I have the following formula that I derived from studying my textbook that generalizes to all ideal gases:

Monoatomic molecular gases ($\ce{He, Ne}$ etc.)

Degree of freedom: 3

$\ce \frac{3}{2}nRT = U$

Diatomic molecular gases ($\ce{O_2, N_2}$ etc.)

Degree of freedom: 5

$\ce \frac{5}{2}nRT = U$

Polyatomic molecular gases ($\ce{CH_4, H_2O}$ etc.)

Degree of freedom: 6

$\ce \frac{6}{2}nRT = U$

As you can see here, we observe that a general trend for the formula for the internal energy of a gas is:

$\frac{\text{degree of freedom}}{2}nRT$ = U

Is this correct?

  • $\begingroup$ Yes it is, look up "equipartition theorem". $\endgroup$ – orthocresol Apr 16 '16 at 23:33
  • $\begingroup$ It's correct for ideal gases. $\endgroup$ – Chet Miller Apr 16 '16 at 23:37
  • $\begingroup$ cool! thank you orthocresol and chester miller $\endgroup$ – phi2k Apr 16 '16 at 23:42

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