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⚛️ Physics  ·  Kinetic Theory  ·  NEET & JEE

The pressure of an ideal gas is given by P = (1/3)nm(v<sub>rms</sub>)², where n is number density and m is the mass of each molecule. If the gas is compressed isothermally to half its volume, the number density n doubles. The new pressure compared to the original is:

Answer: Double.

  • A Same
  • B Double
  • C Half
  • D Four times

Correct answer: B. Double

Explanation: At constant temperature, v<sub>rms</sub> is unchanged. Since P ∝ n and n doubles when volume is halved (n=N/V), the new pressure is double the original, consistent with Boyles law.

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.

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