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

Options

A. increased by 20%
B. decrease by 20%
C. increased by 25%
D. decreased by 25%

Explanation

To solve the problem step by step, we will use the ideal gas law and the relationship between pressure and volume at constant temperature.

### Step 1: Understand the relationship between pressure and volume
According to Boyle's Law, for a given mass of gas at constant temperature, the product of pressure (P) and volume (V) is constant:
\[ P \times V = \text{constant} \]
This means that if the pressure changes, the volume must change in such a way that the product remains constant.

### Step 2: Express the change in pressure
The problem states that the pressure of the gas is decreased by 20%. If the initial pressure is \( P \), the new pressure \( P' \) can be expressed as:
\[ P' = P - 0.20P = 0.80P \]
This means that the new pressure is 80% of the original pressure.

### Step 3: Relate the new volume to the new pressure
Using the relationship from Boyle's Law, we can write:
\[ P \times V = P' \times V' \]
Substituting \( P' \) into the equation gives:
\[ P \times V = (0.80P) \times V' \]

### Step 4: Solve for the new volume \( V' \)
We can simplify the equation:
\[ V' = \frac{P \times V}{0.80P} = \frac{V}{0.80} = \frac{V}{\frac{4}{5}} = \frac{5}{4}V \]
This shows that the new volume \( V' \) is \( \frac{5}{4} \) times the original volume \( V \).

### Step 5: Calculate the percentage change in volume
To find the percentage change in volume, we use the formula:
\[ \text{Percentage Change} = \frac{V' - V}{V} \times 100 \]
Substituting \( V' = \frac{5}{4}V \):
\[ \text{Percentage Change} = \frac{\frac{5}{4}V - V}{V} \times 100 \]
This simplifies to:
\[ = \frac{\frac{5}{4}V - \frac{4}{4}V}{V} \times 100 = \frac{\frac{1}{4}V}{V} \times 100 = \frac{1}{4} \times 100 = 25\% \]

### Step 6: Conclusion
The percentage change in volume is an increase of 25%.