174 
MR. MACQUORN RANK1NE ON THERMO-DYNAMICS. 
Subtracting from each of these equal areas the common area BUG, and adding to 
each of the equal remainders the indefinitely prolonged area LUDN, we form the 
areas MCDN, LBADN ; which are consequently equal. Q.E.D. 
(51.) Of the Total Heat of Evaporation. 
manner. The area LBADN represents the total heat of evaporation, at the tempera- 
ture r x ,from the temperature r 2 , and is composed of two parts, as follows : — 
from r 2 to r 1} and the second is the latent heat of evaporation at t x . 
Let v 2 be the volume of unity of weight of the vapour at the pressure P 2 and tem- 
perature of saturation r 2 ; draw the ordinate v'JL, meeting DF in E, through which 
point draw the indefinitely-prolonged curve of no transmission ER: then is the area 
MCDN divided into two parts, as follows : — 
in which equation r c denotes the temperature corresponding to the point C on the 
curve of free expansion, and K P the specific heat of the vapour, at the constant press- 
ure P 2 when above the temperature of saturation ; so that the first term represents 
the heat abstracted in lowering the temperature of the vapour from r c to the tempe- 
rature of saturation r 2 , at the constant pressure P 2 ; and the second term, the latent 
heat of evaporation at r 2 , abstracted during the liquefaction. 
By equating the formulae (82.) and (83.), the following equation is obtained : — 
which is the symbolical solution of Proposition XIX., and shows a relation between 
the total heat of evaporation of a fluid, the free expansion of its vapour, and the spe- 
cific heat of that vapour at constant pressure. 
(52.) Approximate Law for a Vapour ivhich is a perfect gas. 
If the vapour of the fluid in question be a perfect gas, and of very great volume 
as compared with the fluid in the liquid state, the curve BC will be nearly a hyper- 
bola, and will nearly coincide with the isothermal curve of the higher temperature t„ 
to which, consequently, r c will be nearly equal; and the following equation will be 
approximately true : 
The symbolical expression of the preceding proposition is formed in the following 
LBADN=^ Kj/Zr+L,, (82.) 
. . (82.) 
of which the first is the heat necessary to raise the liquid, whose specific heat is K L , 
. . (83.) 
• (84.) 
( 85 .) 
