The internal energy of an ideal gas is given by:
[tex]U= \frac{k}{2}nRT [/tex]
where
k is the number of degrees of freedom of the molecules of the gas
n is the number of moles
R is the gas constant
T is the absolute temperature.
For a diatomic gas, k=5. In our problem, the number of moles is n=2.00 and the absolute temperature of the gas is T=765 K, so its internal energy is
[tex]U= \frac{5}{2}nRT= \frac{5}{2}(2.00 mol)(8.31 J/mol K)(765 K)=3.18 \cdot 10^4 J [/tex]
