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

Options

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

Answer

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. Boyle's Law states that for a given mass of gas at constant temperature, the product of pressure and volume is constant. Mathematically, this can be expressed as:

\[ P_1 V_1 = P_2 V_2 \]

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

### Step-by-Step Solution:

1. **Identify the known values:**
- Initial pressure, \( P_1 = 1 \, \text{bar} \)
- Initial volume, \( V_1 = 600 \, \text{dm}^3 \)
- Final volume, \( V_2 = 150 \, \text{dm}^3 \)

2. **Set up the equation using Boyle's Law:**
\[ P_1 V_1 = P_2 V_2 \]

3. **Substitute the known values into the equation:**
\[ 1 \, \text{bar} \times 600 \, \text{dm}^3 = P_2 \times 150 \, \text{dm}^3 \]

4. **Rearrange the equation to solve for \( P_2 \):**
\[ P_2 = \frac{1 \, \text{bar} \times 600 \, \text{dm}^3}{150 \, \text{dm}^3} \]

5. **Calculate \( P_2 \):**
\[ P_2 = \frac{600}{150} \, \text{bar} = 4 \, \text{bar} \]

6. **Conclusion:**
The minimum pressure required to compress the gas is \( P_2 = 4 \, \text{bar} \).

### Final Answer:
The minimum pressure required is **4 bar**.