The minimum pressure required to compress `600 dm^3` of a gas at 1 bar to `150 dm^3` at` 40^@C` is :

Options

A. 0.2 bar
B. 1.0 bar
C. 2.5 bar
D. 4.0 bar

Explanation

To solve the problem of finding the minimum pressure required to compress 600 dm³ of a gas at 1 bar to 150 dm³ at 40°C, we can use Boyle's Law, which states that for a given mass of gas at constant temperature, the product of pressure and volume is a constant.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Initial volume (V1) = 600 dm³
- Initial pressure (P1) = 1 bar
- Final volume (V2) = 150 dm³
- Temperature (T) = 40°C (constant)

2. **Apply Boyle's Law:**
According to Boyle's Law:
\[ P1 \times V1 = P2 \times V2 \]
where P2 is the final pressure we need to find.

3. **Rearrange the Equation to Solve for P2:**
\[ P2 = \frac{P1 \times V1}{V2} \]

4. **Substitute the Known Values:**
\[ P2 = \frac{1 \, \text{bar} \times 600 \, \text{dm}^3}{150 \, \text{dm}^3} \]

5. **Calculate P2:**
\[ P2 = \frac{600}{150} \, \text{bar} = 4 \, \text{bar} \]

6. **Conclusion:**
The minimum pressure required to compress the gas from 600 dm³ to 150 dm³ at 40°C is **4 bar**.