Input information
![Maxwell speed distribution probability | temperature | 1200 K (kelvins) mass of molecule | lithium (chemical element) (atomic mass): 6.94 u (unified atomic mass units) minimum velocity | 500 m/s (meters per second) maximum velocity | 1000 m/s (meters per second)](../image_source/cba4d3a46a775e5145e648f33e025d18.png)
Maxwell speed distribution probability | temperature | 1200 K (kelvins) mass of molecule | lithium (chemical element) (atomic mass): 6.94 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/b00c479ef49fba898d69df0b65105701.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 | 0.11](../image_source/1922fc4a6afa4d7d9cb2676725300c0c.png)
probability | 0.11
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/18001346377488aca7f759e472fd1b3f.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 | 1696 m/s (meters per second) = 3790 mph (miles per hour) = 6100 km/h (kilometers per hour) root mean square speed | 2080 m/s (meters per second) = 4650 mph (miles per hour) = 7480 km/h (kilometers per hour) mean speed | 1913 m/s (meters per second) = 4280 mph (miles per hour) = 6890 km/h (kilometers per hour)](../image_source/d07f6e40984ea541e512c8c7fbf8aa65.png)
maximum probability speed | 1696 m/s (meters per second) = 3790 mph (miles per hour) = 6100 km/h (kilometers per hour) root mean square speed | 2080 m/s (meters per second) = 4650 mph (miles per hour) = 7480 km/h (kilometers per hour) mean speed | 1913 m/s (meters per second) = 4280 mph (miles per hour) = 6890 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/099c8867ed9992d3f1d602ca7674523c.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/500141d7e9aa48e072e19d95f96e9983.png)
Probability density vs. speed
Units