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MECHANICAL ACTION OF HEAT. 569 
(50.) In order to investigate the laws according to which heat is converted 
into mechanical power, in a machine working by the expansion of an elastic body, 
it will be convenient to use a function 
B=fZ dV (Q=const.) 
of such a nature that the difference between two of its values, corresponding to dif- 
ferent volumes of the body at the same total heat, represents the ratio of the heat 
converted into power by expansion between those volumes, to the given constant 
total heat. I shall call this function a heat-potential. 
Introducing this function into Equation 72, we find, for the total heat con- 
sumed by a body during the increase of total heat dQ, and the expansion d V, 
dQ+d.8+PdV=(14+9'.Q)) 1Q+Qa.F ts sha Ren 
(observing that 2. F= FHId+ 5 a av= ( Tv.) « aQ+ Seay.) 
Let us now suppose that the body changes its volume without either losing 
or gaining heat by conduction. This condition is expressed by the equation 
0=(1+9’.Q)dQ+Qd.F 
from which we deduce the following, 
-d.F= 8-0) aq ds tat tae Se 
which expresses the following theorem :— 
When the quantity of heat in a body is varied by variation of volume only, the 
variation of the heat-potential depends on the heat only, and is independent of the 
* volume. 
Tn order that a machine working by the expansive power of heat may produce 
its greatest effect, all the heat communicated from external bodies should be em- 
ployed in producing expansive power, and none in producing variations of the 
quantity of heat in the body; for heat employed for the latter purpose would be 
wasted, so far as the production of visible motion is concerned. To effect this, 
the body must receive heat by conduction, and convert it into expansive power, 
while containing a certain constant quantity of heat Q,; give out by conduction 
heat produced by compression, while containing a smaller constant quantity of 
heat Q,; and change between those two quantities of thermometric heat by 
means of changes of volume only, without conduction. For this purpose a cycle 
of operations must be performed similar to that described by Carnot; as fol- 
lows :— 
(I.) Let F, be the initial value of the heat-potential; let the body expand at 
the constant heat Q, , till the heat-potential becomes F,. Then the heat received 
and converted into expansive power is 
H,=Q, (Fs—F,) 
VOL. XX. PART IV. 7P 
