ss° 



Tables 674 and 675 



TABLE 674. — Molecular Velocities 



The probability of a molecular velocity % is (4/\/Tr)x' i e~ l2 , the most probable velocity being taken as unity. The 

 .lumber of molecules at any instant of speed greater than c is 2N(hm/ir)* I Ce'hm^dc + c«"Amc2 \ (see table), 

 where A T is the total number of molecules. The mean velocity G (sq. rt. of mean sq.) is proportional to th e mean 

 kinetic energy and the pressure which the molecules exert on the walls of the vessel and is equal to 15.800 VT/m cm/sec, 

 where T is the absolute temperature and m the molecular weight. The most probable velocity is denoted by W, the 

 average arithmetical velocity by Q. 



G = W Vi/2 = i.22 S W; SI = W Vt/ir = 1.12W; G =fi vV/8 = 1. 086ft. 



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

 of molecules per unit volume; the mass of gas striking is (,i/.\)p£l where p is the density of the gas. For air at normal 

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

 sure of \V) and J. Amer. Ch. Soc. .57, 1915 (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, 1915, and Jeans, 

 Dynamical Theory of Gases, 1916. 



TABLE 675. — Molecular Free Paths, Collision Frequencies, and Diameters 



The following table gives the average free path L derived from Boltzmann's formula p. (.3so2pft), p. being the vis- 

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

 15, 373, 1913) 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 10 cm. The diameters may be deter- 

 mined from L by Sutherland's equation { 1.402/ y/lirNLii + C/T)\%, N being the number of molecules per unit 

 vol. and C Sutherland's constant; from van der Waal's b. ta&^ATTr}^ from the heat conductivity k, the specific 

 heat at constant volume Cv, {.i^bpGcv/Nkii (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)2/:r.V|»> 

 or the index of refraction n, {(» 2 — i)2/irN)3. The table is derived principally from Dushman, I.e. 



Gas. 



Ammonia 



Argon 



Carbon monoxide 

 " dioxide. . 



Helium 



Hydrogen 



Krypton 



Mercury 



Nitrogen 



Oxygen 



Xenon. » 



L X io 6 (cm) 

 Average free path* 



Eoltzmann. 



0° C 20 C 



5 92 

 8.98 

 8.46 

 5.56 

 2525 

 16.00 

 9 5 



8.50 

 9 05 

 5-6 



Meyer. 



20° C 



(13.0) 

 8.21 

 8.78 



Collision 



frequency 



X io" 6 



20° C* 



9I50 

 4OOO 

 5IOO 

 6l20 

 4540 

 IO060 



5070 

 4430 



io' X Molecular diameters (cm): 



From L 



(vis- 

 cosity) 



From 

 van der 



Waal's 

 b 



From 

 heat 

 conduc- 

 tivity 

 k 



3-4° 

 2.30 

 2.32 

 3M 



3-53 



Limiting 



Max. 



density 



P 



Min. 

 D or n 



2.66 

 2-74 

 2.90 

 1 .92 



2. 17 

 (2.70) 



2-95 

 2.71 

 (318) 



* Pressure = io 6 bars = io 6 dynes -5- cm 2 = 75 cm Hg. 



Smithsonian Tables. 



