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, which states that for a given mass of gas at constant temperature, the product of pressure and volume is constant.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Initial Volume (V1) = 600 dm³
- Final Volume (V2) = 150 dm³
- Initial Pressure (P1) = 1 bar
- Temperature (T) = 40°C (not needed for calculations as it remains constant)

2. **Apply Boyle's Law:**
According to Boyle's Law:
\[ P1 \times V1 = P2 \times V2 \]
Rearranging the formula to find P2 gives us:
\[ P2 = \frac{P1 \times V1}{V2} \]

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

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

5. **Conclusion:**
The minimum pressure required to compress the gas is **4 bar**.