Input information
![Maxwell speed distribution probability | temperature | 1200 K (kelvins) mass of molecule | beryllium (chemical element) (atomic mass): 9.0121831 u (unified atomic mass units) minimum velocity | 500 m/s (meters per second) maximum velocity | 1000 m/s (meters per second)](../image_source/2ba18437592ecba44cae85d4af1bb252.png)
Maxwell speed distribution probability | temperature | 1200 K (kelvins) mass of molecule | beryllium (chemical element) (atomic mass): 9.0121831 u (unified atomic mass units) minimum velocity | 500 m/s (meters per second) maximum velocity | 1000 m/s (meters per second)
Equation
![Pr = -sqrt(2/π) sqrt(m/(k T)) (e^(-(m v_max^2)/(2 k T)) v_max - e^(-(m v_min^2)/(2 k T)) v_min) + erf((sqrt(m/(k T)) v_max)/sqrt(2)) - erf((sqrt(m/(k T)) v_min)/sqrt(2)) | | Pr | probability m | mass of molecule T | temperature v_min | minimum velocity v_max | maximum velocity k | Boltzmann constant (≈ 1.381×10^-23 J/K)](../image_source/02cc4e0b08d371c40b07a3de94a05dc4.png)
Pr = -sqrt(2/π) sqrt(m/(k T)) (e^(-(m v_max^2)/(2 k T)) v_max - e^(-(m v_min^2)/(2 k T)) v_min) + erf((sqrt(m/(k T)) v_max)/sqrt(2)) - erf((sqrt(m/(k T)) v_min)/sqrt(2)) | | Pr | probability m | mass of molecule T | temperature v_min | minimum velocity v_max | maximum velocity k | Boltzmann constant (≈ 1.381×10^-23 J/K)
Result
![probability | 0.1486778](../image_source/12d658c6b99830dc7b4e4c41806909e7.png)
probability | 0.1486778
Velocity equations
![v_mp = sqrt(2) sqrt((k T)/m) | v_rms = sqrt(3) sqrt((k T)/m) v^_ = 2 sqrt(2/π) sqrt((k T)/m) | | m | mass of molecule T | temperature v_mp | maximum probability speed v_rms | root mean square speed v^_ | mean speed k | Boltzmann constant (≈ 1.381×10^-23 J/K)](../image_source/0bec1cbdbd7d442e6336846e9e8141f0.png)
v_mp = sqrt(2) sqrt((k T)/m) | v_rms = sqrt(3) sqrt((k T)/m) v^_ = 2 sqrt(2/π) sqrt((k T)/m) | | m | mass of molecule T | temperature v_mp | maximum probability speed v_rms | root mean square speed v^_ | mean speed k | Boltzmann constant (≈ 1.381×10^-23 J/K)
Units
Velocity parameters
![maximum probability speed | 1488.0164 m/s (meters per second) = 3328.5978 mph (miles per hour) = 5356.8589 km/h (kilometers per hour) root mean square speed | 1822.4404 m/s (meters per second) = 4076.6831 mph (miles per hour) = 6560.7855 km/h (kilometers per hour) mean speed | 1679.0467 m/s (meters per second) = 3755.9204 mph (miles per hour) = 6044.568 km/h (kilometers per hour)](../image_source/9d95533b7902d7939082ab231f8a0c4b.png)
maximum probability speed | 1488.0164 m/s (meters per second) = 3328.5978 mph (miles per hour) = 5356.8589 km/h (kilometers per hour) root mean square speed | 1822.4404 m/s (meters per second) = 4076.6831 mph (miles per hour) = 6560.7855 km/h (kilometers per hour) mean speed | 1679.0467 m/s (meters per second) = 3755.9204 mph (miles per hour) = 6044.568 km/h (kilometers per hour)
Probability density function
![P(v) = sqrt(2/π) v^2 sqrt(m^3/(k^3 T^3)) e^(-(m v^2)/(2 k T))](../image_source/03cd2e3aab083d1de6159d8b9def97e9.png)
P(v) = sqrt(2/π) v^2 sqrt(m^3/(k^3 T^3)) e^(-(m v^2)/(2 k T))
Probability density vs. speed
![Probability density vs. speed](../image_source/798c5bfa22d839b05479134bf76303c8.png)
Probability density vs. speed
Units