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An important and revealing idealized special case is to consider applying the Second Law to the scenario of an isolated system (called the total system or universe), made up of two parts: a sub-system of interest, and the sub-system's surroundings. These surroundings are imagined to be so large that they can be considered as an unlimited heat reservoir at temperature T<sub>R</sub> and pressure P<sub>R</sub> so that no matter how much heat is transferred to (or from) the sub-system, the temperature of the surroundings will remain T<sub>R</sub>; and no matter how much the volume of the sub-system expands (or contracts), the pressure of the surroundings will remain P<sub>R</sub>.
An important and revealing idealized special case is to consider applying the Second Law to the scenario of an isolated system (called the total system or universe), made up of two parts: a sub-system of interest, and the sub-system's surroundings. These surroundings are imagined to be so large that they can be considered as an unlimited heat reservoir at temperature T<sub>R</sub> and pressure P<sub>R</sub> so that no matter how much heat is transferred to (or from) the sub-system, the temperature of the surroundings will remain T<sub>R</sub>; and no matter how much the volume of the sub-system expands (or contracts), the pressure of the surroundings will remain P<sub>R</sub>.
考虑将第二定律应用于孤立系统(称为整体系统或宇宙)的情形，是一个重要的、具有启发性的理想情形。孤立系统由两部分组成: 感兴趣的子系统和子系统的环境。这些环境被想象为如此之大，以至于它们可以被认为是一个温度为 t 子 r / sub 和压力为 p 子 r / sub 的无限热源，因此无论有多少热量被转移到(或来自)子系统，周围环境的温度将保持 t 子 r / sub; 无论子系统的体积扩大(或收缩)多少，周围环境的压力将保持 p 子 r / sub。
考虑将第二定律应用于孤立系统(称为整体系统或宇宙)的情形，是一个重要的、具有启发性的理想情形。该系统由两部分组成：感兴趣的子系统和子系统的周围环境。因为环境被想象的非常巨大，它们可以被视为温度为 t 子 r / sub 和压力为 p 子 r / sub 一个无限的蓄热器，无论有多少热量被转移到（或来自）子系统，周围的温度将保持TR；无论子系统的体积膨胀（或收缩）有多大，周围环境的压力都将保持不变。
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的dS 和 dSR发生什么变化，根据第二定律，孤立总体系统的熵 Stot不能减小。
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:
根据能量守恒定律，子系统内部能量的变化 dU 是子系统内部能量 q 的总和，减去子系统所做的任何功，再加上进入子系统 d ∑ sub iR / sub n sub i / sub 的任何净化学能，因此:
根据能量守恒定律，子系统内部能量的变化 dU 是子系统内部能量 q 的总和，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dxxxx，因此
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 iR 是外部环境中化学物类的化学势。
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。
It therefore follows that any net work δw done by the sub-system must obey
It therefore follows that any net work δw done by the sub-system must obey
因此，子系统所做的任何净功δw必须服从
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:
将子系统所做的功δw划分为子系统可以完成的有用功δw，除了子系统在周围外部压力下膨胀所做的功pR dV外，还可以给出以下可用功（放射本能）关系式:
It is convenient to define the right-hand-side as the exact derivative of a thermodynamic potential, called the availability or exergy E of the subsystem,
It is convenient to define the right-hand-side as the exact derivative of a thermodynamic potential, called the availability or exergy E of the subsystem,
为方便起见，可以把右边定义为热力学势的精确导数，称为子系统的可用性或放射本能E
In sum, if a proper infinite-reservoir-like reference state is chosen as the system surroundings in the real world, then the Second Law predicts a decrease in E for an irreversible process and no change for a reversible process.
In sum, if a proper infinite-reservoir-like reference state is chosen as the system surroundings in the real world, then the Second Law predicts a decrease in E for an irreversible process and no change for a reversible process.
总之，如果选择一个合适的类似于无限库的参考状态作为现实世界中的系统环境，那么第二定律预测的不可逆性的 e 值会减少，而可逆过程的 e 值不会变化。
This expression together with the associated reference state permits a design engineer working at the macroscopic scale (above the thermodynamic limit) to utilize the Second Law without directly measuring or considering entropy change in a total isolated system. (Also, see process engineer). Those changes have already been considered by the assumption that the system under consideration can reach equilibrium with the reference state without altering the reference state. An efficiency for a process or collection of processes that compares it to the reversible ideal may also be found (See second law efficiency.)
This expression together with the associated reference state permits a design engineer working at the macroscopic scale (above the thermodynamic limit) to utilize the Second Law without directly measuring or considering entropy change in a total isolated system. (Also, see process engineer). Those changes have already been considered by the assumption that the system under consideration can reach equilibrium with the reference state without altering the reference state. An efficiency for a process or collection of processes that compares it to the reversible ideal may also be found (See second law efficiency.)
这个表达式和相关的参考状态允许在宏观尺度（高于热力学极限）下工作的设计工程师使用第二定律，而无需直接测量或考虑整个孤立系统中的熵变。（另见工艺工程师）。考虑到这些变化，假设所考虑的系统可以在不改变参考状态的情况下与参考状态达到平衡。将其与可逆理想进行比较，还可以找到一个过程或过程集合的效率（见第二定律效率）
第二定律的这种方法被广泛应用于工程实践、环境会计、系统生态学和其他学科。
第二定律的这种方法被广泛应用于工程实践、环境会计、系统生态学和其他学科。
===The second law in chemical thermodynamics===
===The second law in chemical thermodynamics===