Input information
![Maxwell speed distribution probability | temperature | 1200 K (kelvins) mass of molecule | argon (chemical element) (atomic mass): 39.948 u (unified atomic mass units) minimum velocity | 500 m/s (meters per second) maximum velocity | 1000 m/s (meters per second)](../image_source/ea690ecb3cdcfe508534379e53e84dca.png)
Maxwell speed distribution probability | temperature | 1200 K (kelvins) mass of molecule | argon (chemical element) (atomic mass): 39.948 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/fcf395651e9f81b6bbc5d6a79b4b5306.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 | 0.540](../image_source/70381ae40e59a6729551d1110650ccbf.png)
probability | 0.540
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/ede794ee874d037f8691de7938ad3fb5.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 | 706.77 m/s (meters per second) = 1581 mph (miles per hour) = 2544.4 km/h (kilometers per hour) root mean square speed | 865.61 m/s (meters per second) = 1936.3 mph (miles per hour) = 3116.2 km/h (kilometers per hour) mean speed | 797.5 m/s (meters per second) = 1784 mph (miles per hour) = 2871 km/h (kilometers per hour)](../image_source/41c0276680ff32436be7d7cc44cb178c.png)
maximum probability speed | 706.77 m/s (meters per second) = 1581 mph (miles per hour) = 2544.4 km/h (kilometers per hour) root mean square speed | 865.61 m/s (meters per second) = 1936.3 mph (miles per hour) = 3116.2 km/h (kilometers per hour) mean speed | 797.5 m/s (meters per second) = 1784 mph (miles per hour) = 2871 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/4262cc2e872aa3ed342a2469277c5fa2.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/5436520822ce10df316bd4d6ca0532c1.png)
Probability density vs. speed
Units