# Can you derive a formula for any internal energy of a gas as long as you know the degree of freedom?

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?

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