`{:(,"Column I",,"Column 2",,"Column 3",),(,"Enthalpy and",,"Entropy change",,"Entropy change of",),(,"internal energy change",,"of the system",,"the surroundings",),((I),DeltaH=0,(i),(DeltaH)/(T),(P),-(DeltaH)/(T),),((II),DeltaU=0,(ii),0,(Q),0,),((III),DeltaH=+ve,(iii),+ve,(R),+ve,),((IV),DeltaH=-ve,(iv),-ve,(S),-ve,):}`
The only incorrect combination for `P_(4) ("red") rarr P_(4) ("black")` which is a reversible phase transition at constant temperature and pressure.

Options

A. `(IV)-(i)-(P)`
B. `(IV)-(iv)-(P )`
C. `(III)-(i)-(R )`
D. `(IV)-(i)-(R)`

Explanation

To solve the problem, we need to analyze the combinations given in the columns and determine which one is incorrect based on the principles of thermodynamics, specifically focusing on the changes in enthalpy (ΔH), internal energy (ΔU), and entropy (ΔS) during a reversible phase transition at constant temperature and pressure.

### Step-by-Step Solution:

1. **Understanding the Transition**:
- The transition is from P4 (red) to P4 (black), where P4 (red) is the unstable form and P4 (black) is the more stable form.
- Since the transition is from a higher energy state to a lower energy state, energy is released in the process.

2. **Analyzing ΔH**:
- Since energy is released during the transition, the change in enthalpy (ΔH) will be negative (ΔH < 0).

3. **Analyzing ΔS of the System**:
- As the system moves from a less stable (more random) state to a more stable (less random) state, the entropy change of the system (ΔS_system) will also be negative (ΔS_system < 0).
- The relationship between ΔS of the system and ΔH is given by the equation:
\[ ΔS_{system} = \frac{ΔH}{T} \]
- Since ΔH is negative, ΔS_system will also be negative.

4. **Analyzing ΔS of the Surroundings**:
- The entropy change of the surroundings (ΔS_surroundings) is related to the change in enthalpy of the system:
\[ ΔS_{surroundings} = -\frac{ΔH}{T} \]
- Since ΔH is negative, ΔS_surroundings will be positive (ΔS_surroundings > 0).

5. **Matching Combinations**:
- Now we will match the combinations from the columns:
- **(I)**: ΔH = 0, ΔS_system = ΔH/T, ΔS_surroundings = -ΔH/T → Incorrect (ΔH is not 0)
- **(II)**: ΔU = 0, ΔS_system = 0, ΔS_surroundings = Q → Incorrect (ΔU is not 0)
- **(III)**: ΔH = +ve, ΔS_system = +ve, ΔS_surroundings = +ve → Incorrect (ΔH is not positive)
- **(IV)**: ΔH = -ve, ΔS_system = -ve, ΔS_surroundings = +ve → Correct (matches our analysis)

6. **Identifying the Incorrect Combination**:
- The only incorrect combination based on our analysis is from option **(III)**: ΔH = +ve, ΔS_system = +ve, ΔS_surroundings = +ve.

### Conclusion:
The incorrect combination is **(III)**: ΔH = +ve, ΔS_system = +ve, ΔS_surroundings = +ve.