In an irreversible process taking place at constant `T` and `P` and in which only pressure-volume work is being done, the change in Gibbs free energy `(dG)` and the change in entropy `(dS)` satisfy the criteria

Options

A. `(triangleS)_(VE)=0, (triangleG)_(T,P)=0`
B. `(triangleS)_(V,E)=0, (triangleG)_(T,P) gt 0`
C. `(triangleS)_(V,E) lt 0, (triangleG)_(T,P) lt 0`
D. `(triangleS)_(V,E) gt 0, (triangleG)_(T,P) lt 0`

Answer

To solve the question regarding the relationship between the change in Gibbs free energy (dG) and the change in entropy (dS) for an irreversible process occurring at constant temperature (T) and pressure (P), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Process**:
- We are dealing with an irreversible process that occurs at constant temperature and pressure. In such processes, the system is not in equilibrium, and spontaneous changes occur.

2. **Criteria for Spontaneity**:
- For a process to be spontaneous at constant temperature and pressure, the change in Gibbs free energy (ΔG) must be negative. This is a fundamental criterion for spontaneity:
\[ \Delta G < 0 \]

3. **Entropy Change**:
- In an irreversible process, the change in entropy (ΔS) of the universe (system + surroundings) must be positive. This means that the entropy of the system may increase, but the total change in entropy must be greater than zero:
\[ \Delta S > 0 \]

4. **Relationship Between ΔG and ΔS**:
- The relationship between the change in Gibbs free energy and the change in entropy at constant temperature and pressure can be expressed using the equation:
\[ \Delta G = \Delta H - T\Delta S \]
- For spontaneous processes, since ΔG < 0 and ΔS > 0, we can infer that the term \(T\Delta S\) must be greater than ΔH for ΔG to be negative.

5. **Conclusion**:
- Therefore, in an irreversible process at constant temperature and pressure, we conclude:
- **ΔG < 0** (indicating spontaneity)
- **ΔS > 0** (indicating an increase in entropy)

### Summary:
In an irreversible process at constant temperature and pressure, the change in Gibbs free energy (ΔG) is less than zero, and the change in entropy (ΔS) is greater than zero.

---