## Problem 9.13

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

Nicole Gamboa 2M
Posts: 21
Joined: Wed Sep 21, 2016 2:56 pm

### Problem 9.13

Hi All,
I had a question about Chapter 9 Problem 13, where it asks for the change in entropy for the gas assuming ideal behavior. I know that you need to calculate change in entropy for the difference in temperature and for the difference in volume and then add them, however I was confused as to why the calculation for change in entropy using temperature doesn't multiply the gas constant by 5/2 since it has ideal behavior. Can anyone help?
Thanks!

Pauline Tze 3B
Posts: 57
Joined: Sat Jul 09, 2016 3:00 am
Been upvoted: 1 time

### Re: Problem 9.13

Hi Nicole,

When a question asks you to assume ideal behavior, it can also mean that they want you to consider the ideal gas law PV = nRT.
In the calculation for change in entropy using temperature, I believe they combine the relationship of V and T (in that they are directly related) in PV = nRT to the work formula, converted that to heat through the inverse relationship, then combined that result with the change in entropy formula q (rev) / T.

I hope that helps.