Internal energy

Internal energy
Common symbols	${\displaystyle U}$
SI unit	J
In SI base units	m2⋅kg/s2
Derivations from other quantities	${\displaystyle \Delta U=\sum _{i}p_{i}E_{i}\!}$ ${\displaystyle \Delta U=nC_{V}\Delta T\!}$

The internal energy of a thermodynamic system is the energy of the system as a state function, measured as the quantity of energy necessary to bring the system from its standard internal state to its present internal state of interest, accounting for the gains and losses of energy due to changes in its internal state, including such quantities as magnetization. It excludes the kinetic energy of motion of the system as a whole and the potential energy of position of the system as a whole, with respect to its surroundings and external force fields. The notion of internal energy was introduced by Clausius as part of the formulation of the first law of thermodynamics.

Without a thermodynamic process, the internal energy of an isolated system does not change, as expressed in the law of conservation of energy, a foundation of the first law of thermodynamics. Without transfer of matter, internal energy changes equal the algebraic sum of the heat transferred and the thermodynamic work done.

The internal energy cannot be measured absolutely. Thermodynamics concerns changes in the internal energy, not its absolute value. The processes that change the internal energy are transfers, into or out of the system, of matter, or of energy, as heat, or by thermodynamic work. These processes are measured by changes in the system's properties, such as temperature, entropy, volume, electric polarization, and molar constitution. The internal energy depends only on the internal state of the system and not on the particular choice from many possible processes by which energy may pass into or out of the system. It is a state variable, a thermodynamic potential, and an extensive property.

Thermodynamics defines internal energy macroscopically, for the body as a whole. In statistical mechanics, the internal energy of a body can be analyzed microscopically in terms of the kinetic energies of microscopic motion of the system's particles from translations, rotations, and vibrations, and of the potential energies associated with microscopic forces, including chemical bonds.

The unit of energy in the International System of Units (SI) is the joule (J). The internal energy relative to the mass with unit J/kg is the specific internal energy. The corresponding quantity relative to the amount of substance with unit J/mol is the molar internal energy.