Cn RO ES Pla 5 lesen ne 
. 
Mechanical Theory of Heat to the Steam Engine. 201 
maa(er-n/'59) 
Q, signifies herein for our case, the heat communicated in the 
boiler to the mass M, and we have therefore 
Q,=m, ry) +Me (7 Te 
Q1 
oe : d ; se 
In determining the integral [<2 the two single quantities of 
fe 
heat contained in Q,, Mc (7,—7,) and m,r, must be particu- 
larly considered. In order to execute the integration for the 
first, we may write the element of heat d @ in the form Med 7 
then this portion of the integral becomes 
} 5 
Me eB FH sit 
To - : 
During the communication of the last quantity of heat, the 
temperature is constantly equal to 7’,, and the portion of the in- 
: mr 
tegral relating to this quantity of heat is therefore simply wae 
‘ 1 
By substituting these values, the above expression for W’ be- 
comes the following. 
is 
W'=—[m,r, 4Me(2,-7,)- T(" 14 al 108 7.)] 
1 T,-T, T 
=] m7, T. + Me(7,-7,47, lg 7°) | 
and this is the same expression as that contained in equation 
(XI), which we have previously found by the successive deter- 
mination of the single quantities of work done during the circu- 
ess 
process, 
24. Hence it follows that 7 the tem res at which the 
nee conveying the action of the heat takes up the heat delivered 
given, then the steam engine, under the suppositions made in 
deducing equation (x1) is a perfect machine, inasmuch as for a 
etinite quantity of heat communicated to it, it does as much 
oe to the mechanical theory of heat, is possible 
at the same temperatures, 
The matter is otherwise however if we do not regard these 
temperatures as given a priori, but consider them as a variable 
element which must be taken into consideration in judging the 
machine, In consequence of the fact that the liquid, during its 
SECOND SERIES, VOL. XXII, NO. 65.—SEPT., 1856, 
26 
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