ADIABATIC CHANGES OF MOIST AIR NEUHOFF 433 



§2. IN GENERAL 



The elements that represent the condition of a mass of air at any- 

 given moment are temperature (t), pressure (p) and moisture; the 

 latter being considered as to quantity and form of aggregation. 

 If now the mass of air is by any influence whatever forced to rise 

 or sink, then the most important questions are as to the changes 

 that it will experience and as to the altitudes at which these occur. 



The problem is simplest when we assume that the mass of air 

 neither gives up heat to its surroundings nor receives heat from 

 them. Under these circumstances we have to do with adiabatic 

 changes of condition, and the equations that express the relation 

 between the different variables for this condition are called adia- 

 batic equations. If we represent adiabatic conditions by curves, 

 then we obtain adiabatic curves, or, for brevity, "adiabats. " 



If a mass of air is carried upwards to greater heights it comes under 

 lower pressure since the pressure in the atmosphere diminishes with 

 the altitude. Consequently its volume increases and the mass 

 becomes specifically lighter. But by the increase of volume and 

 the overcoming of the external pressure a work of expansion is per- 

 formed; the quantity of heat necessary to perform this work, if the 

 change is an adiabatic one must be drawn from the internal energy 

 of the air. But in the case of gases, this internal energy is deter- 

 mined only by the temperature. Consequently the result of 

 adiabatic expansion is a lowering of temperature. 



In this case for dry air the diminution of temperature for a given 

 diminution of pressure can be expressed by a simple law which 

 reads 



p/po=(T/T r 



or 



log p — m log T = log p — m log T = constant . . (1) 



This law was derived by Poisson by an elementary course of reason- 

 ing but entirely in harmony with the developments of thermody- 

 namics, hence this equation is known as Poisson's equation. In 

 this equation p and p express the atmospheric pressure and T 

 and T the absolute temperature of the free air; the exponent is 



k 



where 



m = 



k - 1 



c- 



