Internal Energy - Description and Definition

Description and Definition

The internal energy (U) is the sum of all forms of energy (E_i) intrinsic to a thermodynamic system:

It is the energy needed to create the system. It may be divided into potential energy (U_pot) and kinetic energy (U_kin) components:

The kinetic energy of a system arises as the sum of the motions of all the system's particles, whether it be the motion of atoms, molecules, atomic nuclei, electrons, or other particles. The potential energy includes all energies given by the mass of particles, by the chemical composition, i.e. the chemical energy stored in chemical bonds having the potential to undergo chemical reactions, the nuclear energy stored by the configuration of protons, neutrons, and other elementary particles in atomic nuclei, and the physical force fields within the system, such as due to internal induced electric or magnetic dipole moment, as well as the energy of deformation of solids (stress-strain).

Internal energy does not include the energy due to motion of a system as a whole. It further excludes any kinetic or potential energy the body may have because of its location in external gravitational, electrostatic, or electomagnetic fields. It does, however, include the contribution to the energy due to the coupling of the internal degrees of freedom of the object to such the field. In such a case, the field is included in the thermodynamic description of the object in the form of an additional external parameter.

For practical considerations in thermodynamics or engineering, it is rarely necessary, convenient, nor even possible, 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. Indeed in most systems under consideration, especially through thermodynamics, it is impossible to calculate the total internal energy. Therefore, a convenient null reference point may be chosen for the internal energy.

The internal energy is an extensive property: it depends on the size of the system, or on the amount of substance it contains.

At any temperature greater than absolute zero, potential energy and kinetic energy constantly converted into one another, but the sum remains constant in an isolated system (cf. table). In the classical picture of thermodynamics, kinetic energy vanishes at zero temperature and the internal energy is purely potential energy. However, quantum mechanics has demonstrated that even at zero temperature particles maintain a residual energy of motion, the zero point energy. A system at absolute zero is merely in its quantum-mechanical ground state, the lowest energy state available. At absolute zero a system has attained its minimum attainable entropy.

The kinetic energy portion of the internal energy gives rise to the temperature of the system. Statistical mechanics relates the pseudo-random kinetic energy of individual particles to the mean kinetic energy of the entire ensemble of particles comprising a system. Furthermore it relates the mean kinetic energy to the macroscopically observed empirical property that is expressed as temperature of the system. This energy is often referred to as the thermal energy of a system, relating this energy, like the temperature, to the human experience of hot and cold.

Statistical mechanics considers any system to be statistically distributed across an ensemble of N microstates. Each microstate has an energy E_i and is associated with a probability p_i. The internal energy is the mean value of the system's total energy, i.e., the sum of all microstate energies, each weighted by their probability of occurrence:

This is the statistical expression of the first law of thermodynamics.