Question

Which among the following is not an exact differential?
A ) $Q\left( {dQ = {\text{heat absorbed}}} \right)$
B ) $U\left( {dU = {\text{change in internal energy}}} \right)$
C ) $S\left( {dS = {\text{Entropy change}}} \right)$
D ) $G\left( {dG = {\text{Gibbs free energy change}}} \right)$

Answer 1

Exact differentials are independent of the path followed. Inexact differentials are dependent on the path followed.

Complete answer:

State functions are defined with exact differentials. Path functions are defined with inexact differentials. State functions depend only on the initial and final state. They are independent of the path followed. Change in internal energy, change in entropy and change in Gibbs free energy are the state functions. They depend on the initial and final states only. Hence, they are described by exact differentials. Integration of exact differentials require only initial and final values. It does not require several integrals and limits of integration.
Thus change in the internal energy is the difference in the value of final internal energy and initial internal energy. Similarly, entropy change is the difference in the value of final entropy and initial entropy. Same is true for Gibbs free energy change.
Path functions depend on the path followed. If change from initial state to final state is done by two different paths, then the values of path functions will be different for these two paths. To integrate inexact differentials used for path functions require several integrals and limits of integration.
$Q\left( {dQ = {\text{heat absorbed}}} \right)$ is not an exact differential as it depends on the path followed.

Hence, the option A) is the correct answer.

Note: Heat absorbed does not only depend on the initial and final values, it also depends on the path followed. It is possible that when two different paths are followed from the same initial state to the same final state, the heat absorbed is different for these two paths.