Input information
![Maxwell speed distribution probability | temperature | 1200 K (kelvins) mass of molecule | sodium (chemical element) (atomic mass): 22.98976928 u (unified atomic mass units) minimum velocity | 500 m/s (meters per second) maximum velocity | 1000 m/s (meters per second)](../image_source/3e80a9db46d8b8bca373817d6ad74c0c.png)
Maxwell speed distribution probability | temperature | 1200 K (kelvins) mass of molecule | sodium (chemical element) (atomic mass): 22.98976928 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/627f398d34feabf540a981a734649950.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 | 0.39017513](../image_source/024e56cf0423cd3f17490ff4995b419e.png)
probability | 0.39017513
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/054ea741d4da7a2038359736bdd36f9d.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 | 931.655618 m/s (meters per second) = 2084.05426 mph (miles per hour) = 3353.96022 km/h (kilometers per hour) root mean square speed | 1141.04044 m/s (meters per second) = 2552.43477 mph (miles per hour) = 4107.74558 km/h (kilometers per hour) mean speed | 1051.26079 m/s (meters per second) = 2351.60341 mph (miles per hour) = 3784.53884 km/h (kilometers per hour)](../image_source/091829f1f76df4403bb7210103c4f48a.png)
maximum probability speed | 931.655618 m/s (meters per second) = 2084.05426 mph (miles per hour) = 3353.96022 km/h (kilometers per hour) root mean square speed | 1141.04044 m/s (meters per second) = 2552.43477 mph (miles per hour) = 4107.74558 km/h (kilometers per hour) mean speed | 1051.26079 m/s (meters per second) = 2351.60341 mph (miles per hour) = 3784.53884 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/2dfe29e594522e99fa8c6fae10fd4525.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/54cc2a8381c4ddb8804c77c5166e53fe.png)
Probability density vs. speed
Units