MR. MACQUORN RANKINE ON THERMO-DYNAMICS. 
167 
proved that those experiments are not relevant against the conclusion in question, by 
showing the difference between the free expansion of an elastic fluid, in which all the 
power due to the expansion is expended in agitating the particles of the fluid, and is 
reconverted into heat, and the expansion of the same fluid under a pressure equal to 
its own elasticity , when the power developed is all communicated to external bodies, 
such, for example, as the piston of an engine. 
The free expansion of a vapour will be considered in the sequel. 
(46.) Efficiency of a Vapour- Engine without heating by compression. 
The numerical example of article (44.) sufficiently illustrates the fact, that the strict 
fulfilment of the condition specified in article (43.), as necessary to the attainment 
of the absolute maximum of efficiency of a vapour-engine, is impossible in practice. 
Let us consider, in the first place, the effect of dispensing with the process DA, 
during which the fluid is supposed to have its high temperature restored solely bv 
compression. 
The effect of this modification is evidently, to add to the heat expended, that which 
is necessary to elevate the temperature of the liquid from r 2 to r,, and to add to the 
power developed an amount represented by the area ADE, fig. 22. 
To express this symbolically, we have — 
The Latent Heat of Evaporation at r 15 as before . . L 1 
The additional heat expended (K L being the mean spe- 
cific heat of the liquid between t, and r 2 ) . . . K l (t, — t 2 ) 
Total heat expended . . L 1 + K l (t 1 — t 2 ) . (77-) 
Then for the power developed, we have 
the area ABCD, as in article (43.), =— — 2 .L„ 
T i — * 
the area ADE, as in Article (40), equation (65.), 
= K l j(r 1 -*)-(r 2 -*)(l+hyp. logjj^j 
the sum of which quantities is the total power developed (78.) 
The efficiency may be expressed hi the following form : — 
Power developed t, — r 2 ^ L ^" 2 T ^_ x 
Heat expended ~ ~ r 2 ) 
an equation which shows at once how far the efficiency falls short of the absolute 
maximum. 
For a numerical example, the same data may be taken as in articles (41.) and (44.). 
Then the heat expended, per pound of steam, is thus made up : — 
Foot-pounds. 
Latent Heat of Evaporation, as in art. (44.) 707,445-36 
Heat required to raise the water 100° C., as in article (41.) . 139,800-00 
Total heat expended, per lb. of water . . . 847,245*36 
