A gas heated from 273 k to 373k at 1atm pressure if the initial volume of the gas is 10L its final volume would be

Options

A. `20dm^3`
B. `13.66dm^3`
C. `10dm^3`
D. `7.32dm^3`

Answer

To solve the problem of finding the final volume of a gas heated from 273 K to 373 K at constant pressure, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature when pressure is held constant.

### Step-by-step Solution:

1. **Understand the relationship**: According to Charles's Law, at constant pressure:
\[ \frac{V_1}{T_1} = \frac{V_2}{T_2} \]
where \(V_1\) is the initial volume, \(T_1\) is the initial temperature, \(V_2\) is the final volume, and \(T_2\) is the final temperature.

2. **Identify the given values**:
- Initial volume \(V_1 = 10 \, \text{L}\)
- Initial temperature \(T_1 = 273 \, \text{K}\)
- Final temperature \(T_2 = 373 \, \text{K}\)

3. **Rearrange the formula to find \(V_2\)**:
\[ V_2 = V_1 \times \frac{T_2}{T_1} \]

4. **Substitute the known values into the equation**:
\[ V_2 = 10 \, \text{L} \times \frac{373 \, \text{K}}{273 \, \text{K}} \]

5. **Calculate \(V_2\)**:
\[ V_2 = 10 \times \frac{373}{273} \approx 10 \times 1.366 = 13.66 \, \text{L} \]

6. **Final result**: The final volume \(V_2\) is approximately \(13.66 \, \text{L}\).

### Conclusion:
The final volume of the gas after heating from 273 K to 373 K at constant pressure is **13.66 L**.