The Molecular Nature of Internal Energy

Molecules show various degrees of freedom, including translational, rotational, and vibrational, which influence their total internal energy.

Electronic energy, intermolecular forces, and the rest-mass energy of electrons and nuclei also influence the molar internal energy of molecules.

For monatomic gases moving in three dimensions at a temperature T, the equipartition theorem calculates the translational kinetic energy as 3/2 kT. Multiplying it by Avogadro’s number gives the molar translational energy of 3/2 RT.

For polyatomic gases, the molar rotational energy contributes an additional ½ RT per rotational mode from three modes in non-linear molecules and two in linear ones.

Molar vibrational energy is a more complex component that varies with temperature and molecule type.

In ideal gases, where intermolecular forces are negligible, molar electronic and rest-mass energies remain constant.

For ideal monatomic gases, the molar internal energy depends solely on molar translational energy, establishing a linear relationship between the molar internal energy and temperature.