Internal energy

Internal energy


A characteristic property of the state of a thermodynamic system, introduced in the first law of thermodynamics. For a static, closed system (no bulk motion, no transfer of matter across its boundaries), the change in internal energy for a process is equal to the heat absorbed by the system from its surroundings minus the work done by the system on its surroundings. Only a change in internal energy can be measured, not its value for any single state. For a given process, the change in internal energy is fixed by the initial and final states and is independent of the path by which the change in state is accomplished.

Overview

Internal energy does not include the translational or rotational kinetic energy of a body as a whole. It also does not include the relativistic mass-energy equivalent E = mc2. It excludes any potential energy a body may have because of its location in external gravitational or electrostatic field, although the potential energy it has in a field due to an induced electric or magnetic dipole moment does count, as does the energy of deformation of solids (stress-strain).

The principle of equipartition of energy in classical statistical mechanics states that each molecular degree of freedom receives 1/2 kT of energy, a result which was modified when quantum mechanics explained certain anomalies; e.g., in the observed specific heats of crystals (when hν > kT). For monatomic helium and other noble gases, the internal energy consists only of the translational kinetic energy of the individual atoms. Monatomic particles, of course, do not (sensibly) rotate or vibrate, and are not electronically excited to higher energies except at very high temperatures.

From the standpoint of statistical mechanics, the internal energy is equal to the ensemble average of the total energy of the system.