Computing...

Input information:

Maxwell speed distribution probability |  \ntemperature | 800 K  (kelvins)\nmass of molecule | neon  (chemical element): 20.1797 u  (unified atomic mass units)\nminimum velocity | 500 m\/s  (meters per second)\nmaximum velocity | 1000 m\/s  (meters per second)


Equation:

Pr = -sqrt(2\/pi) 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)) |   |  \nPr | probability\nm | mass of molecule\nT | temperature\nv_min | minimum velocity\nv_max | maximum velocity\nk | Boltzmann constant (~~ 1.38065×10^-23 J\/K)


Result:

probability | 0.4729


Velocity equations:

v_mp = sqrt(2) sqrt((k T)\/m) | v_rms = sqrt(3) sqrt((k T)\/m)\nv^_ = 2 sqrt(2\/pi) sqrt((k T)\/m) |   |  \nm | mass of molecule\nT | temperature\nv_mp | maximum probability speed\nv_rms | root mean square speed\nv^_ | mean speed\nk | Boltzmann constant (~~ 1.38065×10^-23 J\/K)


Probability density function:

P(v) = sqrt(2\/pi) v^2 sqrt(m^3\/(k^3 T^3)) e^(-(m v^2)\/(2 k T))

Source information
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