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

AI Thread Summary
The discussion revolves around calculating the molar mass and degrees of freedom for a gas using its heat capacities, Cv and Cp. Initially, the user struggled with the correct equations and units, leading to an incorrect calculation of degrees of freedom. After applying the ratio of Cp to Cv, they correctly determined the degrees of freedom to be 5. The user then calculated the molar mass as approximately 31.96 g/mol, concluding that the gas is likely oxygen. Overall, the user resolved their confusion regarding units and successfully completed the calculations.
Junabes
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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.

Homework Statement



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).

Homework 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

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.
 
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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).
 
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.
 
Everything's OK.
 
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