## 9.11 [ENDORSED]

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

Matthew Lee 3L
Posts: 51
Joined: Fri Sep 29, 2017 7:07 am

### 9.11

For this question, we have to change use pressure instead of volume for the formlua deltaS=nRln(V2/V1) and it says we just use the inverse relationship of volume and pressure to do (P1/P2) instead of (V2/V1). Is this the only way to solve it or is this the only way?

Chem_Mod
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### Re: 9.11  [ENDORSED]

We are not given values for V or T in this problem. Only n and P. Thus, two of the unknowns in the ideal gas equation of state PV = nRT are left unknown. The information that the change occurs isothermally is enough for us to use the formula $\Delta S = nRln\frac{V_{f}}{V_{i}}$ but since we are given values of P and no way to pin down V we must use the expression $\Delta S = nRln\frac{P_{i}}{P_{f}}$ which you can derive by substituting V = nRT/P for the final and initial conditions in the first expression.

melissa carey 1f
Posts: 53
Joined: Fri Sep 29, 2017 7:06 am

### Re: 9.11

We also use P1/P2 as opposed to V2/V1 since pressure and volume are inversely related. P1V1=P2V2.

JamesAntonios 1E
Posts: 70
Joined: Fri Sep 29, 2017 7:04 am

### Re: 9.11

Chem_Mod wrote:We are not given values for V or T in this problem. Only n and P. Thus, two of the unknowns in the ideal gas equation of state PV = nRT are left unknown. The information that the change occurs isothermally is enough for us to use the formula $\Delta S = nRln\frac{V_{f}}{V_{i}}$ but since we are given values of P and no way to pin down V we must use the expression $\Delta S = nRln\frac{P_{i}}{P_{f}}$ which you can derive by substituting V = nRT/P for the final and initial conditions in the first expression.

Can you derive the P1/P2 formula from the q/T formula? Or does it just come from the V2/V1 formula?