Table 72 295 



VIRTUAL TEMPERATURE INCREMENT OF SATURATED AIR 



Introduction. — If both dry and moist air obeyed Dalton's law of partial pressures and 

 behaved as a perfect gas, the partial pressures of dry air and water vapor in the moist 

 air could be considered to be (/> — e) and e, respectively, where p is the total barometric 

 pressure, and e is the vapor pressure. Then, according to the perfect gas law, the equa- 

 tions of state for the two constituents could be written 



(p-e)v = RT (1) 



ev = rR,T = - RT (2) 



6 



where 



v = volume of (1 -f- r) gram of moist air, or the volume of the moist air per 



gram of dry air, 

 R = gas constant for dry air, 

 R v = gas constant for water vapor, 

 T= absolute temperature, 



« = -r-r~ = -5- = ratio of molecular weight of water vapor to that of dry air, 



Ma Kv 



r = mixing ratio (grams of water vapor per gram of dry air). 

 Adding equations (1) and (2), and considering that the density p of the moist air is 



given by p = - — — — -, then on the assumption of perfect gas behavior 

 v 



p - d+r) _P_ (3) 



Virtual temperature. — The virtual temperature (7\) as denned by the I. M. O. Aero- 

 logical Commission, Subcommission I, on Physical Functions and Constants (Toronto, 

 1947) * is given by the expression 



>+7 



Then T v is the temperature which dry air must have at the given barometric pressure 

 p in order to have the same density as moist air at the same pressure P, and given tempera- 

 ture T , and mixing ratio r, provided the dry and moist air behave in accordance with the 

 perfect gas equation of state. 



Deviations from perfect gas laws. — To take account of deviations of moist air from 

 perfect gas behavior the I. M. O. 2 introduced the compressibility factor C, a function of 

 pressure, temperature, and relative humidity (see Table 84), which makes the expres- 

 sion for the actual density of moist air 



'=nfe (5) 



where Tv is the virtual temperature defined by equation (4). 

 Similarly the density of dry air (p ) is given by 



where C a , a function of pressure and temperature, is the compressibility factor for dry 

 air. C a is equal to the value of C when the relative humidity is zero. It should be noted 

 that in general C=f=l. 



Adjusted virtual temperature. — In this volume there is introduced the quantity T'v °K., 

 (or t'v °C), termed adjusted virtual temperature, and defined by the expression 



T'v = CTv. (6) 



1 See also Sheppard, P. A., The physical properties of air with reference to meteorological practice 

 and air conditioning engineer. A paper presented before the American Society of Mechanical Engineers 

 in December 1948, Amer. Soc. Mech. Eng. Trans., vol. 71, 1949. 



2 1. M. O. Aerological Commission, Doc. 25, Toronto, 1947. 



{continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



