Q. The root mean square velocity of gas molecules is proportional to:
गैस अणुओं का मूल माध्य वर्ग वेग आनुपातिक है:
Explanation
The root mean square (rms) velocity of gas molecules is given by:
Formula: v_rms = √(3RT/M)
Temperature dependence:
- v_rms ∝ √T (at constant molar mass)
- This comes from kinetic theory: ½mv² = (3/2)kT
- Solving for v: v = √(3kT/m) ∝ √T
Physical interpretation:
- Higher temperature → higher kinetic energy
- Higher kinetic energy → higher molecular speeds
- Square root relationship due to kinetic energy being proportional to v²
Example: Doubling temperature increases rms velocity by √2 ≈ 1.41 times
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