Tables 811-512. 

 TABLE 511. — Molecular Velocities. 



399 



The probability of a molecular velocity x is (4/\/7r);i;-e"-^, the most probable velocity being taken as unity. The 

 number of molecules at any instant of speed greater than c is 2N{hm/Tr)^ I C e'^^mgi dc -\- ce'hmci. \ (see table), 

 where N 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 vr/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 ft. 



G =W y/JFi = i-22sW; il =W Va/tt = i.iiSW; G =0. Va'r/S = 1.086S]. 



The number of molecules striking unit area of inclosing wall is (i/4)iVJ2 (Meyer's equation), where N is the number 

 of molecules per unit volume; the mass of gas striking is (i/4)pft 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. Amer. Ch. Soc. 37, 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. iS, 1915, and Jeans, 

 Dynamical Theory of Gases, 1916. 



Gas. 



Air 



Ammonia 



Argon 



Carbon monoxide 

 Carbon dioxide. . 



Helium 



Hydrogen 



Krypton 



Mercury 



Molybdenum. . . . 



Neon 



Nitrogen 



Oxygen 



Tungsten 



Water vapor 



Xenon 



Molec- 

 ular 



weight. 



28.96 

 17.02 

 39.88 

 28.00 

 44.00 

 4.00 

 2.01 

 82.92 



2CX). 6 



96.0 



20. 2 



28.02 



32.00 



184.0 

 18.02 



130.2 



Sq. rt. mean sq. 

 G X 10"^ cm/sec. 



48s 

 633 

 413 

 493 

 393 

 1311 



184 



584 

 493 

 461 



61s 

 228 



502 



65s 



428 

 511 

 408 

 1358 

 1904 



296 



191 



60s 



S" 



478 



637 

 236 



567 

 740 

 483 

 576 

 459 

 1533 

 2149 

 335 

 215 



683 

 577 

 539 



720 

 267 



Arithmetical average velocity, 

 fl X io"2 cm/sec. 



404 

 527 

 344 

 410 

 327 

 1092 

 1534 

 238 

 154 



410 

 384 



512 

 190 



447 

 583 

 381 

 454 

 362 

 1208 

 1696 

 263 

 170 



S38 

 454 

 425 



566 



463 

 604 

 395 

 471 

 376 



12S2 



1755 



272 



176 



557 

 471 

 440 



587 

 218 



522 



681 



445 

 531 

 434 

 1412 

 1980 

 308 

 199 



629 



531 

 497 



662 

 246 



8S5 



Ills 



729 



870 



694 



2300 



3241 



502 



325 



469 



1030 



869 



813 



339 



1084 



400 



1047 



1367 



892 



106s 



850 



2840 



3970 



618 



398 



575 



1260 



1064 



996 



416 



1317 



493 



1209 



1577 



1030 



1230 



981 



3270 



4583 



712 



459 



664 



1460 



1229 



1150 



4S0 



1533 



570 



6000° 



2094 



2734 , 



1784 



2130 



1700 



s68o 



7940 



1236 



796 

 1150 

 2520 

 212S 

 1992 



832 

 2634 



Free electron, molecular weight 

 at 0° C. 



1/1835 when n — 1; G= 1.114 X 10' at 0° C and Q = 1.026 X 10^ 



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



The following table gives the average free path L derived from Boltzmann's formula M ( . 3S02pf2) , n being the vis- 

 cosity, p the density, and from Meyer's formula M(.3097pft). Experim.ental values (Verb. 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 s to 10 cm. The diameters may be deter- 

 mined from L by Sutherland's equation {i.402/V27riVZ,(i + C/T)]'', N being the number of molecules per unit 

 vol. and C Sutherland's constant; from van der Waal's b, x-ib/iNVTrl^i from the heat conductivity k, the specific 

 heat at constant volume cv, \.ii^6pGcv/Nki' (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/wN\'> 

 or the index of refraction », |(«2 — i)2/7riV)*. The table is derived principally from Dushman, I.e. 



Smithsonian Tables. 



* Pressure = io« bars = 10' dynes -j- cm^ = 75 cm Kg, 



