can be restricted to obtain

where:
* is the entropy of the system
* is the chemical potential of the system

Hence and . Integrating both sides, keeping in mind that is a function of , the following relation is obtained:

where:
* are the initial entropy and temperature respectively
* are the final entropy and temperature respectively
* is the change in entropy of the system

Similarly, for an isobaric system, using and , it can also be derived

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