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⚛️ Physics  ·  Kinetic Theory  ·  NEET & JEE

A gas of N molecules is enclosed in a container. If the container volume is suddenly doubled at constant temperature (free expansion, no heat exchange), the rms speed of the molecules:

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.

Maxwell-Boltzmann Speed Distributionspeed (v)fraction of moleculesv_pv_avgv_rmsv_p < v_avg < v_rms always, for any gas at any temperature

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.

Read the full Kinetic Theory notes →