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 . Internal energy has two major components , kinetic energy and potential energy .