Input information
![Maxwell speed distribution probability | temperature | 1200 K (kelvins) mass of molecule | nihonium (chemical element) (atomic mass): 286 u (unified atomic mass units) minimum velocity | 500 m/s (meters per second) maximum velocity | 1000 m/s (meters per second)](../image_source/49a0a100a15bada7a4e65c8e87ded676.png)
Maxwell speed distribution probability | temperature | 1200 K (kelvins) mass of molecule | nihonium (chemical element) (atomic mass): 286 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/f1fc8eb4eff6ebf4901c4d3f1f4d1a03.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 | 0.067](../image_source/25b832b15ad802e68be4c18c58bc1f43.png)
probability | 0.067
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/7c9d9cc7809ae21791459625a881d262.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 | 264 m/s (meters per second) = 591 mph (miles per hour) = 951 km/h (kilometers per hour) root mean square speed | 324 m/s (meters per second) = 724 mph (miles per hour) = 1165 km/h (kilometers per hour) mean speed | 298 m/s (meters per second) = 667 mph (miles per hour) = 1073 km/h (kilometers per hour)](../image_source/91a3db2e3b758b30b6cb45d702a031e8.png)
maximum probability speed | 264 m/s (meters per second) = 591 mph (miles per hour) = 951 km/h (kilometers per hour) root mean square speed | 324 m/s (meters per second) = 724 mph (miles per hour) = 1165 km/h (kilometers per hour) mean speed | 298 m/s (meters per second) = 667 mph (miles per hour) = 1073 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/4c1300402bdfa12fe2c91dc400d73ee8.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/3de520f4bff1f0f2527534f1203dda97.png)
Probability density vs. speed
Units