## 9.7 and 9.11 formula differences

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

Emily Glaser 1F
Posts: 156
Joined: Thu Jul 27, 2017 3:01 am

### 9.7 and 9.11 formula differences

9.7 uses the formula, deltaS = n C ln(T2/T1)
9.11 uses the formula, deltaS = n R ln (T2/T1)
What's the difference? Why

Andres Reynoso 1J
Posts: 30
Joined: Fri Sep 29, 2017 7:06 am

### Re: 9.7 and 9.11 formula differences

The difference lies in what the question is asking.

For 9.7 part a, the question asks for the entropy change at a constant pressure with a change in temperature. For this we use the known equation $\Delta S=nC_{p}ln\frac{T_{2}}{T_{1}}$ where Cp is the specific heat of a gas at constant pressure.

For 9.11, the question asks for the entropy change at a constant temperature with a change in pressure. For this, we can use $\Delta S=nRln\frac{V_{2}}{V_{1}}$ where R is the gas constant. As the solution manual states, we can rewrite that equation $\Delta S=nRln\frac{P_{1}}{P_{2}}$ since P is the inverse of V for ideal gases.

To summarize, it all really depends on what the question asks. Hope I helped!

Timothy Kim 1B
Posts: 62
Joined: Fri Sep 29, 2017 7:04 am

### Re: 9.7 and 9.11 formula differences

In the first question, we use the first formula because it is asking for entropy at a constant pressure. when you derive the equation, it comes out as that.

For the second problem, the conditions are different because it is isothermal. Thus, you end up using a different equation that keeps into account that the internal energy is zero, which leads to the second equation.

Rakhi Ratanjee 1D
Posts: 59
Joined: Fri Sep 29, 2017 7:04 am

### Re: 9.7 and 9.11 formula differences

For 9.11, the solutions manual states that "since P is the inverse of V for ideal gases, we can write: delta S = n*R*ln(P1/P2).
How can you derive this?

zanekoch1A
Posts: 25
Joined: Thu Jul 13, 2017 3:00 am

### Re: 9.7 and 9.11 formula differences

For 9.7 I understand why you use deltas=nCpln(t2/t1) but what do you use for Cp? Is there a way to solve it without knowing Cp because I don't think its given.