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| − | Clausius was one of the first to work on the idea of entropy and is even responsible for giving it that name. What is now known as the Clausius theorem was first published in 1862 in Clausius' sixth memoir, "On the Application of the Theorem of the Equivalence of Transformations to Interior Work". Clausius sought to show a proportional relationship between entropy and the energy flow by heating (δ''Q'') into a system. In a system, this heat energy can be transformed into work, and work can be transformed into heat through a cyclical process. Clausius writes that "The algebraic sum of all the transformations occurring in a cyclical process can only be less than zero, or, as an extreme case, equal to nothing." In other words, the equation
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| − | Clausius was one of the first to work on the idea of entropy and is even responsible for giving it that name. What is now known as the Clausius theorem was first published in 1862 in Clausius' sixth memoir, "On the Application of the Theorem of the Equivalence of Transformations to Interior Work". Clausius sought to show a proportional relationship between entropy and the energy flow by heating (δQ) into a system. In a system, this heat energy can be transformed into work, and work can be transformed into heat through a cyclical process. Clausius writes that "The algebraic sum of all the transformations occurring in a cyclical process can only be less than zero, or, as an extreme case, equal to nothing." In other words, the equation
| + | Clausius是最早研究熵概念的人之一，甚至负责为其命名。关于现阶段“克劳修斯定理”的称呼最初出现在1862年Clausius的第六本回忆录《关于转换等价定理在定量物质内做功的应用》中。Clausius试图表达熵与通过加热（其热量表示为<math>δ''Q''</math>）进入系统的能量流之间的比例关系。在系统中，这种热能可以转化为功，并且功也可以通过循环过程转化为热。Clausius写道：“在一个循环过程中发生的所有转换的代数和只能小于零，或者说在极端情况下等于零。”也就是如下等式： |
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| − | 克劳修斯是最早研究熵概念的人之一，甚至负责为其命名。关于现阶段“克劳修斯定理”的称呼最初出现在1862年克劳修斯的第六本回忆录《关于转换等价定理在定量物质内做功的应用》中。克劳修斯试图表达熵与通过加热（其热量表示为δ''Q''）进入系统的能量流之间的比例关系。在系统中，这种热能可以转化为功，并且功也可以通过循环过程转化为热。克劳修斯写道：“在一个循环过程中发生的所有转换的代数和只能小于零，或者说在极端情况下等于零。”也就是如下等式：
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| − | with 𝛿''Q'' being energy flow into the system due to heating and ''T'' being absolute temperature of the body when that energy is absorbed, is found to be true for any process that is cyclical and reversible. Clausius then took this a step further and determined that the following relation must be found true for any cyclical process that is possible, reversible or not. This relation is the "Clausius inequality".
| + | 其中<math>𝛿''Q''</math>是由于加热而从外界流入系统的能量，<math>T</math>是吸收能量时该主体的绝对温度，该等式对于任何周期性且可逆的过程均成立。之后，<math>进一步扩展并确定，对于任何可能可逆的或不可逆的周期性过程，必须满足以下关系，即“克劳修斯不等式”。 |
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| − | with 𝛿Q being energy flow into the system due to heating and T being absolute temperature of the body when that energy is absorbed, is found to be true for any process that is cyclical and reversible. Clausius then took this a step further and determined that the following relation must be found true for any cyclical process that is possible, reversible or not. This relation is the "Clausius inequality".
