342 
MR. J. P. JOULE AND PROFESSOR THOMSON ON THE 
work of expansion were precisely equal to the mechanical equivalent of the cold of 
expansion, since not only the whole work of expansion, but also the excess of the 
work done in forcing the gas in above that performed by it in escaping, is spent in 
friction in the plug. Since we have observed actually a cooling effect, it follows that 
the heat absorbed in expansion must exceed the equivalent of the work of expansion, 
enough to over-compensate the whole heat of friction mechanically equivalent, as 
this is, to the work of expansion together with the extra work of sending the gas 
into the plug above that which it does in escaping. In the actual experiment* we 
found a cooling effect of '076°, with a difference of pressures, P— F, equal to 53*7 lbs. 
per square inch, or 3’7 atmospheres. Now the mechanical value of the specific heat 
of a pound of hydrogen is, according to the result stated above, 4732 foot-pounds, 
and hence the mechanical value of the heat that would compensate the observed 
cooling effect per pound of hydrogen passing is 360 foot-pounds. But, according to 
Regnault’s experiments on the compression of hydrogen, quoted above, we have 
PV— FV'=PV X-‘00043^-jp- approximately ; 
and as the temperature was about 10° in our experiment, we have, as stated above, 
PV=393000. 
Hence, for the case of the experiment in which the difference of pressures was 3’7 
atmospheres, or 
we have PV— P'V'=625 ; 
that is, 625 foot-pounds more of work, per pound of hydrogen, is spent in sending the 
hydrogen into the plug at 4*7 atmospheres of pressure, than would be gained in 
allowing it to escape at the same temperature against the atmospheric pressure. 
Hence the heat required to compensate the cold of expansion, is generated by friction 
from (1) the actual work of expansion, together with (2) the extra work of 625 foot- 
pounds per pound of gas, and (3) the amount equivalent to 360 foot-pounds which 
would have to be communicated from without to do away with the residual cooling 
effect observed. Its mechanical equivalent therefore exceeds the work of expansion 
by 985 foot-pounds ; which is g^ of its own amount, since the work of expansion in 
the circumstances is approximately 393000 X log4*7 = 608000 foot-pounds. Con- 
versely, the heat evolved by the compression of hydrogen at 10° Cent., from 1 to 4*7 
atmospheres, exceeds by the work spent. The corresponding excess in the case 
* From the single experiment we have made on hydrogen we cannot conclude that at other pressures a 
cooling effect proportional to the difference of pressures would be observed, and therefore we confine the com- 
parison of the three gases to the particular pressure used in the hydrogen experiment. It should be remarked 
too, that we feel little confidence in the value assigned to the thermal effect for the case observed in the expe- 
riment on hydrogen, and only consider it established that it is a cooling effect, and very small. 
