THERMAL EFFECTS OF FLUIDS IN MOTION. 
337 
“The absolute zeros of gaseous tension and of heat are supposed sensibly to coin- 
cide, i. e. k is supposed inappreciably small. 
“ Formulas : 
PV_T±C 
P o v o — C ~T + C V O’ 
a= 1-9, loga=0'2787536. 
“ Cooling by free expansion, supposing the perfect gas thermometer to give the 
true scale of absolute temperatures : 
P 0 V 0 3a fV 0 Y 0 1 
01 - K P ‘T + C^ V 2 [ • • 
bg ^-^ 2 ' 5111438 ” 
. . ( 2 )* 
V V • • CP CP 
By substituting for ==? and ==? their approximate values ,= — and = — - -i, we 
V] V 2 1+C A q 1+C Pq 
reduce it to 
S — 3P 0 V 0 aC 
K P (T + C) 2 
from which we have calculated the theoretical results for different temperatures shown 
above, which agree remarkably well with those we have obtained from observation. 
The interpretation given above for the experimental results on mixtures of carbonic 
acid and air depends on the assumption (rendered probable as a very close approxi- 
mation to the truth, by Dalton’s law), that in a mixture each gas retains all its 
physical properties unchanged by the presence of the other. This assumption, how- 
ever, may be only approximately true, perhaps similar in accuracy to Boyle’s and Gay- 
Lussac’s laws of compression and expansion by heat; and the theory of gases would 
be very much advanced by accurate comparative experiments on all the physical pro- 
perties of mixtures and of their components separately. Towards this object we have 
experimented on the thermal effect of the mutual interpenetration of carbonic acid 
and air. In one experiment we found that when 7500 cubic inches of carbonic acid 
at the atmospheric pressure were mixed with 1000 cubic inches of common air and 
a perfect mutual interpenetration had taken place, the temperature had fallen by 
about '2° Cent. We intend to try more exact experiments on this subject. 
Theoretical Deductions. 
Section I. On the Relation between the Heat evolved and the W irk spent in Compress- 
ing a Gas kept at constant temperature. 
This relation is not a relation of simple mechanical equivalence, as was sup- 
posed by MAYER-i~ in his ‘ Bemerkungen ueber die Krafte der Unbelebten Natur,’ 
* Obtained by using Mr. Rankine’s formula (1) in the general expression for the cooling effect given in our 
former paper, and repeated below as equation (15) of Section V. 
t Annalen of Wohler and Liebig, May 1842. 
2 x 
MDCCCLIV. 
