318 TABUE 78 



TEMPERATURE AND PRESSURE ALONG SATURATION PSEUDOADIABATS 



The differential equation of the pseudoadiabatic condensation stage involving satura- 

 tion with respect to water (rain stage) as given by von Bezold 1 is 



(c P + c w r w )dT - RT (M:^ + Td (^j^) = 0. (1) 



Where 



c p = specific heat of dry air at constant pressure, 

 c w = specific heat of water, 



T = temperature, C K., 



R = gas constant for dry air, 



/>„ = partial pressure of the dry air, 



L B = lutent heat of condensation of water, 



r w = saturation mixing ratio over water. 



All quantities are to be expressed in cgs work units. 



Integrating equation (1) between nearby values of (p a , T) denoted by subscripts 

 1 and 2, and regarding c p and c w as constants within this interval we get 



c P log, ~+cJ \ v dT-R log. £= (Lgil _ ^l)= 0. (2) 



1 » J Tj T p al \ Tl Tl ) 



The integral in equation (2) may be replaced by its equivalent 



c. [ 'r.%=c.rZlog.I?. (3) 



J ^ T T* 



where rZ is the mean value of r» on a logarithmic basis in the interval. 

 pai is related to the total, barometric pressure pi by 



p a i = p 1 — e w i (4) 



where e w i is the saturation vapor pressure over water at temperatures Tu 

 Similarly, 



pat = pt — e w ». (5) 



Making use of equations (3) and (4), equation (2) can be solved to a close degree 

 of approximation for p at when values of Ti, pi, Tt, are given, provided Ti is sufficiently 

 near 7i. Ususally 2°C. intervals are used, and equation (2) is solved stepwise for a suc- 

 cession of values of p a i on the pseudoadiabat and p* is determined from equation (5). 



The U. S. Weather Bureau has computed the values of p at various values of T along 

 a number of pseudoadiabats. In making the computations it was assumed that YZ> could 

 be adequately represented by the relation rZ = eeZ/p~a~ where eZ, = (e w i + e v *)/2, 

 ~pl= (pai + pai)/2, and e= ratio of molecular weight of water vapor to molecular weight 

 of dry air. The following constants were used in the computations : 



c v — 0.238 cal. g." 1 °K.- 1 = 0.995 X 10 T ergs g." 1 "K." 1 

 cm = 1 cal. g." 1 °K.- 1 = 4.18 X 10 7 ergs g." 1 °K.-' 



R = 28.71 X 10 B cm. 2 deg." 1 sec. -2 = cm. 2 deg." 1 sec." 1 



L.= [596.73-0.601 t (°C.)] cal. g." 1 = [2494.3-2.512 t (°C.)] ergs g." 1 

 « = 0.622 



The values of e w used also differ slightly from those given in this volume. 



Table 78 gives the corresponding pressure for each even whole degree centigrade along 

 the pseudoadiabats having temperatures at 1000 mb. (pseudo-wet-bulb potential tempera- 

 ture) from — 20°C. to 40°C. at 2° intervals. The corresponding equivalent potential 

 temperature for each pseudoadiabat is also indicated. 



1 Von Bezold, Zur Thermodynamik der Atmosphere, Sitzungsber. Berlin Akad., 1888. 



(continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



