TABLE 332.— VISCOSITY OF GASES 

 Variation of viscosity with pressure and temperature 



331 



According_to the kinetic theory of gases the coefficient of viscosity y = \(pcl) t p being 

 the density, c the average velocity of the molecules, / the average path. Since / varies 

 inversely as the number of molecules per unit volume, pi is a constant and y should be 

 independent of the density and pressure of a gas (Maxwell's law). This has been found true 

 for ordinary pressures ; below Vfco atmosphere it may fail, and for certain gases it has been 

 proved untrue for high pressures, e.g., C0 2 at 33° and above 50 atm. See Jeans, "Dynam- 

 ical Theory of Gases." 



If B is the amount of momentum transferred from a plane moving with velocity U and 

 parallel to a stationary plane distant d, and s is a quantity (coefficient of slip) to allow for 

 the slipping of the gas molecules over the plane, then y = (5/(7) (d-\-2s) ; j is of the same 

 magnitude as /, probably between .7 (Timiriazeff) and .9 (Knudsen) of it; at low pres- 

 sures d becomes negligible compared with 2s and the viscosity should vary inversely as 

 the pressure. 



c depends only on the temperature and the molecular weight. Ovaries as the VT, but y 

 has been found to increase much more rapidly. Meyer's formula, y t = i?o(l -f- at), where a 

 is a constant and i?o the viscosity at 0°C, is a convenient approximate relation. Sutherland's 

 formula 



273 + C ( T \| 

 T +C \273J~ 



is the most accurate formula in use, taking into account the effect of molecular forces. It 

 holds for temperatures above the critical and for pressures following approximately Boyle's 



law. It may be thrown into the form T = KT /y — C which is linear of T and T* /y, 

 with a slope equal to K and the ordinate intercept equal to — C. Onnes (see Jeans) shows 

 that this formula does not represent helium at low temperatures with anything like the 

 accuracy of the simpler formula y = y (T/273.l) n = AT". 



The following table m contains the constant a of Meyers formula, C and K of Suther- 

 land's formula, n and A of the exponential formula, and the temperature range for which 

 the constants of the latter two are applicable. 



yt — ^o 



Temperature 

 Gas range °C 



Air 23 to 750 



Ammonia — 77 to 441 



Argon -183 to 827 



Benzene to 313 



Carbon dioxide — 98 to 1052 



Carbon monoxide 



Chloroform 



Ethylene 



Helium —258 to 817 



Hydrogen —258 to 825 



Krypton 



Mercury —218 to 610 



Methane 18 to 499 



Neon 



Nitrogen —191 to 825 



Nitrous oxide 



Oxygen —191 to 829 



Water vapor to 407 



Xenon 



125 Dushman, S., Vacuum technique, p. 37. John Wiley & Sons, New York, 1949; Banerjea, G. B., and 

 Plattanaik, B., Zeit. Physik, vol. 110, p. 676, 1938; Partington, J. R., Phys. Zeit., vol. 34, p. 289, 1933; 

 Fisher, Phys. Rev., vol. 24, 1907. 



SMITHSONIAN PHYSICAL TABLES 



