Q. Most probable velocity of gas molecules is proportional to:
गैस अणुओं का सर्वाधिक संभावित वेग आनुपातिक है:
Explanation
The most probable velocity (v_mp) is the velocity at which the maximum number of molecules move in a Maxwell-Boltzmann distribution.
Formula: v_mp = √(2RT/M) = √(2kT/m)
Temperature dependence:
- v_mp ∝ √T
- This is the same relationship as rms velocity
Maxwell-Boltzmann distribution velocities:
- Most probable: v_mp = √(2RT/M)
- Average: v_avg = √(8RT/πM)
- Root mean square: v_rms = √(3RT/M)
Relationship: v_mp < v_avg < v_rms
Physical interpretation:
- Higher temperature → faster molecular motion
- Square root relationship due to kinetic energy ∝ T
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