A cylinder of 5 L capacity, filled with air at NTP is connected with another evacuated cylinder of 30 L capacity. The resultant air pressure in both the cylinders will be

Options

A. 10.8 cm of Hg
B. 14.9 cm of Hg
C. 21.8 cm of Hg
D. 38.8 cm of Hg

Answer

To solve the problem of finding the resultant air pressure in both cylinders after connecting a 5 L cylinder filled with air at NTP to a 30 L evacuated cylinder, we can use Boyle's Law. Boyle's Law states that at constant temperature, the pressure of a gas is inversely proportional to its volume.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Volume of Cylinder 1 (V1) = 5 L
- Volume of Cylinder 2 (V2) = 30 L (evacuated, so initial pressure P2 = 0)
- Initial Pressure (P1) at NTP = 76 cm of Hg

2. **Total Volume Calculation:**
- The total volume when both cylinders are connected = V1 + V2 = 5 L + 30 L = 35 L

3. **Apply Boyle's Law:**
- According to Boyle's Law, P1 * V1 = P2 * V2
- Rearranging gives us: P2 = (P1 * V1) / V2

4. **Substitute the Known Values:**
- P1 = 76 cm of Hg
- V1 = 5 L
- V2 = 35 L
- Substitute these values into the equation:
\[ P2 = \frac{76 \, \text{cm of Hg} \times 5 \, \text{L}}{35 \, \text{L}} \]

5. **Calculate P2:**
- First, calculate the numerator:
\[ 76 \times 5 = 380 \]
- Now divide by the total volume:
\[ P2 = \frac{380}{35} \approx 10.8 \, \text{cm of Hg} \]

6. **Final Result:**
- The resultant air pressure in both cylinders after connecting them will be approximately **10.8 cm of Hg**.