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| − | 其中𝛿''Q''是由于加热而从外界流入系统的能量，T是吸收能量时该主体的绝对温度，该等式对于任何周期性且可逆的过程均成立。之后，克劳修斯进一步扩展并确定，对于任何可能可逆的或不可逆的周期性过程，必须满足以下关系，即“克劳修斯不等式”。。
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| − | Now that this is known, there must be a relation developed between the Clausius inequality and entropy. The amount of entropy S added to the system during the cycle is defined as
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| − | Now that this is known, there must be a relation developed between the Clausius inequality and entropy. The amount of entropy S added to the system during the cycle is defined as
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| − | 于是现在明确了克劳修斯不等式和熵之间的必然联系。而其周期性过程中所增加的熵量S为：
| + | 于是现在明确了克劳修斯不等式和熵之间的必然联系。而其周期性过程中所增加的熵量<math>S</math>为： |
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| − | It has been determined, as stated in the [[second law of thermodynamics]], that the entropy is a state function: It depends only upon the state that the system is in, and not what path the system took to get there. This is in contrast to the amount of energy added as heat (𝛿''Q'') and as work (𝛿''W''), which may vary depending on the path. In a cyclic process, therefore, the entropy of the system at the beginning of the cycle must equal the entropy at the end of the cycle, <math>\Delta S=0</math>, regardless of whether the process is reversible or irreversible. In the irreversible case, entropy will be created in the system, and more entropy must be extracted than was added <math>(\Delta S_{surr}>0)</math> in order to return the system to its original state. In the reversible case, no entropy is created and the amount of entropy added is equal to the amount extracted.
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| − | It has been determined, as stated in the second law of thermodynamics, that the entropy is a state function: It depends only upon the state that the system is in, and not what path the system took to get there. This is in contrast to the amount of energy added as heat (𝛿Q) and as work (𝛿W), which may vary depending on the path. In a cyclic process, therefore, the entropy of the system at the beginning of the cycle must equal the entropy at the end of the cycle, <math>\Delta S=0</math>, regardless of whether the process is reversible or irreversible. In the irreversible case, entropy will be created in the system, and more entropy must be extracted than was added <math>(\Delta S_{surr}>0)</math> in order to return the system to its original state. In the reversible case, no entropy is created and the amount of entropy added is equal to the amount extracted.
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| | 如热力学第二定律所述，熵已经确定是一个状态函数：它仅取决于系统所处的状态，而不取决于系统传递热量的过程路径。这与通过加热（𝛿''Q''）和作功（𝛿''W''）增加的能量是不同的，后者随路径的变化而变化。因此，在循环过程中，无论其是可逆还是不可逆的，系统在循环开始时的熵必须等于循环结束时的熵，即<math>\Delta S=0</math>。在不可逆的情况下，系统会产生熵，而且其提取的熵量会大于已添加的熵量<math>(\Delta S_{surr}>0)</math>，这样才能使系统回到其原始状态。而在循环过程可逆的情况下，系统则不会产生熵，其所添加熵的量等于其提取的量。 | | 如热力学第二定律所述，熵已经确定是一个状态函数：它仅取决于系统所处的状态，而不取决于系统传递热量的过程路径。这与通过加热（𝛿''Q''）和作功（𝛿''W''）增加的能量是不同的，后者随路径的变化而变化。因此，在循环过程中，无论其是可逆还是不可逆的，系统在循环开始时的熵必须等于循环结束时的熵，即<math>\Delta S=0</math>。在不可逆的情况下，系统会产生熵，而且其提取的熵量会大于已添加的熵量<math>(\Delta S_{surr}>0)</math>，这样才能使系统回到其原始状态。而在循环过程可逆的情况下，系统则不会产生熵，其所添加熵的量等于其提取的量。 |
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| − | If the amount of energy added by heating can be measured during the process, and the temperature can be measured during the process, the Clausius inequality can be used to determine whether the process is reversible or irreversible by carrying out the integration in the Clausius inequality.
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| − | If the amount of energy added by heating can be measured during the process, and the temperature can be measured during the process, the Clausius inequality can be used to determine whether the process is reversible or irreversible by carrying out the integration in the Clausius inequality.
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| | 循环过程中，如果能测量出因加热而增加的能量和其温度，那么通过对克劳修斯不等式进行积分，就能确定其过程是否可逆。 | | 循环过程中，如果能测量出因加热而增加的能量和其温度，那么通过对克劳修斯不等式进行积分，就能确定其过程是否可逆。 |
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| | == Proof 证据 == | | == Proof 证据 == |