Internal energy

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.

The internal energy is a thermodynamic potential and for a closed thermodynamic system held at constant entropy, it will be minimized.

One can also calculate the internal energy of electromagnetic or blackbody radiation. It is a state function of a system, an extensive quantity. The SI unit of energy is the joule although other historical, conventional units are still in use, such as the (small and large) calorie for heat. (Calories that are on classic food labels are actually kilo-calories.)

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.

References

• Alberty, R. A. (2001). "Use of Legendre transforms in chemical thermodynamics" (PDF). Pure Appl. Chem. 73 (8): 1349–1380. doi:10.1351/pac200173081349. S2CID 98264934.

• Lewis, Gilbert Newton; Randall, Merle: Revised by Pitzer, Kenneth S. & Brewer, Leo (1961). Thermodynamics (2nd ed.). New York, NY USA: McGraw-Hill Book Co. ISBN 0-07-113809-9.{{cite book}}: CS1 maint: multiple names: authors list (link)

• Landau, L. D.; Lifshitz, E. M. (1986). Theory of Elasticity (Course of Theoretical Physics Volume 7). (Translated from Russian by J.B. Sykes and W.H. Reid) (Third ed.). Boston, MA: Butterworth Heinemann. ISBN 0-7506-2633-X.