Estimate vibrational frequency of N2 molecule

[Sam J]

Homework Statement

Experimental data for the heat capacity of N2 as a function of temperature are provided.

Estimate the frequency of vibration of the N2 molecule.

Homework Equations

Energy of harmonic oscillator = (n+1/2)ħω

C=7/2k_B

Average molecular energy = C*T

But this is an expression for the total energy of a molecule.
Presumably the amount of energy within the two vibrational modes is:

E=C*T

with

C=k_B

The Attempt at a Solution

All I can think to do is equate the two expressions for the energy of the oscillator:

k_BT=(n+1/2)ħω

But I have no idea where to go now. In order to find frequency I would want to solve for ω, from which frequency can be trivially determined. However, how am I to know which integer value to use for n?

I am also very unsure as to my construction of the problem.

Any help/guidance greatly appreciated.

 

[DrClaude]

Experimental data for the heat capacity of N2 as a function of temperature are provided.

What does this curve look like?

 

[Sam J]

What does this curve look like?

T (Kelvin) 170 500 770 1170 1600 2000 2440
C/NkB 2.5 2.57 2.76 3.01 3.22 3.31 3.4

Apologies, not sure how to post a table of data.

 

[DrClaude]

Clearly, the heat capacity is not constant, whereas you expect it to be of the form C = f k_B T / 2, where f is the number of quadratic degrees of freedom. What could be happening here?

 

[Astrolover]

You access rotational energy as well? So you have more degrees of freedom? But this doesn't answer the question "However, how am I to know which integer value to use for n?'...

 

[DrClaude]

You access rotational energy as well? So you have more degrees of freedom? But this doesn't answer the question "However, how am I to know which integer value to use for n?'...

n is not necessarily an integer. There can be situations where you get an effective number of dofs that is not a whole number.