Internal Energy

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Internal energy

A characteristic property of the state of a thermodynamic system, introduced in the first law of thermodynamics. For a static, closed system (no bulk motion, no transfer of matter across its boundaries), the change in internal energy for a process is equal to the heat absorbed by the system from its surroundings minus the work done by the system on its surroundings. Only a change in internal energy can be measured, not its value for any single state. For a given process, the change in internal energy is fixed by the initial and final states and is independent of the path by which the change in state is accomplished. See Thermodynamic principles

Internal Energy


the energy of an object that depends only on its internal state. The concept of internal energy includes all forms of energy except the energy of its motion as a whole and potential energy, which an object may have if it is in the field of any force (for example, a gravitational field).

The concept of internal energy was introduced by W. Thomson (1851), who defined the change in internal energy (ΔU) of a physical system in any process as the algebraic sum of the amount of heat Q that the system exchanges with the environment during the process and the work A performed by the system or performed on it:


The work A is considered positive if it is performed by the system on external objects, and the amount of heat Q is positive if it is transferred to the system. The above equation expresses the first law of thermodynamics—the law of conservation of energy applied to processes in which heat transfer occurs.

According to the law of conservation of energy, internal energy is a single-valued function of the state of the physical system—that is, of the independent variables that specify the physical system’s state (for example, temperature T and volume V or pressure p). Although each quantity (Q and A) depends on the process that converts a system with internal energy U1 to a system with internal energy U2, the single-valued quality of the internal energy implies that ΔU is determined only by the internal-energy values of the initial and final states: ΔU = U2U1. For any closed process that returns the system to its original state (U2 = U1), the internal energy change is zero, and Q = A.

The change in internal energy of a system in an adiabatic process (without heat exchange with the environment—that is, Q = 0) is equal to the work performed on the system or by the system.

For the simplest physical system, an ideal gas, a change in internal energy, according to the kinetic theory of gases, reduces to a change in the kinetic energy of the molecules, which is determined by the temperature. Consequently, the change in internal energy of an ideal gas (or a close-to-ideal gas with little intermolecular interaction) is determined only by its temperature change (Joule’s law). In physical systems whose particles interact (real gases, liquids, and solids), the internal energy also includes the energy of intermolecular and intramolecular interactions. The internal energy of such systems depends on both temperature and pressure (volume).

It is possible to determine experimentally only the gain or loss of internal energy in a physical process (the initial state, for example, may be taken as the reference point). The methods of statistical physics permit in principle the theoretical calculation of the internal energy of a physical system, but only to within a constant term, which depends on the zero position selected.

At low temperatures, near absolute zero (−273.15° C), the internal energy of a condensed system (of liquids and solids) approaches a specific constant value U0, becoming independent of temperature (the third law of thermodynamics). The value of U0 can be taken as the reference point of internal energy.

Internal energy is among the fundamental thermodynamic potentials. A change in internal energy at constant volume and temperature characterizes the thermal effect of a reaction, and the derivative of the internal energy with respect to temperature at constant volume defines the heat capacity of the system.


internal energy

[in′tərn·əl ′en·ər·jē]
A characteristic property of the state of a thermodynamic system, introduced in the first law of thermodynamics; it includes intrinsic energies of individual molecules, kinetic energies of internal motions, and contributions from interactions between molecules, but excludes the potential or kinetic energy of the system as a whole; it is sometimes erroneously referred to as heat energy.
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