a The three moments of the velocity distribution function have physical significance The zeroth moment, equal to the area under the distribution function, is the gas number density n vav The first moment is the arithmetic mean speed This speed is relevant with the mean free path 8kT wf(v)dv 0 While the second moment is related to the root mean square speed of the particles this speed is relevant with the kinetic energy of the particles (h yf(v)dy) 3kT 2=m
n The three moments of the velocity distribution function have physical significance: n The zeroth moment,equal to the area under the distribution function, is the gas number density n: n The first moment is the arithmetic mean speed; This speed is relevant with the mean free path n While the second moment is related to the root mean square speed of the particles. This speed is relevant with the kinetic energy of the particles. 0 f ( v ) dv n 2 1 0 ) 8 ( ) ( 1 m kT vf v dv n v 2 1 0 2 1 ) 3 ( ( ) ) ( 1 m kT vf v dv n vrms
■ Another dn小 characteristic speed dv is the most probable speed 2kT VmⅤVms Total velocity
n Another characteristic speed is the most probable speed: 2 1 ) 2 ( m kT vm
2.2.2 Energy distribution functions a When the gases is in Energy probabilty density kinetic or dw thermodynamic most probable energy equilibrium, the energy of individual particle also obeys a mean energy Maxswell-Boltzmann distribution 1/213/223 Dimensionless energy w/kT
2.2.2 Energy distribution functions n When the gases is in kinetic or thermodynamic equilibrium,the energy of individual particle also obeys a Maxswell-Boltzmann distribution. 2 2 w 1 mv
a The distribution function of energies between w and w+dw 2 f(w) r(7) exp -i-1 kT wf( w)dw 2 exp dh=是kT √丌 kT kT T wf(w)dw 3kn
n The distribution function of energies between w and w+dw: exp[ ] ( ) 2 ( ) 2 3 2 1 2 1 kT w kT n w dw dn f w w 0 ( ) 1 wf w dw n w dw kT kT w kT w w 2 3 0 2 3 ( ) exp[ ] 2 0 ( ) 3 2 wf w dw kn Tef
23 Particle collisions a Principal kinds of collision Electrons e+A→A++2e Ionization e+A→→A→e+A+ hy Excitation e+A→2e+A+ Penning ionization e+A→e+A Elastic scattering e+AB→e+A+B Dissociation e+AB→→2e+A++B Dissociative ionization e+AB→→A+B Dissociative attachment e+A++B→→A+B Recombination
2.3 Particle collisions n Principal kinds of collision Electrons e+A→A++2e Ionization e+A→A* →e +A+hν Excitation e+ A* →2e + A+ Penning ionization e+A→e + A Elastic scattering e+AB→e+ A+B Dissociation e+AB→2e + A++B Dissociative ionization e+AB→A-+B Dissociative attachment e+ A+ +B→A+B Recombination