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Internal energy

The internal energy of a system (abbreviated E or U) is the total kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the total potential energy associated with the vibrational and electric energy of atoms within molecules. Internal energy is a quantifiable state function of a system. The SI unit of internal energy is the same as for energy, and is the joule.

For systems consisting of molecules, the internal energy is partitioned among all of these types of motion. In systems consisting of monatomic particles, such as helium gas and other noble gases, the internal energy consists only of the translational kinetic energy of the individual atoms. Monatomic particles, of course, do not rotate or vibrate, and are not excited to higher electrical energies, except at very high temperatures.

Each molecular energy state has its own internal energy.


Internal energy can not be measured directly; it is only measured as a change (ΔU). The equation for change in internal energy is

\Delta U = Q + W \,


Q is heat, measured in joules

W is work, measured in joules

When heat or work transfers energy from the system to the surroundings, Q or W is negative. R. Tao R. H.

Duhem-Gibbs Relation

For quasistatic processes, the following relation holds:

dU = TdS - pdV + \mu dN \,


T is the temperature, measured in kelvin

S the entropy, measured in joule / kelvin

p the pressure, measured in pascals

μ the chemical potential, measured in

N the number of particles in the system, measured in

d denotes the differential, the instantaneous change.

See also

Last updated: 02-08-2005 20:17:01
Last updated: 03-18-2005 11:16:12