For a spontaneous process the correct statement is -

Options

A. entropy of the system always increases
B. free energy of the system always increases
C. total entropy change is always negative
D. total entropy change is always positive.

Explanation

To determine the correct statement regarding spontaneous processes, we need to analyze the conditions that define spontaneity in thermodynamics.

### Step-by-Step Solution:

1. **Understanding Spontaneous Processes**:
- A spontaneous process is one that occurs without needing to be driven by an external force.

2. **Gibbs Free Energy (ΔG)**:
- The Gibbs free energy change (ΔG) is a key factor in determining spontaneity. The relationship is given by the equation:
\[ \Delta G = \Delta H - T \Delta S \]
- For a process to be spontaneous at constant temperature and pressure, ΔG must be negative:
\[ \Delta G < 0 \]

3. **Entropy Change (ΔS)**:
- The second law of thermodynamics states that the total entropy change (ΔS_total) of the universe (system + surroundings) must be greater than zero for a spontaneous process:
\[ \Delta S_{total} = \Delta S_{system} + \Delta S_{surroundings} > 0 \]

4. **Analyzing the Statements**:
- **Statement 1**: "The entropy of the system always increases."
- This is incorrect because the entropy of the system can decrease while the surroundings' entropy increases, leading to a positive total entropy change.
- **Statement 2**: "The free energy change of the system always increases."
- This is also incorrect as ΔG must be negative for spontaneity.
- **Statement 3**: "The total entropy change is always negative."
- This is incorrect because, for spontaneity, the total entropy change must be positive.
- **Statement 4**: "The total entropy change is greater than zero."
- This is correct as it aligns with the second law of thermodynamics.

5. **Conclusion**:
- The correct statement regarding spontaneous processes is:
\[ \text{The total entropy change is greater than zero.} \]

### Final Answer:
The correct statement is: **The total entropy change is greater than zero.**

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