Input information
![Maxwell speed distribution probability | temperature | 1200 K (kelvins) mass of molecule | osmium (chemical element) (atomic mass): 190.23 u (unified atomic mass units) minimum velocity | 500 m/s (meters per second) maximum velocity | 1000 m/s (meters per second)](../image_source/636c66700a0c40648e6fd468f100098a.png)
Maxwell speed distribution probability | temperature | 1200 K (kelvins) mass of molecule | osmium (chemical element) (atomic mass): 190.23 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/7feb99cf6cd8de53a4bb0c852cc01ced.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 | 0.1894](../image_source/35d7b7fe0961a0c5cc6b432271dde701.png)
probability | 0.1894
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/24968a16b7f7c76dce3f15128e647b68.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 | 323.88 m/s (meters per second) = 724.5 mph (miles per hour) = 1166 km/h (kilometers per hour) root mean square speed | 396.67 m/s (meters per second) = 887.32 mph (miles per hour) = 1428 km/h (kilometers per hour) mean speed | 365.46 m/s (meters per second) = 817.51 mph (miles per hour) = 1315.7 km/h (kilometers per hour)](../image_source/38264478463ad638f700c8e8379ba583.png)
maximum probability speed | 323.88 m/s (meters per second) = 724.5 mph (miles per hour) = 1166 km/h (kilometers per hour) root mean square speed | 396.67 m/s (meters per second) = 887.32 mph (miles per hour) = 1428 km/h (kilometers per hour) mean speed | 365.46 m/s (meters per second) = 817.51 mph (miles per hour) = 1315.7 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/ebfc1f892d61845a993284d2dc1dbbac.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/4d888995cd2008d1a83245721e0602b8.png)
Probability density vs. speed
Units