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Here are the "knowns" that I'm working with.

Internal Energy for a monatomic gas is

$$U = (3/2)nRT$$

For a diatomic gas its

$$U = (5/2)nRT$$

All of my textbooks and online sources indicate that it's a (1/2)nRT contribution from each degree of freedom. So monatomic gets 3 spatial degrees of freedom. Diatomic gets 3 spatial PLUS 2 rotational - rotation along primary axis does not represent any difference.

So my primary question is, what is the internal energy of water vapor? I would guess

$$U = (6/2)nRT$$

We ought to get one extra degree of rotational freedom. But I'm worried that I'm missing out on vibrational degrees of freedom.

Further inquiries:

  • Why do we not account for the 1 degree of vibrational freedom in diatomic molecules?
  • Do the vibrational degrees of freedom account for a negligible amount of the internal energy, or is it small, but significant?
  • Do the vibrational degrees of freedom take up different proportions of the internal energy at different temperatures or pressures?
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  • $\begingroup$ I don't know about the degrees of freedom, but the molar heat capacity (const. volume) of water vapor is 4.32R based on info from the web. So, it's almost 9R/2. $\endgroup$
    – Chet Miller
    Commented Nov 24, 2020 at 23:28
  • $\begingroup$ Related: physics.stackexchange.com/questions/398848/… Especially, see the plot. $\endgroup$
    – Sean E. Lake
    Commented Nov 25, 2020 at 4:23

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