## Winter 2013 Final 1B

Volume: $\Delta S = nR\ln \frac{V_{2}}{V_{1}}$
Temperature: $\Delta S = nC\ln \frac{T_{2}}{T_{1}}$

Joseph_Ghaly_2L
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### Winter 2013 Final 1B

For question 1B, aren't you supposed to use Cp instead of Cv? In the answer, Cv is used but volume is not constant while temperature is. The variable in the subscript in these is supposed to be the variable held constant, right?

ntruong2H
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### Re: Winter 2013 Final 1B

Joseph_Ghaly_2L wrote:For question 1B, aren't you supposed to use Cp instead of Cv? In the answer, Cv is used but volume is not constant while temperature is. The variable in the subscript in these is supposed to be the variable held constant, right?

No. This is supposed to be constant volume. This is basically a two step process. Since dS is a state function, it can be added. Therefore, first find the change in entropy that results from the expansion (change in volume). Then, hold volume as constant, and find the change in entropy that results from the cooling (temp change). The total/overall change in entropy is the sum of these two values

Joseph_Ghaly_2L
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Joined: Fri Jul 22, 2016 3:00 am

### Re: Winter 2013 Final 1B

Why do we assume that the expansion and temperature change aren't simultaneous? My intuition is to assume that since volume expands from 3.0 to 3.5 liters, we wouldn't use the equation with constant volume but with constant pressure. Are these types of problems usually this way (where volume expands isothermally and then temperature changes)?

ntruong2H
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### Re: Winter 2013 Final 1B

Joseph_Ghaly_2L wrote:Why do we assume that the expansion and temperature change aren't simultaneous? My intuition is to assume that since volume expands from 3.0 to 3.5 liters, we wouldn't use the equation with constant volume but with constant pressure. Are these types of problems usually this way (where volume expands isothermally and then temperature changes)?

Yes. For the most part if you look at book problems as well as past exams you find the change in entropy from the volume first, then find the entropy change after the temperature changes.

Eliza_Beglari_2L
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### Re: Winter 2013 Final 1B

If volume increases and temperature decreases, pressure MUST decrease to satisfy the PV=nRT equation, so there's actually no way pressure would have been constant. With that said, the above post is correct.