A gas is copmressed isothermally to half its volume. BY what factor does the pressure of the gas increase ? Given `gamma=1.4`

Options

A. 2
B. `lt2`
C. `gt2`
D. `1/2`

Explanation

To solve the problem of how much the pressure of a gas increases when it is compressed isothermally to half its volume, we can use Boyle's Law, which states that the product of pressure and volume for a given amount of gas at constant temperature is a constant.

### Step-by-Step Solution:

1. **Understand Boyle's Law**: Boyle's Law states that for a given mass of gas at constant temperature, the product of pressure (P) and volume (V) is constant. Mathematically, this is expressed as:
\[ P_1 V_1 = P_2 V_2 \]
where \( P_1 \) and \( V_1 \) are the initial pressure and volume, and \( P_2 \) and \( V_2 \) are the final pressure and volume.

2. **Define Initial Conditions**: Let the initial volume be \( V_1 \) and the initial pressure be \( P_1 \).

3. **Define Final Conditions**: The gas is compressed to half its volume, so:
\[ V_2 = \frac{V_1}{2} \]

4. **Apply Boyle's Law**: Substitute the values into Boyle's Law:
\[ P_1 V_1 = P_2 \left(\frac{V_1}{2}\right) \]

5. **Rearranging the Equation**: We can rearrange the equation to solve for \( P_2 \):
\[ P_2 = P_1 \cdot \frac{V_1}{\frac{V_1}{2}} = P_1 \cdot 2 \]

6. **Conclusion**: This shows that the final pressure \( P_2 \) is twice the initial pressure \( P_1 \):
\[ P_2 = 2P_1 \]
Therefore, the pressure of the gas increases by a factor of 2.

### Final Answer:
The pressure of the gas increases by a factor of **2**.