TABLE 692.— MOLECULAR VELOCITIES AND ENERGIES 639 



Part 1. — Discussion 



Let o denote the most probable velocity, v a , the average velocity and v r , the mean velocity 

 (the square root of the mean square). Then 



a = v2R n T/M — 12,895 V T/M cm sec" 1 



v a = (2/Vtt) a = 1.1284 a = 14,5 51 VT /M cm sec" 1 

 Vr = V3/2 a = 1.225 a — 15,794 VT/Af cm sec" 1 

 The probability of a random velocity v = ca is 

 f c = O/V^nVfexp-c 2 ] 



The fraction of the total number of molecules, N, which have a random velocity equal to 

 or less than v = ca is 



Part 2 of this table gives values of f c and of v for a series of values of c. The third 

 column gives values of A3', which is the fraction of the total number that have values of c 

 between that given in the same horizontal row and that in the preceding row. 



From the relation for f c we obtain the relation for the probability that a molecule pos- 

 sesses the translational energy E. Let x = E/(kT) where x is a dimensionless quantity. 

 Then 



f z = 2Vx/w (exp — x) 



and the average kinetic energy is £01. = (3/2)kT 



where k = Boltzmann constant 



= 1.3805 X 10- 10 erg deg 1 K 



The last two columns in Part 2, below, give values of fz for a series of values of x. 

 Part 2. — Values of functions for application of distribution laws 



Part 3. — Rates of incidence and of evaporation of molecules 



The rate at which molecules strike a surface is given by 

 v= (\/A)nv a cm -2 sec" 1 

 = 2.635 X 10 1B (P^)/(VMT) cm" 2 sec" 1 

 = 3.513 X 10 22 Pmm/VA/r cm' 2 sec" 1 

 G = mass of gas of molecular wt, M, 



= 1.6604 X 10- 24 Mv 



= 4.375 X 10- B (P^j^ M/T) gem' 2 sec' 1 

 = 5.833 X 10" 2 (P mm )(VM/r) gem^sec" 1 



If we assume that the accommodation coefficient for condensation is unity, then the rate 

 of evaporation is equal to the rate of condensation and the vapor pressure, Pmm, is given 

 by the relation 



P mm = 17.UGVT/M 



SMITHSONIAN PHYSICAL TABLES 



