Which of following factor always increases for spontaneous process

Options

A. `DeltaS`
B. `DeltaH`
C. `DeltaH-T DeltaS`
D. `DeltaS-(DeltaH)/(T)`

Explanation

To solve the question "Which of the following factors always increases for a spontaneous process?", we will analyze the relationship between Gibbs free energy (ΔG) and entropy (ΔS) in spontaneous processes.

### Step-by-Step Solution:

1. **Understanding Spontaneous Processes**:
- A spontaneous process is one that occurs without needing to be driven by an external force. For a process to be spontaneous at constant temperature and pressure, the change in Gibbs free energy (ΔG) must be negative.
- **Hint**: Remember that spontaneity is linked to the sign of ΔG.

2. **Gibbs Free Energy Equation**:
- The relationship between Gibbs free energy, enthalpy (ΔH), and entropy (ΔS) is given by the equation:
\[ \Delta G = \Delta H - T \Delta S \]
- **Hint**: This equation shows how ΔG depends on both ΔH and ΔS.

3. **Entropy of the Universe**:
- According to the second law of thermodynamics, the total entropy of the universe (ΔS_total) always increases for spontaneous processes. This can be expressed as:
\[ \Delta S_{total} = \Delta S_{system} + \Delta S_{surroundings} > 0 \]
- **Hint**: Focus on the concept that the total entropy must increase for spontaneity.

4. **Calculating ΔS_total**:
- We can express the change in Gibbs free energy in terms of entropy:
\[ \Delta G = -T \Delta S_{total} \]
- Rearranging gives:
\[ \Delta S_{total} = -\frac{\Delta G}{T} \]
- **Hint**: This shows that if ΔG is negative (for spontaneous processes), ΔS_total must be positive.

5. **Conclusion**:
- Since ΔS_total is always greater than zero for spontaneous processes, we conclude that the factor that always increases for spontaneous processes is the entropy of the universe.
- **Hint**: Look for the option that states that entropy increases.

### Final Answer:
The factor that always increases for a spontaneous process is the **entropy of the universe** (ΔS_total).