# Specific heat for a triatomic gas

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1. Aug 8, 2016

### Titan97

1. The problem statement, all variables and given/known data
Using equipartition law, find specific heat of gas containing triatomic linear molecules. Will the result be different if the molecule was non- linear? In what way?

2. Relevant equations
According to equipartion theorem, each degree of freedom gets (1/2)kT kinetic energy and (1/2)kT potential energy.

3. The attempt at a solution
For a linear arrangement,

• number of translational degrees of freedom is $3$
• number of rotational degrees of freedom is $2$ (or is it 6 because the atom can rotate about the central atom or about one of the atoms at the end)
• number of vibrational degrees of freedom is $1$
At room T, i will neglect point 3.

My second doubt is, the internal energy is $\frac{1}{2}NkT\times f$

Why is it only 1/2 the value of kT (which is the sum of kinetic and potential energies as my prof says in one of the slides which i have attached below)?

In the slide, $$U=\frac{h\nu}{e^{\frac{h\nu}{kT}}-1}$$

Why isn't it $$U=\frac{h\nu}{e^{\frac{h\nu}{\frac{1}{2}\times kT}}-1}?$$

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2. Aug 8, 2016

### Bystander

Total number of degrees of freedom is 3n.

3. Aug 18, 2016

### Titan97

How did you get that expression?