162 
MR. MACQUORN RANKINE ON THERMO-DYNAMICS. 
The other numerical data are, — 
dP 
at 40° Centigrade = 8-2075 lbs. per square foot, per Centigrade degree ; 
t?=mean volume of 1 lb. of liquid water = 0"017 cubic foot, nearly. 
Let it be required to find, in the first place, V B , the volume to which the water 
must be allowed to expand by partial evaporation under pressure, in order that its 
temperature may fall to 40° Centigrade ; and secondly, how much power will be de- 
veloped in all, after the water has been totally reliquefied by refrigeration at constant 
pressure, at the temperature of 40°. 
First , by the equation (63.), 
/7P 412i 
A<P=^t(V b — v) = 1398 X hyp. log ^| = 402-624 ; 
dP 
divide by ^- = 8-2075 ; then V B — t> = 49 - 055 cubic feet. 
add v— 0-017 
Aggregate volume of water and steam at 40°, V B = 49-072 cubic feet. 
As the volume of one pound of steam at 40° Centigrade, according to the fourth 
column of the table in article (38.), is 313’56 cubic feet, it appears from this calcu- 
lation that somewhat less than one-sixth of the water will evaporate. 
Secondly , it appears, from equation (65.), that after the water has been restored to 
the liquid state by refrigeration at 40° Centigrade, the whole power developed, that 
is to say, the area A Ba, will be 
1398 foot-pounds x |412 0, 5 — 312 0, 5 ^1 +hyp. log j 
= 1398 ft. lb. X 10° Centigrade= 13,980 ft. lb., 
or one-tenth of the equivalent of the heat expended. The other nine-tenths constitute 
the heat abstracted during the reliquefaction at 40° Centigrade. 
This calculation further shows, that in order that one pound of water and steam 
at 40° C. may be raised to 140° C. solely by compressing it into the liquid state, it 
must occupy at the commencement of the operation the volume V B = 49"072 cubic 
feet ; and that the power expended in the compression will be as follows : — 
Foot-pounds. 
Area of the curvilinear triangle ABa, fig. 21, as already calculated 13,980 
Area of the rectangle «BV B t>=P 2 (V B — v)= 7,522 
Total 21,502 
(42.) Proposition XVIJI. — Problem. Having the same data as in the last proposi- 
tion, it is required to draw a curve of no transmission through any point on the diagram 
of energy for the aggregate of a liquid and its vapour. 
