Table 160. 



VISCOSITY OF GASES. 



Variation of Viscosity with Pressure and Temperature. 



165 



According to ^.he kinetic theory of gases the coefficient of viscosity n = i{pcl), 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 fx should be independent of the 

 density and pressure of a gas (Maxwell's law). This has been found true for ordinary pressures; 

 below ?V atmosphere it may fail, and for certain gases it has been proved untrue for high pres- 

 sures, e.g., CO2 at ss° and above 5c atm. See Jeans, " Dynamical 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 5 is a quantity (coefficient of slip) to allow for the slipping 

 of the gas molecules over the plane, then fi = (B/U) {d -{- 2s); s is of the same magnitude as /, 

 probably between .7 (Timiriazeff) and .9 (Knudsen) of it; at low pressures d becomes negligible 

 compared with 25 and the viscosity should vary inversely as the pressure. 



c depends only on the temperature and the molecular weight; viscosity should, therefore, 

 increase with the pressures for gases, c varies as the Vr, but p. has been found to increase much 

 more rapidly. Meyer's formula, pt = Mo(i + aO, where a is a constant and /lo the viscosity at 

 0° C, is a convenient approximate relation. Sutherland's formula (Phil. Mag. 31, 1893). 



273 + c 



fit = Po 



T +C 



\273/ 



is the most accurate formula in use, taking in 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^/p - C which is linear in terms of T and T^/p, with a 

 slope equal to K and the ordinate intercept equal to -C See Fisher, Phys. Rev. 24, 1907, 

 from which most of the following table is taken. Onnes (see Jeans) shows that this formula does 

 not represent Helium at low temperatures with anything like the accuracy of the simpler formula 

 p = )Uo(r/273.i)". 



The following table contains the constants for the above three formulae, T being always the 

 absolute temperature, Centigrade scale. 



* The authorities for n are: Air, Rayleigh; Ar, Mean, Rayleigh, Schultze; CO, CO2, N2, 

 N2O, von Obermayer; Helium, Mean, Rayleigh, Schultze; 2d value, low temperature work of. 

 Onnes; H2, O2, Mean, Rayleigh, von Obermayer. 



Smithsonian Tables. 



