Thermodynamics
Mean Speed
Average speed of gas molecules from Maxwell-Boltzmann distribution.
Variables
v_meanm/s
Mean speed
Average molecular speed
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
v_mean = ∫v f(v)dv = √(8kT/πm). Order: v_p < v_mean < v_rms.
Your notes
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Common questions
What is the Mean Speed formula?
Mean Speed is written vₘₑₐₙ = √(8k_B T/πm) = √(8RT/πM). Average speed of gas molecules from Maxwell-Boltzmann distribution. It belongs to Thermodynamics, under Kinetic Theory.
What are the units in vₘₑₐₙ = √(8k_B T/πm) = √(8RT/πM)?
In SI units, v_mean is mean 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 Mean Speed formula derived?
v_mean = ∫v f(v)dv = √(8kT/πm). Order: v_p < v_mean < v_rms. The result is vₘₑₐₙ = √(8k_B T/πm) = √(8RT/πM).