Page 1 of 1

### deltaS=nCvln(t2/t1) what is Cv?

Posted: Sat Feb 09, 2019 5:39 pm
what does the Cv mean in the equation deltaS=nCvln(t2/t1) ? what does it stand for, and when should i use it as opposed to deltaS=nRln(V2/v1)?

### Re: deltaS=nCvln(t2/t1) what is Cv?

Posted: Sat Feb 09, 2019 5:43 pm
Cv is constant volume, which is $\frac{3}{2}$ times the constant R. You use this in deltaS=nCvln(t2/t1) instead of deltaS=nRln(V2/v1) when you have a monatomic ideal gas at constant volume to calculate for entropy.

### Re: deltaS=nCvln(t2/t1) what is Cv?

Posted: Sat Feb 09, 2019 5:44 pm
Cv is the heat capacity of the system when the volume is constant.

### Re: deltaS=nCvln(t2/t1) what is Cv?

Posted: Sun Feb 10, 2019 10:56 pm
where does the 3/2 come from?

### Re: deltaS=nCvln(t2/t1) what is Cv?

Posted: Sun Feb 10, 2019 11:01 pm
when would you use deltaS=nRln(V2/v1) ?

### Re: deltaS=nCvln(t2/t1) what is Cv?

Posted: Sun Feb 10, 2019 11:48 pm
If the problem gives you temperature and the system is not isothermal, deltaS=nCvln(t2/t1) is used to determine the change in entropy. To calculate the change in entropy of an ideal gas in a reversible isothermal expansion, use deltaS=nRln(V2/V1).

### Re: deltaS=nCvln(t2/t1) what is Cv?

Posted: Mon Feb 11, 2019 10:14 am
Emily Kennedy 4L wrote:where does the 3/2 come from?

For heat capacities of ideal gases, we use Cv=3/2R for a monoatomic gas and Cv=5/2R for a diatomic gas such as N2 or H2. The constant being multiplied to R is determined by the greater number of degrees of freedom in diatomic as opposed to monoatomic gases, so 5/2 (diatomic) is much bigger than 3/2 (monoatomic).

### Re: deltaS=nCvln(t2/t1) what is Cv?

Posted: Mon Feb 11, 2019 11:37 am
If a gas is compressed suddenly and irreversibly, treat it as a two step process where the dS from dT and dS from dV need to be accounted for. In this case, you would do dS=nCvln(T2/T1) if v was constant + deltaS=nRln(V2/V1).