Input information
![Maxwell speed distribution probability | temperature | 1200 K (kelvins) mass of molecule | bromine (chemical element) (atomic mass): 79.904 u (unified atomic mass units) minimum velocity | 500 m/s (meters per second) maximum velocity | 1000 m/s (meters per second)](../image_source/a83041f50522c8bb3a5334916355d6f0.png)
Maxwell speed distribution probability | temperature | 1200 K (kelvins) mass of molecule | bromine (chemical element) (atomic mass): 79.904 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/e4c85fc2c5060303f6853f4478310b9b.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 | 0.5261](../image_source/6c8881ae95b04e3e2a52e0a762a43838.png)
probability | 0.5261
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/fca50854171ff2c3865381a7e017deaf.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 | 499.73 m/s (meters per second) = 1117.9 mph (miles per hour) = 1799 km/h (kilometers per hour) root mean square speed | 612.05 m/s (meters per second) = 1369.1 mph (miles per hour) = 2203.4 km/h (kilometers per hour) mean speed | 563.89 m/s (meters per second) = 1261.4 mph (miles per hour) = 2030 km/h (kilometers per hour)](../image_source/e2645b0dd958d2fe45d6c8c8db708938.png)
maximum probability speed | 499.73 m/s (meters per second) = 1117.9 mph (miles per hour) = 1799 km/h (kilometers per hour) root mean square speed | 612.05 m/s (meters per second) = 1369.1 mph (miles per hour) = 2203.4 km/h (kilometers per hour) mean speed | 563.89 m/s (meters per second) = 1261.4 mph (miles per hour) = 2030 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/efb105af3200f7901e52e3f77db201da.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/c714e191ce321e7a467a95d789799568.png)
Probability density vs. speed
Units