\[v_p=\sqrt{\frac{2RT}{M}}\]
Variables
vpmost probable molecular speed (m/s)
Runiversal gas constant (J/(mol·K))
Tabsolute temperature (K)
Mmolar mass (kg/mol)
Description
What is this formula?
The Maxwell most probable speed formula calculates the molecular speed that occurs most frequently in an ideal gas according to the Maxwell-Boltzmann distribution.
When to use it
Use this formula in kinetic theory, statistical mechanics, thermodynamics, and gas dynamics when studying molecular velocity distributions.
Example
Oxygen gas at:
T = 300 K
Data:
R = 8.314 J/(mol·K)
M = 0.032 kg/mol
Formula:
vp = sqrt((2*R*T)/M)
Substitution:
vp = sqrt((2 × 8.314 × 300)/0.032)
Result:
vp ≈ 395 m/s
The most probable molecular speed of oxygen at 300 K is approximately 395 m/s.
Applications
- Maxwell-Boltzmann distributions
- Gas kinetic theory
- Molecular transport
- Statistical thermodynamics
- Thermal physics