Internal energy of an ideal gas

The internal energy of an ideal gas is the sum of the kinetic energies of all its molecules. It depends only on temperature, the number of moles and the structure of the molecule:

$U=\frac{i}{2}\,nRT$

where $i$ is the number of degrees of freedom: a monatomic gas (He, Ar) has $i=3$ (translation only), a diatomic one (O₂, N₂, air) $i=5$ (+ 2 rotations) and a polyatomic one (CO₂, H₂O) $i=6$. The gas constant is $R=8.314\ \tfrac{\text{J}}{\text{mol·K}}$.

An important consequence: the internal energy of an ideal gas does not depend on pressure or volume — it is a function of temperature alone (for a fixed $n$ and type of gas). That is why $\Delta U=0$ in an isothermal process.