A vessel containing 5 litres of a gas at 0.8 m pressure is connected to an evacuated vessel of volume 3 litres. The resultant pressure inside with be (assuming whole system to be isolated)

Options

A. `(4)/(3)m`
B. `0.5m`
C. `2.0m`
D. `(3)/(4)m`

Explanation

To solve the problem, we will use the concept of the ideal gas law and the principle of conservation of energy in an isolated system. The key idea is that the product of pressure and volume (PV) remains constant before and after the gas expands into the evacuated vessel.

### Step-by-Step Solution:

1. **Identify Initial Conditions:**
- Initial pressure (P1) = 0.8 m (or 0.8 atm)
- Initial volume (V1) = 5 L
- Volume of the evacuated vessel (V2) = 3 L

2. **Calculate Total Final Volume:**
- The total volume after the gas expands into the evacuated vessel is:
\[ V_{total} = V1 + V2 = 5 \, \text{L} + 3 \, \text{L} = 8 \, \text{L} \]

3. **Apply the Ideal Gas Law (PV = constant):**
- According to the principle of conservation of energy in an isolated system, we have:
\[ P1 \times V1 = P2 \times V_{total} \]
- Rearranging the equation to solve for P2 gives:
\[ P2 = \frac{P1 \times V1}{V_{total}} \]

4. **Substitute the Known Values:**
- Substitute the values into the equation:
\[ P2 = \frac{0.8 \, \text{m} \times 5 \, \text{L}}{8 \, \text{L}} \]

5. **Calculate P2:**
- Performing the calculation:
\[ P2 = \frac{4 \, \text{m}}{8} = 0.5 \, \text{m} \]

6. **Conclusion:**
- The resultant pressure inside the system after the gas expands into the evacuated vessel is:
\[ P2 = 0.5 \, \text{m} \]

### Final Answer:
The resultant pressure inside the system will be 0.5 m.

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