Internal Energy

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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 particles (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 of the chemical bonds, and the energy of the free, conduction electrons in metals.

Internal energy does not include the translational or rotational kinetic energy of a body as a whole. 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 quadratic degree of freedom receives 1/2 kT of energy, a result which had to be modified when quantum mechanics explained certain anomalies, such as discrepancies in the observed specific heats of crystals when the expected thermal energy per degree of freedom is less than the energy necessary to move that degree of freedom up one quantum energy level.

Internal energy is the sum of all forms of energy of a system. It is related to the molecular structure and the degree of molecular activity and may be viewed as the sum of kinetic and potential energies of the molecules; it is composed of the following types of energies:

Type Composition of Internal Energy (U)
Sensible energy the portion of the internal energy of a system associated with kinetic energies (molecular translation, rotation, and vibration; electron translation and spin; and nuclear spin) of the molecules.
Latent energy the internal energy associated with the phase of a system.
Chemical energy the internal energy associated with the chemical bonds in a molecule.
Nuclear energy the very large amount of energy associated with the bonds within the nucleus of the atom itself.
Energy interactions those types of energies not stored in the system (e.g. heat transfer, mass transfer, and work), but which are recognized at the system boundary as they cross it, which represent gains or losses by a system during a process.

Sensible energy and latent energy together can be referred to as thermal energy.

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