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| | 此词条由Jie翻译 | | 此词条由Jie翻译 |
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| − | {{short description|A version of the second law of thermodynamics}}
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| − | {{Thermodynamics|cTopic=[[Thermodynamic equations|Equations]]}}
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| − | 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]],
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| − | 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,
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| | '''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， |
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| | :<math>\oint \frac{\delta Q}{T_{\text{surr}}} \leq 0,</math> | | :<math>\oint \frac{\delta Q}{T_{\text{surr}}} \leq 0,</math> |
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| − | 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.
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| − | 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.
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| | 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。 |
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| − | If there are multiple reservoirs with different temperatures <math>\left(T_1,T_2, \cdots T_n\right)</math>, then Clausius inequality reads:
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| − | If there are multiple reservoirs with different temperatures <math>\left(T_1,T_2, \cdots T_n\right)</math>, then Clausius inequality reads:
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| | 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： |