In this text we compare the internal energy concept usually given in thermodynamics and physical chemistry textbooks with that from continuum mechanics. We review some continuum mechanics local balance equations. Next, we define internal and rigid energies for systems of particles. By comparing the internal energy balance for the systems of particles to that of continuum mechanics, we confirm that the work included in the usual presentation of the first law is related to motions that conserve both linear and angular momenta. We also confirm the existence of an internal energy conservation law.