| 第3行： |
第3行： |
| | | | |
| | | | |
| − |
| |
| − |
| |
| − | The '''Clausius theorem''' (1855) states that for a [[thermodynamic system]] (e.g. [[heat engine]] or [[Heat pump and refrigeration cycle|heat pump]]) exchanging heat with [[Thermal reservoir|external reservoirs]] and undergoing a [[thermodynamic cycle]],
| |
| − |
| |
| − | The Clausius theorem (1855) states that for a thermodynamic system (e.g. heat engine or heat pump) exchanging heat with external reservoirs and undergoing a thermodynamic cycle,
| |
| | | | |
| | '''克劳修斯定理 Clausius theorem'''（1855）指出，对于'''<font color="#ff8000"> 热力学系统 Thermodynamic system </font>'''（例如，热机或热泵），当其与'''<font color="#ff8000"> 外部热库External reservoirs</font>'''进行热交换并经历'''<font color="#ff8000"> 热力学循环Thermodynamic cycle</font>'''时， | | '''克劳修斯定理 Clausius theorem'''（1855）指出，对于'''<font color="#ff8000"> 热力学系统 Thermodynamic system </font>'''（例如，热机或热泵），当其与'''<font color="#ff8000"> 外部热库External reservoirs</font>'''进行热交换并经历'''<font color="#ff8000"> 热力学循环Thermodynamic cycle</font>'''时， |
| 第14行： |
第9行： |
| | :<math>\oint \frac{\delta Q}{T_{\text{surr}}} \leq 0,</math> | | :<math>\oint \frac{\delta Q}{T_{\text{surr}}} \leq 0,</math> |
| | | | |
| − |
| |
| − | where <math>\delta Q</math> is the infinitesimal amount of heat absorbed by the system from the reservoir and <math>T_{\text{surr}}</math> is the [[temperature]] of the external reservoir (surroundings) at a particular instant in time. The closed integral is carried out along a [[thermodynamic process path]] from the initial/final state to the same initial/final state. In principle, the closed integral can start and end at an arbitrary point along the path.
| |
| − |
| |
| − | where <math>\delta Q</math> is the infinitesimal amount of heat absorbed by the system from the reservoir and <math>T_{\text{surr}}</math> is the temperature of the external reservoir (surroundings) at a particular instant in time. The closed integral is carried out along a thermodynamic process path from the initial/final state to the same initial/final state. In principle, the closed integral can start and end at an arbitrary point along the path.
| |
| | | | |
| | 其中<math>\delta Q</math>是系统从热库吸收的热量极小值，<math>T_{\text{surr}}</math>是特定时间点外部热库（周围环境）的温度。该表达式是指，沿着'''<font color="#ff8000"> 热力学过程路径 Thermodynamic process path</font>'''（从初始/最终状态到相同的初始/最终状态下）所执行的闭合积分。原则上，该闭合积分可以沿路径的任意点开始和结束。 | | 其中<math>\delta Q</math>是系统从热库吸收的热量极小值，<math>T_{\text{surr}}</math>是特定时间点外部热库（周围环境）的温度。该表达式是指，沿着'''<font color="#ff8000"> 热力学过程路径 Thermodynamic process path</font>'''（从初始/最终状态到相同的初始/最终状态下）所执行的闭合积分。原则上，该闭合积分可以沿路径的任意点开始和结束。 |
| | | | |
| − |
| |
| − | If there are multiple reservoirs with different temperatures <math>\left(T_1,T_2, \cdots T_n\right)</math>, then Clausius inequality reads:
| |
| − |
| |
| − | If there are multiple reservoirs with different temperatures <math>\left(T_1,T_2, \cdots T_n\right)</math>, then Clausius inequality reads:
| |
| | | | |
| | 如果存在有多个具有不同温度<math>\left(T_1,T_2, \cdots T_n\right)</math>的热库，则克劳修斯不等式为： | | 如果存在有多个具有不同温度<math>\left(T_1,T_2, \cdots T_n\right)</math>的热库，则克劳修斯不等式为： |
| 第32行： |
第19行： |
| | | | |
| | | | |
| − | In the special case of a reversible process, the equality holds.<ref>[http://scienceworld.wolfram.com/physics/ClausiusTheorem.html '''Clausius theorem'''] at [[Wolfram Research]]</ref> The reversible case is used to introduce the [[state function]] known as [[entropy]]. This is because in a cyclic process the variation of a state function is zero. In other words, the Clausius statement states that it is impossible to construct a device whose sole effect is the transfer of heat from a cool reservoir to a hot reservoir.<ref>Finn, Colin B. P. ''Thermal Physics''. 2nd ed., CRC Press, 1993. </ref> Equivalently, heat spontaneously flows from a hot body to a cooler one, not the other way around.<ref>Giancoli, Douglas C. ''Physics: Principles with Applications''. 6th ed., Pearson/Prentice Hall, 2005. </ref>
| |
| | | | |
| − | In the special case of a reversible process, the equality holds. The reversible case is used to introduce the state function known as entropy. This is because in a cyclic process the variation of a state function is zero. In other words, the Clausius statement states that it is impossible to construct a device whose sole effect is the transfer of heat from a cool reservoir to a hot reservoir. Equivalently, heat spontaneously flows from a hot body to a cooler one, not the other way around.
