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How do we know when to use Cv vs. Cp? I know one is for constant volume and one is for constant pressure, but what about for a sudden irreversible compression of gas where there is a temperature and volume change? For the temperature part of the entropy calculation, how would we know which c value to use?
When there is a change in entropy due to temperature and volume changes you would break up the problem as follows: deltaS total = deltaS due to volume change + deltaS due to temperature change. The idea is to split the problem up and calculate deltaS due to volume change and then deltaS due to temperature change. Because in part 1 we've already calculated the deltaS due to a change in volume when it comes to calculating the deltaS due to temperature change, we assume that the volume isn't changing and therefore use Cp.
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