## 9.7 vs 9.13

$\Delta S = \frac{q_{rev}}{T}$

Angela 1K
Posts: 80
Joined: Fri Sep 29, 2017 7:05 am

### 9.7 vs 9.13

I'm confused about the equations that we use in 9.7 vs the equation used in 9.13.

9.7 asks to calculate the entropy change associated with raising the temperature of 1.00 mol of ideal gas atoms reversibly from 37.6 C to 157.9 C at (a) constant pressure and (b) constant volume and to assume that the heat capacity of an ideal gas is independent of temperature. The equation used for part a is $\Delta S=nCln\frac{T2}{T1}$.

9.13 asks to find the change in entropy of the gas when 3.00 L of nitrogen gas at 18.5 C is compressed suddenly (and irreversibly) to 0.500 L by driving in a piston. In the process, the temperature of the gas increased to 28.1 C. The equation for the change in enthalpy resulting from the increase in temperature used is $\Delta S=nRln\frac{T2}{T1}$.

I don't understand why for the first equation we use C but we use R for the second equation.

Thanks!

Lisa Tang 1C
Posts: 62
Joined: Fri Sep 29, 2017 7:05 am
Been upvoted: 2 times

### Re: 9.7 vs 9.13

There is a mistake in the solutions manual for 9.13. So, for both problems you should use C in the equation, not R. If you look at the Solution Manual Errors page from Dr. Lavelle's website, he has it corrected on there. Hope this helps!

Alvin Tran 2E
Posts: 39
Joined: Fri Sep 29, 2017 7:06 am

### Re: 9.7 vs 9.13

You actually use C in the second equation too when dealing with temperature changes, but the different entropy equations come from ∆S=q/T so they basically function the same. C depends on whether you are calculating constant pressure or constant volume and is actually a multiple of R. In 9.13, you have both an increase in temperature and a volume change. So first calculate the decrease in entropy resulting from the decrease in volume using ∆S = nR ln(V2/V1). Then calculate the increase in entropy resulting from the increase in temperature using ∆S =nCv ln(T2/T1). Add these two together to get the net entropy change.

Gurkriti Ahluwalia 1K
Posts: 37
Joined: Fri Sep 29, 2017 7:07 am

### Re: 9.7 vs 9.13

how do we know to use 5/2R for heat capacity?? what words or phrases in the question hint at this??

Alvin Tran 2E
Posts: 39
Joined: Fri Sep 29, 2017 7:06 am

### Re: 9.7 vs 9.13

When you use the equation with specific heat capacity and constant volume or pressure you use (5/2)R. For monatomic ideal gases Cv=(3/2)R and Cp=(5/2)R. For diatomic gases, such as nitrogen in this problem, Cv=(5/2)R and Cp=(7/2)R