If pressure of an ideal gas is reduced to 1/4, then volume of the gas at the same temperature will become… times.

Explanation

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

\[ P_1 V_1 = P_2 V_2 \]

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

### Step 1: Define the initial conditions
Let's assume:
- Initial pressure \( P_1 = P \)
- Initial volume \( V_1 = V \)

### Step 2: Define the final conditions
According to the problem, the pressure is reduced to \( \frac{1}{4} \) of the initial pressure:
- Final pressure \( P_2 = \frac{P}{4} \)

### Step 3: Apply Boyle's Law
Using Boyle's Law, we can write:

\[ P_1 V_1 = P_2 V_2 \]

Substituting the values we have:

\[ P \cdot V = \left(\frac{P}{4}\right) V_2 \]

### Step 4: Simplify the equation
Now, we can simplify the equation:

\[ P \cdot V = \frac{P}{4} V_2 \]

To eliminate \( P \) from both sides (assuming \( P \neq 0 \)), we can divide both sides by \( P \):

\[ V = \frac{1}{4} V_2 \]

### Step 5: Solve for \( V_2 \)
Now, we can solve for \( V_2 \):

\[ V_2 = 4V \]

### Conclusion
Thus, when the pressure of an ideal gas is reduced to \( \frac{1}{4} \), the volume of the gas at the same temperature will become **4 times** the initial volume.

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