in thermodynamics, the internal energy of a thermodynamic system, or a body with well-defined boundaries, denoted by "u", or sometimes "e", is the total of the kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the potential energy associated with the vibrational and electric energy of atoms within molecules or crystals. it includes the energy in all the chemical bonds, and the energy of the free, conduction electrons in metals.