| + | 当在过程可逆的特殊情况下，该等式成立<ref>[http://scienceworld.wolfram.com/physics/ClausiusTheorem.html '''Clausius theorem'''] at [[Wolfram Research]]</ref> 。其可逆过程可用于引入'''<font color="#ff8000"> [[熵]] Entropy </font>'''的 '''<font color="#ff8000"> 状态函数State function </font>'''。这是因为在循环过程中，状态函数的变化为零。换句话说，'''<font color="#ff8000"> 克劳修斯表述Clausius statement</font>'''指出，不可能构造出一种装置，使其仅仅将热从低温热库传递至高温热库而不引起其他变化<ref>Finn, Colin B. P. ''Thermal Physics''. 2nd ed., CRC Press, 1993. </ref>。相当于说，热量只能自发地从高温物体流向相对低温的物体，反向则不行。<ref>Giancoli, Douglas C. ''Physics: Principles with Applications''. 6th ed., Pearson/Prentice Hall, 2005. </ref> |
| | | | |
| − | 当在过程可逆的特殊情况下，该等式成立。其可逆过程可用于引入'''<font color="#ff8000"> 熵Entropy </font>'''的 '''<font color="#ff8000"> 状态函数State function </font>'''。这是因为在循环过程中，状态函数的变化为零。换句话说，'''<font color="#ff8000"> 克劳修斯表述Clausius statement</font>'''指出，不可能构造出一种装置，使其仅仅将热从低温热库传递至高温热库而不引起其他变化。相当于说，热量只能自发地从高温物体流向相对低温的物体，反向则不行。
| |
| | | | |
| | | | |
| | | | |
| − | The generalized "inequality of Clausius"<ref>Mortimer, R. G. ''Physical Chemistry''. 3rd ed., p. 120, Academic Press, 2008. </ref>
| + | 克劳修斯的广义不等式为<ref>Mortimer, R. G. ''Physical Chemistry''. 3rd ed., p. 120, Academic Press, 2008. </ref> ： |
| − | | |
| − | The generalized "inequality of Clausius"
| |
| − | | |
| − | 克劳修斯的广义不等式为：
| |
| | | | |
| | | | |
| 第50行： |
第31行： |
| | | | |
| | | | |
| − | for an infinitesimal change in entropy ''S'' applies not only to cyclic processes, but to any process that occurs in a closed system.
| |
| − |
| |
| − | for an infinitesimal change in entropy S applies not only to cyclic processes, but to any process that occurs in a closed system.
| |
| − |
| |
| − | 对于熵趋近于无穷小变化时，S不仅适用于循环过程，而且适用于封闭系统中发生的任何过程。
| |
| | | | |
| | + | 对于熵趋近于无穷小变化时，<math>S</math>不仅适用于循环过程，而且适用于封闭系统中发生的任何过程。 |
| | | | |
| | | | |
| − | == History 历史 ==
| |
| | | | |
| | + | == 历史 == |
| | | | |
| | | | |
| − | The Clausius theorem is a mathematical explanation of the [[second law of thermodynamics]]. It was developed by [[Rudolf Clausius]] who intended to explain the relationship between the heat flow in a system and the entropy of the system and its surroundings. Clausius developed this in his efforts to explain entropy and define it quantitatively. In more direct terms, the theorem gives us a way to determine if a cyclical process is reversible or irreversible. The Clausius theorem provides a quantitative formula for understanding the second law.
| |
| | | | |
| − | The Clausius theorem is a mathematical explanation of the second law of thermodynamics. It was developed by Rudolf Clausius who intended to explain the relationship between the heat flow in a system and the entropy of the system and its surroundings. Clausius developed this in his efforts to explain entropy and define it quantitatively. In more direct terms, the theorem gives us a way to determine if a cyclical process is reversible or irreversible. The Clausius theorem provides a quantitative formula for understanding the second law.
| |
| | | | |
| − | 克劳修斯定理是'''<font color="#ff8000"> 热力学第二定律Second law of thermodynamics</font>'''的数学解释。它是由鲁道夫·克劳修斯Rudolf Clausius提出的。他的目的是解释系统中的热量传递与系统及其周围环境熵之间的关系。当初他为了解释并定量熵而逐步发展出了该公式。更直接地讲，该定理为我们提供了一种确定热循环过程是否可逆的方法，为理解第二定律提供了一个定量公式。 | + | 克劳修斯定理是'''<font color="#ff8000"> [[热力学第二定律]] Second law of thermodynamics</font>'''的数学解释。它是由鲁道夫·克劳修斯 Rudolf Clausius提出的。他的目的是解释系统中的热量传递与系统熵及其周围环境之间的关系。当初他为了解释熵并定量表示熵，而逐步发展出了该公式。更直接地讲，该定理为我们提供了一种确定热循环过程是否可逆的方法，为理解热力学第二定律提供了一个定量公式。 |
| | | | |
| | | | |