Inexact differential

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An inexact differential (also called incomplete differential ) is a differential that is not a complete differential . In mathematical terms, it is a level 1 differential form that is not the total differential of a function .

Inexact differentials are often notated as if they were the differential of a function, but with one instead of one . For example is

an inexact differential, if , since then the integrability condition is not fulfilled.

In thermodynamics , process variables , e.g. B. the heat , inexact differentials: the heat that a system exchanges with its environment depends on the process control (see path integral ) and is not a thermodynamic potential .

In some cases, an inexact differential can be converted into an exact differential by multiplying it by an integrating factor .

See also

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