Particles Velocity Calculator
Calculate average velocity of gas particles using Maxwell-Boltzmann distribution
Calculate Particle Velocity
1 u ≈ 1.66054 × 10⁻²⁷ kg (mass of one nucleon)
Velocity Results
Velocity Comparison
Formula used: v̄ = √(8kT/πm) for average velocity
Parameters: T = 300.0 K, m = 48.106 × 10⁻²⁷ kg
Average kinetic energy: 6.213 × 10⁻²¹ J
Physics Insights
Example Calculation
Air Molecules at Room Temperature
Molecule: Air (average molecular mass)
Mass: 28.97 u ≈ 4.81 × 10⁻²⁶ kg
Temperature: 300 K (27°C, 80°F)
Calculation
v̄ = √(8kT/πm)
v̄ = √(8 × 1.381×10⁻²³ × 300 / (π × 4.81×10⁻²⁶))
v̄ = √(3.313×10⁻²⁰ / 1.511×10⁻²⁵)
v̄ = √(219,255)
v̄ = 468 m/s (1,685 km/h)
Types of Particle Velocity
Average Velocity
√(8kT/πm)
Mean velocity from Maxwell-Boltzmann distribution
RMS Velocity
√(3kT/m)
Root mean square velocity
Most Probable
√(2kT/m)
Peak of velocity distribution
Common Gas Molecules
Physical Constants
Understanding Particle Velocity in Gases
Maxwell-Boltzmann Distribution
The Maxwell-Boltzmann distribution describes the velocities of particles in a gas at thermal equilibrium. It shows that most particles have velocities near the average, with fewer particles having very high or very low velocities.
Key Principles
- •Temperature is a measure of average kinetic energy
- •Heavier particles move slower at the same temperature
- •Higher temperature increases particle speeds
- •Particle velocities follow a statistical distribution
Mathematical Formulas
Average Velocity
v̄ = √(8kT/πm)
RMS Velocity
v_rms = √(3kT/m)
Most Probable Velocity
v_mp = √(2kT/m)
Where: k = Boltzmann constant, T = temperature (K), m = particle mass (kg)
Applications and Examples
Atmospheric Science
Understanding molecular velocities helps explain:
• Why lighter gases escape Earth's atmosphere
• Gas diffusion and mixing rates
• Pressure and temperature relationships
Engineering Applications
Particle velocities are crucial for:
• Gas separation and purification
• Chemical reaction kinetics
• Vacuum system design