What characterizes an exact differential?

An exact differential is characterized by its independence from the path taken during integration. This means that the value of the integral is determined solely by the initial and final states of the system, rather than the specific route taken between those states. In thermodynamics and physical chemistry, exact differentials are typically associated with state functions, such as internal energy, enthalpy, and free energy.

For a differential to be considered exact, it must satisfy the condition that the mixed second derivatives are equal, which is a mathematical requirement indicating that the order of differentiation does not matter. As a result, exact differentials lead to path-independent results, allowing for the straightforward calculation of changes in state functions, which is essential in the analysis of thermodynamic processes.

In contrast, path-dependent quantities, such as work or heat, cannot be represented by an exact differential because their values depend on the specific process through which the system is taken. Hence, the concept of exact differentials is foundational for understanding thermodynamic potentials and transformations in physical chemistry.