Input information
![Maxwell speed distribution probability | temperature | 1200 K (kelvins) mass of molecule | platinum (chemical element) (atomic mass): 195.084 u (unified atomic mass units) minimum velocity | 500 m/s (meters per second) maximum velocity | 1000 m/s (meters per second)](../image_source/adc40cceaa39bd4c059be2be6ab12bf3.png)
Maxwell speed distribution probability | temperature | 1200 K (kelvins) mass of molecule | platinum (chemical element) (atomic mass): 195.084 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/7073876b7b16ae1c66b2873c2cca4a05.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 | 0.17996](../image_source/eae1cbe42d2fbc1975c774e3129a5958.png)
probability | 0.17996
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/96449fd47967fc194bf3cde03ada2f91.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 | 319.825 m/s (meters per second) = 715.427 mph (miles per hour) = 1151.37 km/h (kilometers per hour) root mean square speed | 391.704 m/s (meters per second) = 876.216 mph (miles per hour) = 1410.13 km/h (kilometers per hour) mean speed | 360.883 m/s (meters per second) = 807.273 mph (miles per hour) = 1299.18 km/h (kilometers per hour)](../image_source/8f58514f4354a9b6b800eacf22205d2b.png)
maximum probability speed | 319.825 m/s (meters per second) = 715.427 mph (miles per hour) = 1151.37 km/h (kilometers per hour) root mean square speed | 391.704 m/s (meters per second) = 876.216 mph (miles per hour) = 1410.13 km/h (kilometers per hour) mean speed | 360.883 m/s (meters per second) = 807.273 mph (miles per hour) = 1299.18 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/145b0156f58da3025ed8e7e39f28457b.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/04c858d10c50b028909b9ac99041ef25.png)
Probability density vs. speed
Units