when
and
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(12)
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(the latter relation generally holds for adiabatic state changes, according to (7)).
We notice that according to (10) and (2)
If we also insert for its value from (5), then it is given
or
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(13)
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Then it is
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If we insert this value into (11) and consider (12), then we see that indeed .
The simultaneous change of is:
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