# Find molar mass and number of degrees of freedom from heat capacities.

1. May 2, 2014

### Junabes

Hey having a bit of trouble with this one. I really don't know how to start. Think I just simply don't have the right equations or I'm using the wrong units. Hopefully you guys can help me.

1. The problem statement, all variables and given/known data

Find the molar mass and the number of degrees of freedom of molecules in a gas with known heat capacities: Cv = 650 J/(KgK) and Cp=910 J/(KgK).

2. Relevant equations

The equations that I can find in my book that I've been trying to figure out are :

1.Cv = (nRP)/2 where R = Gas constant and P = number of degrees of freedom. n= number of moles

2.Cp = nR(1+P/2)

3.Cp = Cv + R

3. The attempt at a solution

Well when I first started off I simply applied the Cv formula to the value of Cv and solve for P, the number of degrees of freedom. However when I did this, i got an answer of ~156 which I can immediately tell is not correct.

I am led to believe that I'm not using the correct units for Cv and Cp as they don't solve the last equation(3) correctly.

Last edited: May 2, 2014
2. May 2, 2014

### Junabes

Ok I just found the degrees of freedom.

Cp/Cv=1 + 2/P
7/5=1+2/P
P = 5 degrees of freedom.

Even though I'm still sure I have to change the units to find the Molar mass. I only found the degrees of freedom due to Cp/Cv is a ratio so units did not matter.

I have to somehow change the Cv and Cp units from J/(K*Kg) to J/(K*mol). My reasoning for this is that the gas constant R is J/(K*mol).

3. May 2, 2014

### Junabes

I think I might be correct here: If anyone can confirm? Turns out I didn't really need to change any units just yet.

Cv = nRp/2
n=31.28moles/kg

Molecular mass = Mass/n = 1kg/31.28moles = 31.96g/mol.

I assume this would be Oxygen molecules.

4. May 2, 2014

### projjal

Everything's OK.