How Do You Calculate the Specific Heat of a Nitrogen Molecule at 13.6K?

[Finaid]

Homework Statement

Estimate the precise value for the specific heat of a nitrogen molecule at T=13.6K

Homework Equations

I'm pretty sure the correct equation is:
Cp = (7/2)*R + R((hv)/(kT))² *((e^(hv/kT))/(e^(hv/kT)-1)²
So R=8.314 J K^-1mol^-1
T=13.6K
h=6.626*10^-34m²kg s^-1
k=2pi/λ
v= ?

The Attempt at a Solution

Well, I know that diatomic molecules oscillate at a single characteristic frequency,v, but I'm not sure how to find what frequency that is and without it I can't finish the equation. I figure if I had the frequency, I could find λ or vice versa but I need both to finish the problem. Or am I approaching this in too straightforward a manner?
Any help or confirmation that I'm at least headed in the right direction would be appreciated.

 

[rude man]

Such equations are always approximate and of questionable value to physicists, chemists and engineers from a practical view.

Bryant in 1934 came up with a formula for molar specific heat at constant pressure:
c_p = a + bT + cT²

For N₂ he gave
a = 6.30 cal/mole-K
b = 1.819e-3 cal/mole-K
c = -0.345e-6 cal/mole-K.

It depends on what stage of thermodynamics you're at. Modern expressions have indeed increased the accuracy of this parameter. Afraid I'm not knowledgeable about them.


Of course, to get the specific heat of a single molecule you have to divide by Avogadro's number.

 

[Finaid]

Well, I'm a 3rd year Physics Undergrad and this is a question for my Quantum Physics class, not Thermodynamics. I think that's why I have to use the equation above and in the derivation I have for that, Avogadro's number cancels out somewhere along the way. There's a section in my lecture notes deriving this equation for specific heat of a diatomic molecule, but no examples or mention of how to find v.

 

[rude man]

That's what I ws afraid of!

 

[Finaid]

Thanks for giving it a go anyway!

 

[Finaid]

Could I put the frequency v=c/λ? I don't know whether I'm able to assume the conditions for a vacuum, but it would cancel out λ, the wavelength and then ((e(hv/kT))/(e(hv/kT)-1) would go to zero, which would leave Cp=7R/2. This doesn't seem right but it's more than I had yesterday.

 

[qazwsx13]

You're in PH356, yeah?

 

[Finaid]

Yes, sadly.