## Cp v. Cv!

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

Wilson Yeh 1L
Posts: 42
Joined: Fri Sep 29, 2017 7:06 am

### Cp v. Cv!

Can someone explain to me when to use Cv and when to use Cp? My TA discussed this in my discussion section but I still don't understand when to use either. Yes, I get that you use Cv under constant volume and you use Cp under constant pressure, but I still don't understand when you would use it. These questions below are what's confusing me:

Calculate the change in entropy when the pressure of 23.5g of oxygen gas is increased from 2.00 kPa to 8.00 kPa while temperature increases from 240K to 360K.

According to my TA, we use Cv for that problem. The next problem...

In one experiment, 1.00 mol oxygen gas was compressed suddenly (and irreversibly) from 5.00 L to 1.00 L by driving in a piston, and in the process its temperature was increased from 20.0 degrees C to 25.2 degrees C. What is the change in entropy of the gas?

According to the textbook, you ALSO use Cv for this problem.

One question gives us a change in pressure while another gives us a change in volume, yet both use Cv. So do we just not use Cp ever? I'm so confused!

Jiun Yue Chung 2I
Posts: 27
Joined: Fri Sep 29, 2017 7:06 am

### Re: Cp v. Cv!

I remember from going to the midterm review session that unless the question specifically says at constant pressure, to assume using constant volume heat capacity. I think inuitively, however, that Cv should be used in the first question since yes, the pressure is the one that is changing. The second one should be divided into two parts. To solve the problem, delta S is equal to two changes in entropy: the first change being the entropy change under conditions of changing volume (nRln(V2/V1) and the second change being the temperature change equation (nCln(T2/T1)). The reason why you use heat capacity at constant volume for the temperature equation is because these are two separate changes (first, entropy change from bringing the volume down and second, bring the tempearture up). Hope that helps a little bit!

dS(total) = dS1(volume change) +dS2(temperature change)

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

### Re: Cp v. Cv!

In which cases would we use Cp?

Mishta Stanislaus 1H
Posts: 45
Joined: Fri Sep 29, 2017 7:04 am

### Re: Cp v. Cv!

Hi! I've been struggling with the same question but in the review session we were told that unless the problem specifically says that pressure is constant we use Cv.

604807557
Posts: 51
Joined: Wed Nov 16, 2016 3:02 am

### Re: Cp v. Cv!

I kept wondering the same thing but during today's review session Lyndon said you'd use Cp when it specifically states "at constant pressure" in the problem.

Kayla Tchorz-Dis 1F
Posts: 30
Joined: Thu Jul 13, 2017 3:00 am

### Re: Cp v. Cv!

You use Cp when there is constant pressure and Cv when you are delaing with constant volume