ADIABATIC CHANGES OF MOIST AIR NEUHOFF 443 



£ , so that £ = x + y for this stage. On the assumption that all 

 of the water remains in the air we have £ = x z or the same quantity 

 of vapor that existed in the dry stage. On the other hand, if we 

 take account of the loss of the precipitation by its fall from the cloud 

 then £ will have a smaller value on the average. 



The heat necessary for any change of condition involving con- 

 densation when £ = (x + y) kilograms of moisture are present is 



dQ" = ZcdT + Td(** 



where c is the specific heat of water or on the average 1.013 accord- 

 ing to Clausius and r is the latent heat of evaporation of water which 

 latent heat being set free from the condensing vapor does a part of 

 the work of expansion as the air ascends and thus diminishes the 

 rate of fall of temperature with altitude, r is a function of the tem- 

 perature and according to Regnault can be expressed by the empiric 

 formula r = 606.5 — 06952. The total quantity of heat required 

 for the change in condition of the mixture of dry air and vapor is 

 equal to the sum of these two quantities or 



/ x r \ dp' 



dQ= (c p + Zc)dT + Td{ -)-ART-p 



In adiabatic expansions we have dQ — whence we obtain the 

 following as the differential equation of the adiabatic for this case 



dT (xr\ dp' 



0=(c p + ?c)^ +dy-j)-AR— 



If we indicate the initial conditions by the subscript index o we 

 obtain by integration and a simple transformation 



p' c n + £ c , T M / xr x r \ . T 



'< - 'a r log r + ar ( f - t ) = m " log r 



+ AR\ T T / 

 where we have introduced the notation 



•»»- *jjt - hi 1 +r/) - 3 - 441 (1 + 4265 « 



