THERMAL EFFECTS OF FLUIDS IN MOTION. 
339 
unknown; and as yet no experimental data exist by which it can be determined” 
(x, denoting in his expressions a quantity the vanishing of which for any gas would 
involve the equivalence in question). In further observing that probably x is small 
in comparison with the reciprocal of the coefficient of expansion, Mr. Rankine 
virtually adopted the equivalence as probably approximate; but in his article “ On 
the Thermic Phenomena of Currents of Elastic Fluids*,” he took the first opportunity 
of testing it closely, afforded by our preliminary experiments on the thermal effects 
of air escaping through narrow passages. 
We are now able to give much more precise answers to the question regarding 
the heat of compression, and to others which rise from it, than those preliminary 
experiments enabled us to do. Thus if K denote the specific heat under constant 
pressure, of air or any other gas, issuing from the plug in the experiments described 
above, the quantity of heat that would have to be supplied, per pound of the fluid 
passing, to make the issuing stream have the temperature of the bath, would be K$, or 
Km 
(P-PQ 
n 
5 
where m is equal to - 26° for air and IT 5° for carbonic acid, since we found that the 
cooling effect was simply proportional to the difference of pressure in each case, and 
was ’0176° per pound per square inch, or *26 per atmosphere, for air, and about 4| times 
as much for carbonic acid. This shows precisely how much the heat of friction in the 
plug falls short of compensating the cold of expansion. But the heat of friction is the 
thermal equivalent of all the work done actually in the narrow passages by the air 
expanding as it flows through. Now this, in the cases of air and carbonic acid, is 
really not as much as the whole work of expansion, on account of the deviation from 
Boyle’s law to which these gases are subject ; but it exceeds the whole work of 
expansion in the case of hydrogen which presents a contrary deviation ; since P'V', 
the work which a pound of air must do to escape against the atmospheric pressure, 
is, for the two former gases, rather greater, and for hydrogen rather less, than PV, 
which is the work done on it in pushing it through the spiral up to the plug. In 
any case, w denoting the whole work of expansion, w— (P'V'— PV) will be the work 
actually spent in friction within the plug ; and 
j{w-(P'V'-PV)} 
will be the quantity of heat into which it is converted, a quantity which, in the cases 
of air and carbonic acid, falls short by 
P-P 
Km 
n 
of compensating the cold of expansion. If therefore H denote the quantity of heat 
* Mechanical Action of Heat, Subsection 4, communicated to the Roy. Soc. Edinb. Jan. 4, 1853, Transac- 
tions, vol. xx. p. 580. 
2x2 
