Which among the following is not an exact differential?

Options

A. Q (dQ = heat absorbed)
B. U (dU = Internal energy change)
C. S (dS = Entropy change)
D. G (dG = Gibbs free energy change)

Answer

To determine which among the given options is not an exact differential, we first need to understand the concepts of exact and inexact differentials.

### Step-by-Step Solution:

1. **Definition of Exact Differential**:
- An exact differential is a differential that is independent of the path taken between two states. It corresponds to a state function, meaning its value depends only on the initial and final states, not on how the transition occurs.

2. **Definition of Inexact Differential**:
- An inexact differential, on the other hand, is dependent on the path taken. It corresponds to a path function, meaning its value can change based on the specific route taken from the initial state to the final state.

3. **Examples of Exact Differentials**:
- Common examples of exact differentials include:
- Change in internal energy (ΔU)
- Change in entropy (ΔS)
- Change in Gibbs free energy (ΔG)
- These quantities are state functions and depend only on the initial and final states.

4. **Identifying Inexact Differential**:
- Heat (Q) is an example of an inexact differential. The amount of heat absorbed or released depends on the specific process (path) taken to go from one state to another. Therefore, it is a path function.

5. **Analyzing the Options**:
- If we consider the options provided:
- Option 1: ΔQ (heat absorbed) - This is an inexact differential.
- Option 2: ΔU (internal energy) - This is an exact differential.
- Option 3: ΔS (entropy) - This is an exact differential.
- Option 4: ΔG (Gibbs free energy) - This is an exact differential.

6. **Conclusion**:
- Since ΔQ is dependent on the path taken, it is not an exact differential. Therefore, the correct answer is Option 1.

### Final Answer:
**Option 1: ΔQ (heat absorbed) is not an exact differential.**