\[v_{rms}=\sqrt{\frac{3RT}{M}}\]
Variables
vrmsroot mean square molecular speed (m/s)
Runiversal gas constant (J/(mol·K))
Tabsolute temperature (K)
Mmolar mass (kg/mol)
Description
What is this formula?
The RMS molecular speed formula calculates the root mean square speed of gas molecules in an ideal gas based on temperature and molar mass.
When to use it
Use this formula in kinetic theory, thermodynamics, statistical mechanics, and gas dynamics to estimate the characteristic molecular speed of gases.
Example
Nitrogen gas at:
T = 300 K
Data:
R = 8.314 J/(mol·K)
M = 0.028 kg/mol
Formula:
vrms = sqrt((3*R*T)/M)
Substitution:
vrms = sqrt((3 × 8.314 × 300)/0.028)
Result:
vrms ≈ 517 m/s
The RMS molecular speed of nitrogen at 300 K is approximately 517 m/s.
Applications
- Kinetic theory of gases
- Thermodynamics
- Gas transport analysis
- Molecular physics
- Fluid dynamics