the system. The advantage of this formulation is that it shows the effect of the entropy production. The rate of entropy production is a very important concept since it determines (limits) the efficiency of thermal machines. Multiplied with ambient temperature <math>T_{a}</math> it gives the so-called dissipated energy <math> P_{diss}=T_{a}\dot S_{i}</math>.