\[\bar{v}=\sqrt{\frac{8RT}{\pi M}}\]
Variables
vavgmean molecular speed (m/s)
Runiversal gas constant (J/(mol·K))
Tabsolute temperature (K)
Mmolar mass (kg/mol)
Description
What is this formula?
The mean molecular speed formula calculates the average speed of molecules in an ideal gas according to the Maxwell-Boltzmann distribution.
When to use it
Use this formula in kinetic theory, thermodynamics, statistical mechanics, and gas transport analysis to estimate the average molecular motion in gases.
Example
Hydrogen gas at:
T = 300 K
Data:
R = 8.314 J/(mol·K)
M = 0.002 kg/mol
Formula:
vavg = sqrt((8*R*T)/(pi*M))
Substitution:
vavg = sqrt((8 × 8.314 × 300)/(pi × 0.002))
Result:
vavg ≈ 1777 m/s
The mean molecular speed of hydrogen at 300 K is approximately 1777 m/s.
Applications
- Kinetic theory of gases
- Gas transport calculations
- Thermodynamics
- Molecular motion analysis
- Statistical physics