THERMAL EFFECTS OF FLUIDS IN MOTION. 
341 
in the compression, we may use the expression 
w;=PV log 
as approximately equal to the mechanical value of either of those energies ; and we 
thus find for the proportionate excess, 
XT _1 
11 j w p pf p pf 
— y — — p= 0024 p for air, 
jw niogp-, niogp, 
p— p' 
or =-013 p for carbonic acid. 
niogp 
This equation shows in what proportion the heat evolved exceeds the equivalent of 
the work spent in any particular case of compression of either gas. Thus for a very 
small compression from P'=II, the atmospheric pressure, we have 
P / P— TI\ P— TT 
l°gp= iog^H-— p— j =— p— approximately, 
II — jl6> 
and therefore — =*0024 for air, 
J w 
or =-013 for carbonic acid. 
Therefore, when slightly compressed from the ordinary atmospheric pressure, and 
kept at a temperature of about 60°Fahr., common air evolves more heat by and 
carbonic acid more by than the amount mechanically equivalent to the work of 
compression. For considerable compressions from the atmospheric pressure, the pro- 
portionate excesses of the heat evolved are greater than these values, in the ratio of 
the Napierian logarithm of the number of times the pressure is increased, to this 
number diminished by 1. Thus, if either gas be compressed from the standard state 
to double density, the heat evolved exceeds the thermal equivalent of the work spent, 
by in the case of air, and by ^ in the case of carbonic acid. 
As regards these two gases, it appears that the observed cooling effect was chiefly 
due to an actual preponderance of the mechanical equivalent of the heat required to 
compensate the cold of expansion over the work of expansion, but that rather more 
than one-fourth of it in the case of air, and about one-third of it in the case of 
carbonic acid, depended on a portion of the work of expansion going to do the 
extra work spent by the gas in issuing against the atmospheric pressure above that 
gained by it in being sent into the plug. On the other hand, in the case of hydrogen, 
in such an experiment as we have performed, there would be a heating effect, if the 
