A 1 L sample of `CO` initially at S.T.P. is heated to `546^(@)C` and its volume is increased to 2 L. Which of the following is affected to the maximum extent ?

Options

A. R.M.S. velocity
B. Kinetic energy
C. Average velocity
D. Most probable velocity

Explanation

To solve the problem, we need to analyze the changes that occur when a 1 L sample of carbon monoxide (CO) is heated from standard temperature and pressure (STP) conditions and its volume is increased.

### Step-by-Step Solution:

1. **Identify Initial Conditions**:
- At STP, the standard temperature (T1) is 0°C, which is equivalent to 273 K. The pressure is 1 atm, and the volume is 1 L.

2. **Convert Final Temperature**:
- The final temperature (T2) after heating is given as 546°C. To convert this to Kelvin:
\[ T2 = 546 + 273 = 819 \text{ K} \]

3. **Determine the Change in Temperature**:
- The change in temperature can be calculated as:
\[ \Delta T = T2 - T1 = 819 \text{ K} - 273 \text{ K} = 546 \text{ K} \]

4. **Understand the Effect on Kinetic Energy**:
- Kinetic energy (KE) of gas molecules is directly proportional to the absolute temperature. Therefore, if the temperature increases, the kinetic energy will also increase.
- The formula for kinetic energy is:
\[ KE \propto T \]
- Since the temperature increased from 273 K to 819 K, the kinetic energy is affected significantly.

5. **Determine the Effect on Velocities**:
- The root mean square velocity (RMS velocity), average velocity, and most probable velocity of gas molecules are related to the square root of the temperature:
\[ V_{RMS} \propto \sqrt{T} \]
- Thus, the velocities will change as the square root of the temperature change, which is less than the linear change in kinetic energy.

6. **Conclusion**:
- Among the kinetic energy and the velocities, the kinetic energy is affected to the maximum extent because it is directly proportional to the temperature, while the velocities are affected to a lesser extent (as they depend on the square root of the temperature).

### Final Answer:
The quantity that is affected to the maximum extent is **kinetic energy**.