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Whatever changes to dS and dS<sub>R</sub> occur in the entropies of the sub-system and the surroundings individually, according to the Second Law the entropy S<sub>tot</sub> of the isolated total system must not decrease:
Whatever changes to dS and dS<sub>R</sub> occur in the entropies of the sub-system and the surroundings individually, according to the Second Law the entropy S<sub>tot</sub> of the isolated total system must not decrease:
无论子系统和周围环境<font color = 'red'><s>的 ''dS''和''dS<sub>R</sub>'' 发生</s></font><font color = 'blue'>单独地发生什么熵的变化 ''dS''和dS<sub>R</sub></font>，根据第二定律，孤立总体系统的熵S<sub>tot</sub>不能减小。
<math> dS_{\mathrm{tot}}= dS + dS_R \ge 0 </math>
<math> dS_{\mathrm{tot}}= dS + dS_R \ge 0 </math>
<math> dS_{\mathrm{tot}}= dS + dS_R \ge 0 </math>
According to the first law of thermodynamics, the change dU in the internal energy of the sub-system is the sum of the heat δq added to the sub-system, less any work δw done by the sub-system, plus any net chemical energy entering the sub-system d ∑μ<sub>iR</sub>N<sub>i</sub>, so that:
According to the first law of thermodynamics, the change dU in the internal energy of the sub-system is the sum of the heat δq added to the sub-system, less any work δw done by the sub-system, plus any net chemical energy entering the sub-system d ∑μ<sub>iR</sub>N<sub>i</sub>, so that:
根据<font color = 'red'><s>能量守恒定律</s></font><font color = 'blue'>热力学第一定律</font>，子系统<font color = 'red'><s>内部能量</s></font><font color = 'blue'>内能</font>的变化 dU 是<font color = 'red'><s>子系统内部能量 q 的总和</s></font>加在子系统上的热δq的和<font color = 'blue'></font>，减去子系统所做的任何功w，再加上进入子系统的任何净化学能 d ∑μ<sub>iR</sub>N<sub>i</sub>，因此
<math> dU = \delta q - \delta w + d(\sum \mu_{iR}N_i) \,</math>
<math> dU = \delta q - \delta w + d(\sum \mu_{iR}N_i) \,</math>
<math> dU = \delta q - \delta w + d(\sum \mu_{iR}N_i) \,</math>
where μ<sub>iR</sub> are the chemical potentials of chemical species in the external surroundings.
where μ<sub>iR</sub> are the chemical potentials of chemical species in the external surroundings.
其中μ<sub>iR</sub>是外部环境中<font color = 'red'><s>化学物类</s></font><font color = '#FFD700'>'''化学形态 chemical species'''</font>的化学势。
Now the heat leaving the reservoir and entering the sub-system is
Now the heat leaving the reservoir and entering the sub-system is
现在热<font color = 'red'><s>量</s></font>离开<font color = 'red'><s>储存器</s></font><font color = 'blue'>热源</font>进入子系统是
where we have first used the definition of entropy in classical thermodynamics (alternatively, in statistical thermodynamics, the relation between entropy change, temperature and absorbed heat can be derived); and then the Second Law inequality from above.
where we have first used the definition of entropy in classical thermodynamics (alternatively, in statistical thermodynamics, the relation between entropy change, temperature and absorbed heat can be derived); and then the Second Law inequality from above.
在这个过程中，首先使用了经典热力学中熵的定义(在统计热力学中，熵变、温度和吸收热量之间的关系可以将其推导出来) ，然后从上面的公式可以推导出第二定律的不等式。
在这个过程中，首先使用了经典热力学中熵的定义(在统计热力学中，熵变、温度和吸收热量之间的关系<font color = 'green'>可以将其推导出来</font>) ，然后从上面的公式可以推导出第二定律的不等式。
It is useful to separate the work ''δw'' done by the subsystem into the ''useful'' work ''δw<sub>u</sub>'' that can be done ''by'' the sub-system, over and beyond the work ''p<sub>R</sub> dV'' done merely by the sub-system expanding against the surrounding external pressure, giving the following relation for the useful work (exergy) that can be done:
It is useful to separate the work ''δw'' done by the subsystem into the ''useful'' work ''δw<sub>u</sub>'' that can be done ''by'' the sub-system, over and beyond the work ''p<sub>R</sub> dV'' done merely by the sub-system expanding against the surrounding external pressure, giving the following relation for the useful work (exergy) that can be done:
==here0811==
It is useful to separate the work δw done by the subsystem into the useful work δw<sub>u</sub> that can be done by the sub-system, over and beyond the work p<sub>R</sub> dV done merely by the sub-system expanding against the surrounding external pressure, giving the following relation for the useful work (exergy) that can be done:
It is useful to separate the work δw done by the subsystem into the useful work δw<sub>u</sub> that can be done by the sub-system, over and beyond the work p<sub>R</sub> dV done merely by the sub-system expanding against the surrounding external pressure, giving the following relation for the useful work (exergy) that can be done: