Table 112 (continued) 39 j 



VELOCITY OF SOUND IN AIR 



Therefore on the assumption that the medium behaves as a perfect gas, 



VRTo ... 



HT (4) 



and 



= *>\ 



(5) 



1 



In the case where the perfect-gas law does not apply, the equation of state for one 

 component (dry air) may be written 



pV = RT — Aaap — Aaaap 2 — etc. (6) 



The corresponding equation for pure water vapor unadmixed with air is similar to 

 equation (6) except that Aw replaces A aa , A «,«,» replaces A aaa , etc., where p then 

 denotes the pressure exerted by the vapor. For dry air the third (Aaaa) and higher 

 virial coefficients are negligible in the range of ordinary atmospheric temperatures and 

 pressures. When these terms are neglected, equation (6) yields for dry air 1 



«).-(§)('-#)' 



For the case of dry air this expression may be substituted in equation (2) to provide 

 a relation for c more exact than equation (3). 



Table 112 B presents values of the second virial coefficient Aaa for dry air; the second 

 and third virial coefficients A wv , and Anw, respectively, for water vapor; and the 

 interaction coefficient A av) for a mixture of dry air and water vapor, based on the 

 formulation of Goff and Gratch. 2 ' 8 



Neglecting the third virial coefficient for dry air and the interaction coefficient Aaaa 

 and Aaau, which are of higher order than A aV) the equation of state of moist air 

 according to Goff and Gratch ' may be written 



pV = RT lv 2 A aa + x(l-x)2A wvl + (l-xyA aw ]p-[(l-xyAu, mv ,]p 2 (8) 



where p is in atmosphere. Since p =M/V, this equation is applicable for the evaluation of 



(~r) in the case of moist air. 



Hardy, Telfair, and Pielemeier, 4 taking account of the fact that 



'-'-£(»)m- 



have shown that equation (1) becomes 



where the quantities /, g, and h are denned by the equations 



f=-(V/RT)(&) T (11) 



hid: 



1 Roberts, J. K., Heat and Thermodynamics, 3d ed., p. 141, 1940. 



2 Goff, J. A., Standardization of thermodynamic properties of moist air. Final report of the 

 Working Subcommittee of the International Joint Committee on Psychrometric Data, ASHVE 

 Journal Section, Heating, Piping and Air Conditioning, pp. 118-128, November 1949. 



8 Goff, J. A., and Gratch, S., Thermodynamic properties of moist air, Trans. Amer. Soc. Heat, 

 and Vent. Eng., vol. 51, pp. 125-158, 1945. 



4 Hardy, H. C, Telfair, D., and Pielemeier, W. H., The velocity of sound in air, Journ. Acous. 

 Soc. Amer., vol. 13, pp. 226-233, 1942. 



(continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



