If the pressure is doubled for a fixed mass of gas, its volume will become

Options

A. 4 times
B. 1/2 times
C. 2 times
D. No change

Answer

To solve the question "If the pressure is doubled for a fixed mass of gas, its volume will become?", we can follow these steps:

### Step-by-Step Solution:

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

2. **Set Up the Initial Conditions**: Let's denote the initial pressure as \( P \) and the initial volume as \( V \). According to Boyle's Law:
\[ PV = k \]

3. **Consider the Change in Pressure**: If the pressure is doubled, the new pressure \( P' \) can be expressed as:
\[ P' = 2P \]

4. **Apply Boyle's Law to the New Conditions**: Using Boyle's Law for the new conditions, we have:
\[ P'V' = k \]
where \( V' \) is the new volume.

5. **Substitute the New Pressure into the Equation**: Substituting \( P' \) into the equation gives:
\[ (2P)V' = k \]

6. **Relate the New Volume to the Initial Volume**: Since \( PV = k \), we can substitute \( k \) from the initial condition:
\[ (2P)V' = PV \]

7. **Solve for the New Volume \( V' \)**: Rearranging the equation to find \( V' \):
\[ V' = \frac{PV}{2P} = \frac{V}{2} \]

8. **Conclusion**: Therefore, if the pressure is doubled, the new volume \( V' \) will be half of the original volume \( V \):
\[ V' = \frac{V}{2} \]

### Final Answer:
If the pressure is doubled for a fixed mass of gas, its volume will become half.

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