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Specific heat for a triatomic gas

  1. Aug 8, 2016 #1

    Titan97

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    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 $$U=\frac{h\nu}{e^{\frac{h\nu}{\frac{1}{2}\times kT}}-1}?$$
     

    Attached Files:

  2. jcsd
  3. Aug 8, 2016 #2

    Bystander

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    Total number of degrees of freedom is 3n.
     
  4. Aug 18, 2016 #3

    Titan97

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    How did you get that expression?
     
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