Internal energy Totally Explained

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'll 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.

Overview

Internal energy doesn't include the translational or rotational kinetic energy of a body as a whole. It also doesn't 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; for example, 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, don't (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.

Composition

Internal energy – the sum of all microscopic 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's comprised 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 atomic bonds in a molecule.
Nuclear energy	the tremendous amount of energy associated with the strong bonds within the nucleus of the atom itself.
Energy interactions	those types of energies not stored in the system (for example 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.
Thermal energy	the sum of sensible and latent forms of internal energy.

The first law of thermodynamics

The internal energy is essentially defined by the first law of thermodynamics which states that energy is conserved:
�

Delta U = Q + W + W' ,

where � ΔU is the change in internal energy of a system during a process.

� Q is heat added to a system (measured in joules in SI); that is, a positive value for Q represents heat flow into a system while a negative value denotes heat flow out of a system.

� W is the mechanical work done on a system (measured in joules in SI)

� W' is energy added by all other processes

The first law may be equivalently in infinitesimal terms as:
�

mathrm

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