Input information
![Maxwell speed distribution probability | temperature | 1200 K (kelvins) mass of molecule | tin (chemical element) (atomic mass): 118.71 u (unified atomic mass units) minimum velocity | 500 m/s (meters per second) maximum velocity | 1000 m/s (meters per second)](../image_source/ff2664c367db75cd131e0aada799f818.png)
Maxwell speed distribution probability | temperature | 1200 K (kelvins) mass of molecule | tin (chemical element) (atomic mass): 118.71 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/c025fbbeab5f118399aa150dbe3a9fed.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 | 0.38783](../image_source/d4fc15d157a44374a1b8f97173c467dd.png)
probability | 0.38783
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/905bdcc1c66890d31e0613fc7cfe4cad.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 | 409.995 m/s (meters per second) = 917.134 mph (miles per hour) = 1475.98 km/h (kilometers per hour) root mean square speed | 502.14 m/s (meters per second) = 1123.25 mph (miles per hour) = 1807.7 km/h (kilometers per hour) mean speed | 462.63 m/s (meters per second) = 1034.87 mph (miles per hour) = 1665.47 km/h (kilometers per hour)](../image_source/a2c74429a5eebfd7e6e400ee0caac077.png)
maximum probability speed | 409.995 m/s (meters per second) = 917.134 mph (miles per hour) = 1475.98 km/h (kilometers per hour) root mean square speed | 502.14 m/s (meters per second) = 1123.25 mph (miles per hour) = 1807.7 km/h (kilometers per hour) mean speed | 462.63 m/s (meters per second) = 1034.87 mph (miles per hour) = 1665.47 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/fdaf97a10083c57c666837cf32be901b.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/f0836b50960db84392189e38344a4279.png)
Probability density vs. speed
Units