Internal Energy of Ideal Gas

Internal energy U: total energy of all microscopic motions and interactions inside a system.

For an ideal gas, U depends ONLY on temperature: U = (f/2)·n·R·T, where f = degrees of freedom.

Monatomic gas (He, Ar): f = 3, U = (3/2)nRT. Diatomic gas (N₂, O₂): f = 5, U = (5/2)nRT (translation + rotation).

Polyatomic: more degrees of freedom (translation + rotation + vibration).

ΔU depends only on initial and final STATES — not on path (state function).

Real gases also have potential energy of intermolecular forces; U depends on V slightly.

First law of thermodynamics: ΔU = Q − W. U changes when heat enters or work is done by gas.

Equipartition theorem: each degree of freedom contributes ½k_BT per molecule (½RT per mole).