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

  1. May 2, 2014 #1
    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. jcsd
  3. May 2, 2014 #2
    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).
     
  4. May 2, 2014 #3
    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.
     
  5. May 2, 2014 #4
    Everything's OK.
     
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