TABLES 511-512. 

 TABLE 511. - Molecular Velocities. 



399 



The probability of a molecular velocity * is ( 4 / VTT)^*, the most probable velocity being taken as unity. The 

 number of molecules at any instant of speed greater than c is tlT(fa/*)i /jfrto* &+*** } (see table), 

 where .V is the total number of molecules. The mean velocity G (sq. it. of mean'sq.) is proportional to the mean 

 kinetic energy and the pressure which the molecules exert on the walls of the vessel and Is equal to i s 800 VfTm cm/* 

 where T is the absolute temperature and m the molecular weight. The most probable velocity U denoted b 

 average arithmetical velocity by ft. 



G = w V77^ = i . 225^; a = w V4/r 



by W, the 



1.I2&W; 



C - 



- I.086Q. 



The number of molecules striking unit area of inclosing wall is (i/ 4 )tfQ (Meyer's equation), where N is the number 

 of molecules per unit volume; the mass of gas striking is (i/4)pfi where p is the density of the gas. For air at normal 

 pressure and room temperature (20 C) this is about 14 g/cmVsec. See Langmuir, Phys. Rev. 2. 1913 (vapor pres- 

 sure of W) and J . Arner. Ch. Soc. 37, iQiS (Chemical Reactions at Low Pressures), for fertile applications of these latter 

 equations. The following table is based on Kinetic Theory of Gases, Dushman, Gen. Elec. Rev 18 xois and Jeans 

 Dynamical Theory of Gases, igi6. 



TABLE 512. Molecular Free Paths, Collision Frequencies and Diameters. 



The following table gives the average free path L derived from Boltzmann's formula n ( . 35O2pl2), n being the vis- 

 cosity, p the density, and from Meyer's formula At (.3097pQ). Experimental values (Verb. d. Phys. Ges. 14, 596, 1912: 

 15, 373. I9J3) agree better with Meyer's values, although many prefer Boltzmann's formula. As the pressure decreases, 

 the free path increases, at one bar (ordinary incandescent lamp) becoming 5 to io cm. The diameters may be deter- 

 mined from L by Sutherland's equation {i.402/"\/27r./VL(i + C/T)}$, N being the number of molecules per unit 

 vol. and C Sutherland's constant; from van der Waal's b. {zb/2NVir}$'> from the heat conductivity k, the specific 

 heat at constant volume c v , {.itfpGcv/Nk}} (Laby and Kaye); a superior limit from the maximum density in solid 

 and liquid states (Jeans, Sutherland, 1916) and an inferior limit from the dielectric constant D, [(D i)j/r.V}l 

 or the index of refraction n, {(n 2 i)2/7r/vH. The table is derived principally from Dushman, I.e. 



* Pressure = io 8 bars = io dynes -i- cm 1 = 75 cm Hg. 



SMITHSONIAN TABLES. 



