In a closed vessel, a gas is heated from `300 `K to `600 K` the kinetic energy becomes/remains

Options

A. half
B. double
C. same
D. four times

Explanation

To solve the question regarding the change in kinetic energy of a gas when heated from 300 K to 600 K in a closed vessel, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship Between Temperature and Kinetic Energy**:
The kinetic energy (KE) of an ideal gas is directly proportional to its absolute temperature (T). The formula for the average kinetic energy of a gas is given by:
\[ KE = \frac{3}{2} nRT \]
where:
- \( KE \) = kinetic energy
- \( n \) = number of moles of gas
- \( R \) = ideal gas constant
- \( T \) = absolute temperature in Kelvin

2. **Identify the Initial and Final Temperatures**:
- Initial Temperature, \( T_1 = 300 \, K \)
- Final Temperature, \( T_2 = 600 \, K \)

3. **Determine the Change in Temperature**:
The temperature has increased from 300 K to 600 K. This is a doubling of the temperature:
\[ \frac{T_2}{T_1} = \frac{600 \, K}{300 \, K} = 2 \]

4. **Calculate the Change in Kinetic Energy**:
Since kinetic energy is directly proportional to temperature, if the temperature doubles, the kinetic energy will also double. Therefore:
\[ KE_2 = 2 \times KE_1 \]
This indicates that the kinetic energy has increased.

5. **Conclusion**:
The kinetic energy of the gas in the closed vessel increases when the temperature is raised from 300 K to 600 K.

### Final Answer:
The kinetic energy becomes **double** when the gas is heated from 300 K to 600 K.

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