Estimate vibrational frequency of N2 molecule

  • #1
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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=7/2kB

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=kB

The Attempt at a Solution


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

kBT=(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.
 

Answers and Replies

  • #2
DrClaude
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Experimental data for the heat capacity of N2 as a function of temperature are provided.
What does this curve look like?
 
  • #3
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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.
 
  • #4
DrClaude
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Clearly, the heat capacity is not constant, whereas you expect it to be of the form C = f kB T / 2, where f is the number of quadratic degrees of freedom. What could be happening here?
 
  • #5
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?'..........
 
  • #6
DrClaude
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7,554
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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.
 

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