Two vessels of capacities 3 litres and 4 litres are separately filled with a gas. The pressure are respectively 202 KPa and 101 KPa. The two vessels are connected. The gas pressure will be now, at constant temperature,

Options

A. 151.5 KPa
B. 144 KPa
C. 303 KPa
D. 175 KPa

Answer

To solve the problem of finding the gas pressure when two vessels are connected, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- For Vessel 1:
- Volume (V1) = 3 L
- Pressure (P1) = 202 kPa
- For Vessel 2:
- Volume (V2) = 4 L
- Pressure (P2) = 101 kPa

2. **Use the Formula for Total Pressure:**
When two vessels containing gas at different pressures are connected, the total pressure can be calculated using the formula:
\[ P_{\text{total}} = \frac{P_1 V_1 + P_2 V_2}{V_1 + V_2} \]
where \(P_{\text{total}}\) is the final pressure after the vessels are connected.

3. **Substitute the Values into the Formula:**
\[ P_{\text{total}} = \frac{(202 \, \text{kPa} \times 3 \, \text{L}) + (101 \, \text{kPa} \times 4 \, \text{L})}{3 \, \text{L} + 4 \, \text{L}} \]

4. **Calculate the Numerator:**
- Calculate \(P_1 V_1\):
\[ 202 \, \text{kPa} \times 3 \, \text{L} = 606 \, \text{kPa L} \]
- Calculate \(P_2 V_2\):
\[ 101 \, \text{kPa} \times 4 \, \text{L} = 404 \, \text{kPa L} \]
- Add these values:
\[ 606 \, \text{kPa L} + 404 \, \text{kPa L} = 1010 \, \text{kPa L} \]

5. **Calculate the Denominator:**
\[ V_1 + V_2 = 3 \, \text{L} + 4 \, \text{L} = 7 \, \text{L} \]

6. **Calculate the Total Pressure:**
\[ P_{\text{total}} = \frac{1010 \, \text{kPa L}}{7 \, \text{L}} \approx 144.29 \, \text{kPa} \]

7. **Final Answer:**
The pressure of the gas when the two vessels are connected at constant temperature is approximately **144.29 kPa**.