Answer: Remains the same since temperature is unchanged.
- A Doubles, as if the rms speed scaled directly with the container volume
- B Halves, as if the rms speed scaled inversely with the container volume
- C Remains the same since temperature is unchanged
- D Becomes zero, as if all molecular motion stopped after expansion
Correct answer: C. Remains the same since temperature is unchanged
Explanation: In free expansion of an ideal gas at constant temperature, since v<sub>rms</sub> depends only on T and M, and T is unchanged (ideal gas, no work done against external pressure in free expansion), v<sub>rms</sub> remains the same.
Not all gas molecules move at the same speed - the Maxwell-Boltzmann distribution shows the spread, with the most probable speed vp slightly less than the average vavg, which is slightly less than the root-mean-square speed vrms used in the pressure formula.
Concept context
Kinetic theory of gases connects molecular motion to pressure and temperature, explaining gas laws, specific heats, and molecular speeds.