What are exact and inexact differentials?

Answer 1

Exact differentials refer to changes in a function that can be expressed as the total differential of that function, meaning there exists a scalar function whose differential equals the given expression. Inexact differentials, on the other hand, cannot be derived from a single function and typically arise in contexts like thermodynamics, where they represent changes in quantities that are path-dependent. In mathematical terms, an exact differential ( df ) satisfies the condition ( \frac{\partial^2 f}{\partial y \partial x} = \frac{\partial^2 f}{\partial x \partial y} ), while inexact differentials, such as ( dQ ) or ( dW ), do not meet this criterion.