MR. MACQUORN RANKINE ON THERMO-DYNAMICS. 
I f>4 
If in this equation be substituted the value of v'—v in terms of the latent heat of 
evaporation at the higher temperature, given by equation (60.), it becomes 
L, 
V c — V D = 
( 68 .) 
In this case the diagram ABCD, fig. 22, is evidently that of a vapour-engine work- 
ing with the absolute maximum of efficiency between the absolute temperatures r, 
and r 2 . The heat expended at each single stroke, per unit of weight of fluid, is the 
latent heat of evaporation at the higher temperature, or L, ; the area of the diagram 
is given by the following equation, 
E=(r, — r 2 )AO = ^zJ-L, » (69.) 
This is the mechanical power developed at each single stroke by a unit of weight 
of the substance employed. The efficiency is represented by 
1 =^ <w 
being the expression for the maximum efficiency of thermo-dynamic engines in 
general. 
The conditions of obtaining this efficiency are the following : — 
First; that the elevation of temperature from r 2 to r„ during the operation repre- 
sented by the curve DA on the diagram, shall be produced entirely by compression. 
The volume at which this heating by compression must commence is given, according 
to Proposition XVII., by the following equation : — 
v »= H^jr.K L hy P .iog^. (-1.) 
dr 
Secondly ; that the expansive working of the vapour shall be carried on until the 
temperature falls, by expansion alone, to its lower limit; that is to say, until the 
volume reaches the following value, obtained by adding together equations (68.) 
and (71.) 
V 0 =»+jjr.{K L hyp.log^i+AL.} (72.) 
dr 
(44.) Numerical example. 
To exemplify this numerically, let the same data be employed as in article (41.), 
the substance working being one pound avoirdupois of water. These data, with 
some additional data deduced from them, are given in the following table : — 
