Input information
![Maxwell speed distribution probability | temperature | 1200 K (kelvins) mass of molecule | germanium (chemical element) (atomic mass): 72.63 u (unified atomic mass units) minimum velocity | 500 m/s (meters per second) maximum velocity | 1000 m/s (meters per second)](../image_source/75dc4f031ea2cd93244ea6c514e2ce09.png)
Maxwell speed distribution probability | temperature | 1200 K (kelvins) mass of molecule | germanium (chemical element) (atomic mass): 72.63 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/ed3e41b8969a4f3d30d05b782534f634.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 | 0.547](../image_source/868ab2c146cd596df1391fecf6c83f75.png)
probability | 0.547
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/46eafc7de1e29ff4aba18577e19b5977.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 | 524.16 m/s (meters per second) = 1172.5 mph (miles per hour) = 1887 km/h (kilometers per hour) root mean square speed | 641.96 m/s (meters per second) = 1436 mph (miles per hour) = 2311.1 km/h (kilometers per hour) mean speed | 591.45 m/s (meters per second) = 1323 mph (miles per hour) = 2129.2 km/h (kilometers per hour)](../image_source/e991327fd59131671573f1b24aa9e2eb.png)
maximum probability speed | 524.16 m/s (meters per second) = 1172.5 mph (miles per hour) = 1887 km/h (kilometers per hour) root mean square speed | 641.96 m/s (meters per second) = 1436 mph (miles per hour) = 2311.1 km/h (kilometers per hour) mean speed | 591.45 m/s (meters per second) = 1323 mph (miles per hour) = 2129.2 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/aba877809dcdb0aa6130995c6ba90410.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/7216611ecbc7e64d2dd288590f826606.png)
Probability density vs. speed
Units