What are exact differential? If volume V is a function of temperature T & pressure P then show that for ideal gas dv is a exact differential?

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Answer

Exact differentials are differentials that can be expressed as the exact derivative of a function. In other words, if a differential can be written as the differential of a particular function, it is said to be an exact differential.

If volume (V) is a function of temperature (T), then the differential of volume (dV) can be expressed as an exact differential if there exists a function f such that:

dV = (∂f/∂T) dT

In simpler terms, if the change in volume (dV) can be precisely determined by taking the derivative of a function f with respect to temperature (dT), then dV is an exact differential.

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