## 4F.11 when to use Cvln(T2/T1) vs nRln(T2/T1)

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

JulieAljamal1E
Posts: 71
Joined: Fri Sep 28, 2018 12:24 am

### 4F.11 when to use Cvln(T2/T1) vs nRln(T2/T1)

For question 4F.11 we're asked to calculate the change of entropy of a gas where there was 3 L of N2 at 18.5 degrees Celsius compressed to 0.5 L. In the process the temp increased to 28.1 degrees Celsius. I know we have to calculate the change of entropy for both the volume and temperature change and add the two. In an example in the book it does this by findinding the change in entropy of temp using the equation deltaS=Cv ln(T2/T1). Why don’t we use that equation in the case of 4F.11 and instead we use nR ln(T2/T1)?

Tuong-Minh Tran 1C
Posts: 30
Joined: Fri Sep 28, 2018 12:19 am

### Re: 4F.11 when to use Cvln(T2/T1) vs nRln(T2/T1)

In the end, it shouldn't matter which equation you use to find the change in entropy. I believe that ΔS=nR ln(T2/T1) was used over ΔS=Cv ln(T2/T1) simply because it you can derive the number of moles (using PV=nRT) more easily than trying to find the heat capacity. If you can find the heat capacity, however, then there's nothing wrong with using the latter equation.

JulieAljamal1E
Posts: 71
Joined: Fri Sep 28, 2018 12:24 am

### Re: 4F.11 when to use Cvln(T2/T1) vs nRln(T2/T1)

Tuong-Minh Tran 1C wrote:In the end, it shouldn't matter which equation you use to find the change in entropy. I believe that ΔS=nR ln(T2/T1) was used over ΔS=Cv ln(T2/T1) simply because it you can derive the number of moles (using PV=nRT) more easily than trying to find the heat capacity. If you can find the heat capacity, however, then there's nothing wrong with using the latter equation.

But this would give you different values for delta S of the temperature change. Because the number of moles is still 1mol in either case but in one case you multiple by the gas constant (8.314) and in the other case it’s 1mol times Cv,m which is a different value than the gas constant and gives you a different delta S value overall.