
HEAT PRODUCED BY THE COMPRESSION OF A GAS. 295 
closely as possible at the same temperature. If there be any elevation or depres- 
sion of temperature of the fluid in passing through the orifice, it may only be 
after passing through a considerable length of the second spiral that it will again 
arrive sensibly at the temperature, ¢, and the spiral must be made at least so long 
that the fluid issuing from the open end of it, when accurately tested, may be 
found not to differ appreciably from the primitive temperature, ¢. 
14. Let H be the total quantity of heat emitted from the portion of the tube 
containing the orifice, and the second spiral, during the passage of a volume w 
through the first spiral, or of an equivalent volume w’ through the parts of the 
second where the temperature is sensibly ¢. This will consist of two parts; one 
(positive) the heat produced by the fiuid friction, and the other (negative) the 
heat emitted by that portion of the fluid which passes from one side to the other 
of the orifice, in virtue of its expansion. To find these two parts, let us first sup- 
pose the transference of the fluid to take place without loss of mechanical effect 
in fluid friction, as it would do if, instead of the partition with a small orifice, 
there were substituted a moveable piston, and if a volume zw of fluid, on the side 
where the pressure is higher (p), were enclosed between that and another piston, 
and allowed to slide through the tube till the second piston should take the place 
of the first, and to expand till its volume should be w. If we adopt the same 
notation with reference to the volume, v, of the substance between the pistons, 
kept at a constant temperature, 7, as has been used uniformly in this and the 
preceding paper; we shall have, for the quantity of heat absorbed during the 
motion of the piston, 
fe % Mdv; 
u 
or, by the second fundamental equation of the theory, (3) of § 21 of the pre- 
ceding paper, 
1 wae 
pS, at 
where zw denotes the actual pressure (intermediate between p and p’) of the sub- 
stance when its volume is v. Again, the work done by the pistons will be given 
by the equation 
dv, 
/ 
u 
Wis pf @dv+pu—pu ‘ ? : ‘ (e). 
u 
If now the transference of the substance from the one portion of the tube, where 
the pressure is p, to the other, where the pressure is p’, take place through a 
small orifice, exactly that amount, W, of work will be lost as external mechanical 
effect, and will go to generate thermal vis viva. The quantity of heat thus pro- 
duced will be ; 
i{f. Baetpe—p w} 3 
