# Internal Energy

In thermodynamics, the internal energy is the total energy contained by a thermodynamic system. It is the energy needed to create the system, but excludes the energy to displace the system's surroundings, any energy associated with a move as a whole, or due to external force fields. Internal energy has two major components, kinetic energy and potential energy. The kinetic energy is due to the motion of the system's particles (translations, rotations, vibrations), and the potential energy is associated with the static rest mass energy of the constituents of matter, static electric energy of atoms within molecules or crystals, and the static energy of chemical bonds. The internal energy of a system can be changed by heating the system or by doing work on it; the first law of thermodynamics states that the increase in internal energy is equal to the total heat added and work done by the surroundings. If the system is isolated, its internal energy cannot change.

For practical considerations in thermodynamics or engineering it is rarely necessary, nor convenient, to consider all energies belonging to the total intrinsic energy of a sample system, such as the energy given by the equivalence of mass. Typically, descriptions only include components relevant to the system under study. Thermodynamics is chiefly concerned only with changes of the internal energy.

The internal energy is a state function of a system, because its value depends only on the current state of the system and not on the path taken or process undergone to arrive at this state. It is an extensive quantity. The SI unit of energy is the joule (J). Sometimes a corresponding intensive thermodynamic property called specific internal energy is defined, which is internal energy per a unit of mass (kilogram) of the system in question. As such, the SI unit of specific internal energy is J/kg. If intensive internal energy is expressed relative to units of amount of substance (mol), then it is referred to as molar internal energy and the unit is J/mol.

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

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... The inequality can be expressed in terms of the internal energy as where is the time derivative of the specific internal energy (the internal energy per unit mass), is the Cauchy stress ... This inequality incorporates the balance of energy and the balance of linear and angular momentum into the expression for the Clausius–Duhem inequality ... index notation with respect to a Cartesian coordinate system , Hence, From the balance of energy Therefore, Rearranging ...
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... its chemical structure undergoes some stress which raises its internal energy in comparison to a strain-free reference compound ... The internal energy of a molecule consists of all the energy stored within it ... A strained molecule has an additional amount of internal energy which an unstrained molecule does not ...

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