show that the entropy remains constant in a reversible process, but increases in an irreversible one
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A reversible process is one carried out in infinitesimal steps after which, when undone, both the system and surroundings (that is, the world) remain unchanged (see the example of gas expansion-compression below). Although true reversible change cannot be realized in practice, it can always be approximated.
As a process is carried out in a more reversible manner, the value of w approaches its maximum possible value, and q approaches its minimum possible value.
Although q is not a state function, the quotient qrev/T is, and is known as the entropy.
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