SPECIFIC HEATS 
77 
(317) Ÿf + Cî - Cl = A 
0Vi— vf) dP 
M dT 
in heat units. 
The Specific Heats in Terms of the Latent Heats 
It can be proved by differentiation of the first forms of (309) 
and (310) and the necessary substitutions that, 
vapor-liquid. 
liquid-solid. 
Compare Planck’s “Thermodynamik.” 
Examples of the Thermodynamic Data 
1. Carnot’s Cycle. In Fig. 3 the area enclosed between the 
isotherms (1.3) and the adiabats (2.4) represents the work 
done, W, in the cyclic process, and the figure is called the indicator 
diagram. This is used in studying the efficiency of engines, 
whether the process is natural or mechanical, and there is a very 
large literature on the subject. No applications have as yet 
been made in the atmosphere, for two reasons, the first because 
of the difficulty of tracing out the history of a given mass, and 
the second because the values of Cv in the formula are not 
constant, and the true values of it have not heretofore been 
computed. However, it is possible to take a standard mass, 
as one kilogram of air at an initial point, and trace out the 
conditions through which it must have passed in rising from the 
surface through changing P. v. T. till it arrives at the surface 
again in the original state, even though the path during its 
circulation may not be known. This work will be reserved for 
further studies. 
2. Cyclic Process for Vapors. In Fig. 4, we have, 
(320) (z> 2 — i>i) d Mi the mass which evaporates in expansion. 
(321) (v* — Vi) d M2 the mass which condenses in compression.