A gas at the temperature 250 K is contained in a closed vessel. If the gas is heated through 1K, then the percentage increase in its pressure will be

Options

A. `0.4%`
B. `0.2%`
C. `0.1%`
D. `0.8%`

Explanation

To find the percentage increase in pressure when a gas is heated in a closed vessel, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Initial Conditions**:
- Initial temperature \( T_1 = 250 \, \text{K} \)
- The gas is heated by \( 1 \, \text{K} \), so the new temperature \( T_2 = T_1 + 1 = 250 + 1 = 251 \, \text{K} \).

2. **Understand the Relationship Between Pressure and Temperature**:
- For an ideal gas in a closed vessel (constant volume), the pressure \( P \) is directly proportional to the temperature \( T \). This can be expressed as:
\[ \frac{P_2}{P_1} = \frac{T_2}{T_1} \]

3. **Substitute the Known Values**:
- Substitute \( T_1 \) and \( T_2 \) into the equation:
\[ \frac{P_2}{P_1} = \frac{251}{250} \]

4. **Express \( P_2 \) in Terms of \( P_1 \)**:
- Rearranging gives:
\[ P_2 = \frac{251}{250} P_1 \]

5. **Calculate the Change in Pressure**:
- The change in pressure \( \Delta P \) is given by:
\[ \Delta P = P_2 - P_1 = \left(\frac{251}{250} P_1\right) - P_1 \]
- Simplifying this:
\[ \Delta P = \left(\frac{251 - 250}{250}\right) P_1 = \frac{1}{250} P_1 \]

6. **Calculate the Percentage Increase in Pressure**:
- The percentage increase in pressure is given by:
\[ \text{Percentage Increase} = \frac{\Delta P}{P_1} \times 100 = \frac{\frac{1}{250} P_1}{P_1} \times 100 \]
- This simplifies to:
\[ \text{Percentage Increase} = \frac{1}{250} \times 100 = 0.4\% \]

7. **Conclusion**:
- Therefore, the percentage increase in pressure when the gas is heated by \( 1 \, \text{K} \) is \( 0.4\% \).

### Final Answer:
The percentage increase in pressure is **0.4%**.