The condition of spontaneity of process is

Options

A. Lowering of entropy at constant temperature and pressure
B. Lowering of Gibbs free energy of system at constant temperature and pressure
C. Increase of entropy of system at constant temperature and pressure
D. Increase of Gibbs free energy of the universe at constant temperature and pressure

Explanation

To determine the conditions for spontaneity of a process, we can analyze the statements provided in the question. Here’s a step-by-step solution:

### Step 1: Understand Spontaneity
A spontaneous process is one that occurs naturally without the need for external energy. Examples include the melting of ice or the rusting of iron.

**Hint:** Remember that spontaneity is related to natural processes that happen on their own.

### Step 2: Analyze the First Option
The first option states "lowering of entropy at constant temperature and pressure." For a process to be spontaneous, the change in entropy (ΔS) must be positive, indicating an increase in disorder. Therefore, this statement is incorrect.

**Hint:** Consider what happens to disorder in a spontaneous process.

### Step 3: Analyze the Second Option
The second option states "lowering of Gibbs free energy of the system at constant temperature and pressure." For a process to be spontaneous, the change in Gibbs free energy (ΔG) must be negative. This means that the Gibbs free energy of the products must be less than that of the reactants. Thus, this statement is correct.

**Hint:** Recall that a negative ΔG indicates a spontaneous process.

### Step 4: Analyze the Third Option
The third option states "increase of entropy of the system at constant temperature and pressure." As mentioned earlier, for a spontaneous process, the change in entropy (ΔS) should be positive, which means the entropy of the system increases. Therefore, this statement is also correct.

**Hint:** Think about how entropy relates to the disorder of a system.

### Step 5: Analyze the Fourth Option
The fourth option states "increase of Gibbs free energy of the universe at constant temperature and pressure." This statement is incorrect because for a spontaneous process, the Gibbs free energy of the universe must decrease (or be negative). Thus, this statement is wrong.

**Hint:** Remember that the universe's Gibbs free energy should decrease for spontaneity.

### Conclusion
Based on the analysis, the conditions for spontaneity are:
- Lowering of Gibbs free energy of the system at constant temperature and pressure (correct).
- Increase of entropy of the system at constant temperature and pressure (correct).

Thus, the correct options are the second and third statements.

**Final Answer:** The conditions of spontaneity of a process are:
1. Lowering of Gibbs free energy of the system at constant temperature and pressure.
2. Increase of entropy of the system at constant temperature and pressure.