For a given mass of a gas at constant temperature, if the volume `V` becomes three times, then the pressure (`p`) will become :

Options

A. `3p`
B. `p//3`
C. `3p//T`
D. `9p^(2)`

Explanation

To solve the problem, we will use the ideal gas law and the principles of Boyle's Law, which states that for a given mass of gas at constant temperature, the product of pressure and volume is a constant.

### Step-by-Step Solution:

1. **Identify Initial Conditions**:
- Let the initial volume \( V_1 = V \).
- Let the initial pressure \( P_1 = P \).

2. **Determine Final Conditions**:
- The volume is increased to three times its original value, so the final volume \( V_2 = 3V \).

3. **Apply Boyle's Law**:
- According to Boyle's Law, for a constant temperature, the relationship between pressure and volume is given by:
\[ P_1 V_1 = P_2 V_2 \]
- Here, \( P_2 \) is the final pressure we need to find.

4. **Substitute Known Values**:
- Substitute \( V_1 \) and \( V_2 \) into the equation:
\[ P \cdot V = P_2 \cdot (3V) \]

5. **Rearrange the Equation**:
- To isolate \( P_2 \), rearrange the equation:
\[ P_2 = \frac{P \cdot V}{3V} \]

6. **Simplify**:
- The \( V \) terms cancel out:
\[ P_2 = \frac{P}{3} \]

7. **Conclusion**:
- The final pressure \( P_2 \) is one-third of the initial pressure \( P \):
\[ P_2 = \frac{P}{3} \]

### Final Answer:
The pressure will become \( \frac{P}{3} \).

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