x̄ - > Statistical Physics, work, Maxwell speed distribution probability, Probability density function

work
 | collinear force | 30 N (newtons) distance | 100 meters work | 3 kJ (kilojoules) = 0.8333 W h (watt hours) = 2.843 BTU_IT (IT British thermal units) = 3000 J (joules) 
 W = F d | W | work F | collinear force d | distance

Maxwell speed distribution probability

 | temperature | 800 K (kelvins) mass of molecule | neon (chemical element) (atomic mass): 20.1797 u (unified atomic mass units) minimum velocity | 500 m/s (meters per second) maximum velocity | 1000 m/s (meters per second)

Statistical Physics

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 the molecule

T | temperature

v_min | minimum velocity

v_max | maximum velocity

k | Boltzmann constant (≈ 1.381×10^-23 J/K)

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 the 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)

Probability density function

P(v) = sqrt(2/π) v^2 sqrt(m^3/(k^3 T^3)) e^(-(m v^2)/(2 k T))