If the volume of a given mass of a gas at constant temperature becomes three times, the pressure will be

Options

A. 3p
B. p/3
C. 9p
D. p

Answer

To solve the problem, we can use Boyle's Law, which states that for a given mass of gas at constant temperature, the product of pressure (P) and volume (V) is constant. This can be expressed mathematically as:

\[ P_1 V_1 = P_2 V_2 \]

Where:
- \( P_1 \) = initial pressure
- \( V_1 \) = initial volume
- \( P_2 \) = final pressure
- \( V_2 \) = final volume

### Step-by-Step Solution:

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

2. **Determine the Final Volume**:
- According to the problem, the final volume \( V_2 \) is three times the initial volume:
\[ V_2 = 3V_1 \]

3. **Apply Boyle's Law**:
- Using Boyle's Law, we can set up the equation:
\[ P_1 V_1 = P_2 V_2 \]

4. **Substitute for \( V_2 \)**:
- Substitute \( V_2 \) with \( 3V_1 \):
\[ P_1 V_1 = P_2 (3V_1) \]

5. **Simplify the Equation**:
- Divide both sides by \( V_1 \) (assuming \( V_1 \neq 0 \)):
\[ P_1 = 3P_2 \]

6. **Solve for \( P_2 \)**:
- Rearranging gives:
\[ P_2 = \frac{P_1}{3} \]

7. **Conclusion**:
- If the initial pressure is \( P_1 \), then the final pressure \( P_2 \) is:
\[ P_2 = \frac{P_1}{3} \]

### Final Answer:
The pressure will be \( \frac{P_1}{3} \) or one-third of the original pressure.

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