Temperature remaining constant, the pressure of gas is decreased by 20%. The percentage change in volume

Options

A. increases by 20%
B. decreases by 20%
C. increases by 25%
D. decreases by 25%

Explanation

To solve the problem of finding the percentage change in volume when the pressure of a gas is decreased by 20% at constant temperature, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: According to Boyle's Law, for a given mass of gas at constant temperature, the pressure (P) is inversely proportional to the volume (V). This can be expressed as:
\[ P \propto \frac{1}{V} \quad \text{or} \quad PV = \text{constant} \]

2. **Initial and Final Pressures**: Let the initial pressure be \( P_1 \). If the pressure is decreased by 20%, the final pressure \( P_2 \) can be calculated as:
\[ P_2 = P_1 - 0.20 \times P_1 = 0.80 \times P_1 \]

3. **Using the Inverse Relationship**: Since \( P_1 V_1 = P_2 V_2 \), we can set up the equation:
\[ P_1 V_1 = P_2 V_2 \]
Substituting \( P_2 \):
\[ P_1 V_1 = (0.80 \times P_1) V_2 \]

4. **Canceling \( P_1 \)**: We can cancel \( P_1 \) from both sides (assuming \( P_1 \neq 0 \)):
\[ V_1 = 0.80 V_2 \]

5. **Rearranging for \( V_2 \)**: Rearranging the equation gives:
\[ V_2 = \frac{V_1}{0.80} = 1.25 V_1 \]

6. **Calculating Percentage Change in Volume**: The percentage change in volume can be calculated using the formula:
\[ \text{Percentage Change} = \frac{V_2 - V_1}{V_1} \times 100 \]
Substituting \( V_2 \):
\[ \text{Percentage Change} = \frac{1.25 V_1 - V_1}{V_1} \times 100 \]
Simplifying this:
\[ = \frac{0.25 V_1}{V_1} \times 100 = 25\% \]

7. **Conclusion**: The volume increases by 25%. Therefore, the correct answer is that the percentage change in volume is an increase of 25%.