Thermodynamics
Most Probable Speed
Speed at which Maxwell-Boltzmann distribution peaks.
Variables
v_pm/s
Most probable speed
Peak of Maxwell distribution
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
Set df/dv = 0 for Maxwell-Boltzmann distribution f(v) ∝ v²e^(-mv²/2kT). v_p < v_mean < v_rms.
Your notes
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Common questions
What is the Most Probable Speed formula?
Most Probable Speed is written vₚ = √(2k_B T/m) = √(2RT/M). Speed at which Maxwell-Boltzmann distribution peaks. It belongs to Thermodynamics, under Kinetic Theory.
What are the units in vₚ = √(2k_B T/m) = √(2RT/M)?
In SI units, v_p is most probable 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 Most Probable Speed formula derived?
Set df/dv = 0 for Maxwell-Boltzmann distribution f(v) ∝ v²e^(-mv²/2kT). v_p < v_mean < v_rms. The result is vₚ = √(2k_B T/m) = √(2RT/M).