PhysicsChapter 2: Statistical Mechanics and Thermodynamics
Rms Speed of An Ideal Gas
For an ideal gas, RMS molecular speed is related to absolute temperature and molecular mass by: c_rms = √(3kT/m)
Definition
For an ideal gas, RMS molecular speed is related to absolute temperature and molecular mass by: crms = √(3kT/m) or for one mole using molar mass `M`: crms = √(3RT/M) RMS-speed calculation is explicitly a summative FBISE SLO. ([Scribd][2])
Formula
crms =
Temperature Effect
Kinetic theory gives: pV=(13)Nmc_rms² Ideal gas law gives: pV=NkT Equating: (13)Nmcrms² = NkT Cancel `N`: (13)mcrms²=kT Therefore: crms²=3kT/m and: crms=√(3kT/m) Using: R = NAk and molar mass `M=NAm`: crms=√(3RT/M) **c_rms ∝ √T**
Molecular Mass Effect
**c_rms ∝ 1/√M** At the same temperature, lighter gas molecules have greater RMS speeds.
Formula / Key Relation
**crms=√(3kT/m) crms=√(3RT/M)**
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Review the key facts, formulas and checks before you move on.Rms Speed of An Ideal Gas
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`c_rms ∝ √T`
- `c_rms ∝ 1/√M`
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- Hotter → faster.
- Lighter → faster.
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