CATALOGUE.-HEAT, CAPACITIES.
temperature is to be diffused through x times as much air,and itwillthen become ax”- 1 —ax- calling 1450 a,which becomes a maximum when (a — +
ax-*i = o, or (n — l).x" + i — », or x — (l _ n) ”,which, as n becomes small, approaches to 2 . 71 8 as itslimit. Consequently the greatest heat that can be pro-duced in this manner is when the air has been exhaustedto about .* of the atmospheric density, wherever we place1450 X 2-7"— 1450
the natural zero. Putting then-;-= 50,
2 • 7
50 X 2 7
we have 2.7"=-— + l = 1.003, whence n it
1450
about ——, and the heat produced by compression to x
times the density shouldbe 1450 (x^-i) , which, if x— 2 , becomes 03° ; and such should have been the de-gree of cold produced by the return of air of double thenatural density to the state of equilibrium. Whether thiseffect was lost by the difficulty of making the observationwith accuracy, or whether the friction produces some heatwhich is confounded with the effect of expansion, mayperhaps be determined by future experiments: but in thiscase Mr. Dalton observed only a heat of 50°,. as in theformer experiment. We may, however, deduce from thatexperiment an acceleration of about J to be added to thecalculation of the velocity of sound ; and since the resultsof experiments on sound require an acceleration of j, oronly \ more, which has been ascertained with great accu-racy, it may be fair to allow the supposition of Laplace andHiot, that the whole acceleration of sound is owing to thiscause, and we may at least assume that acceleration, asaffording a limit, which the heat produced by condensation,certainly cannot exceed. We may therefore make the ex-ponent of the density J, for expressing the change of ca-
( » ^
pacity, and the heat produced 1450 yr —i J, which,when the density is doubled or halved, becomes 131.2°.A compression of will produce a heat of 1 °.
Now it appears from experiments on the sounds of dif-ferent gases, and from the sound of a pipe in air of densitiesthe most various, that the correction. of the velocity ofsound is nearly the same in all; hence it may be inferredthat the heat produced by condensation follows nearly thesame law with respect to all gases. This principle maytherefore probably be extended to steam. Supposing theconversion of water into steam to absorb as much heat aswould raise its temperature 940°, we may call its capacityat 212 ° 1 . 60 , and may calculate a table for other tempe-ratures, assuming, with Mr. Dalton, that its simple ex-pansion by heat is equal to that of air. Mr. Watt has
409
shown, by direct experiment, that steam has a greater ca-pacity as its temperature is lower.
Specific
gravity.
Capacity.
]82 fi F.
.56
1.73
Uvx
.08
3.08
20 a
.83
1.64
212
1.00
1.60
222
1.21
1.56
232
1.44
1.53
242
l.?l
1.50
252
2.03
3.47
202
2.38
1.44
272
2.80
1.41
Hence, if a steam
engine work
with double atmo-
spheres, the heat being about 247°,
it will require 3.87
times as much water,
of which the
capacity is 1.4 8, its
excess above that of i
ft-ater { as much as at 212°, it will
therefore absorb about
752°, and the heat required for
raising water from 100
will be as 1.87 (147 + 752 ), to
112 + 940, or nearly
as 8 to 5,
while the effect is
doubled.
Robison says, that four ounces of water at loo°, willcondense in a second nearly 200 cubic feet of steam, re-ducing its expansive force to one fifth. If this is correct,it sets at defiance all theories of capacity. The only dis-tant analogy that can be found for it, is the facility withwhich rarefied air is found to carry off heat, which wouldinduce us to suppose that the capacity of a given bulk ofair is much less affected by its density than this calculationappears to demonstrate.
Natural Zero.
Opinions of Amontons , Lambert, and
Dalton. See Expansion. ,
Seguin on heat. Ann. Ch. III. 148. Ac-count of the theories of specific heat. V.
191 . Nich. 8. IV. 221.
Observes, that front experiments on the mixture of sul-furic acid and water, it might be inferred that the naturalzero is 7292 0 below the zero of Fahrenheit, but fromKirwan’s experiments on ice only 1350°. Other experi-ments on ice give 1461°, Dalton 1547 °.
Dalton 011 the natural zero. Gill). XIV. 287.
Gay Lussac ’s experiments on Dalton’s supposition give1556°. Gilb.
Heat denominated latent.
Landriani. Opusc. fisicodi. viii. lloz.
XXVI. 88, 197.
3 G
VOL. II.