Thermodynamics
Root Mean Square Speed
RMS speed of gas molecules.
Variables
v_rmsm/s
RMS speed
Root mean square velocity
k_BJ/K
Boltzmann constant
1.38×10⁻²³
TK
Temperature
Absolute temperature
mkg
Molecular mass
Mass per molecule
RJ/(mol·K)
Gas constant
8.314
Mkg/mol
Molar mass
Mass per mole
Derivation
From ½m⟨v²⟩ = (3/2)kT: v_rms = √(3kT/m).
Your notes
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Common questions
What is the Root Mean Square Speed formula?
Root Mean Square Speed is written vᵣₘₛ = √(3k_B T/m) = √(3RT/M). RMS speed of gas molecules. It belongs to Thermodynamics, under Kinetic Theory.
What are the units in vᵣₘₛ = √(3k_B T/m) = √(3RT/M)?
In SI units, v_rms is rms speed, measured in m/s; k_B is boltzmann constant, measured in kg·m²/(s²·K); T is temperature, measured in K; m is molecular mass, measured in kg; R is gas constant, measured in kg·m²/(s²·mol·K); M is molar mass, measured in kg/mol.
How is the Root Mean Square Speed formula derived?
From ½m⟨v²⟩ = (3/2)kT: v_rms = √(3kT/m). The result is vᵣₘₛ = √(3k_B T/m) = √(3RT/M).