Variables
Description
What is this formula?
The thermal velocity formula calculates the characteristic random speed of particles in a plasma or gas due to thermal energy.
It is derived from kinetic theory and is closely related to the Maxwell-Boltzmann velocity distribution.
Higher temperatures produce larger thermal velocities, while heavier particles move more slowly.
When to use it
Use this formula when studying plasma particle motion, gas kinetics, fusion plasmas, semiconductor plasmas, space plasmas, and thermodynamic particle behavior.
Example
Electrons in a plasma have:
T = 1×10^6 K
Using:
kB = 1.381×10^-23 J/K
m = 9.109×10^-31 kg
Formula:
vth = √((2*kB*T)/m)
Substitution:
vth = √((2×1.381×10^-23 × 1×10^6)/(9.109×10^-31))
Result:
vth ≈ 5.51×10^6 m/s
Applications
- Plasma kinetic theory
- Fusion plasma analysis
- Gas dynamics
- Semiconductor plasma studies
- Space plasma physics
- Thermodynamic particle modeling
- Maxwellian distribution analysis