CATALOGUE. HEAT, CAPACITIES. 



409 



temperature is to be diffused through x times as much air, 

 audit will then become ax"-' — ax—', callmg 14 JO a, 

 which becomes a maximum when (» — l).ai''-'i + 

 o«-'i = o, or (n — l).i"+ 1 :=o, ot x — (l — ri) ", 

 which, as n becomes small, approaches to 2.718 as its 

 limit. Consequently the greatest heat that can be pro- 

 duced in this manner is when the air has been exhausted 

 to about I of the atmospheric density, wherever we place 



the natural zero. Putting then 

 50 X 2.7 



1450 X2.7'' — 1450 



2T7 



-=50, 



we have 2.7"=:- 



1450 



+ 1 =: l.ogs, whence n i« 



about , and the heat produced by compression to x 



= 1450 V'^'*"'^— 1/, ' 



times the density should be 1450 \x "•"■'— i/, which, if x 

 r: 2, becomes 93° ; and such should have been the de- 

 gree of cold produced by the return of air of double the 

 natural density to the state of equilibrium. Whether this 

 effect was lost by the difficulty of making the observation 

 with accuracy, or whether the friction produces some heat 

 which is confounded with the sffect of expansion, may 

 perhaps be determined by future experiments : but in this 

 case Mr. Dalton observed only a heat of so°, at in the 

 former experiment. We may, however, deduce from that 

 experiment an acceleration of about f to be added to the 

 calculation of the velocity of sound ; and since the results 

 of experiments on sound require an acceleration of J, or 

 only i more, which has been ascertained with great accu- 

 racy, it may be feir to allow the supposition of I^place and 

 Biot, that the whole acceleration of sound is owing to this 

 cause, and we may at least assume that acceleration, as 

 affording 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 V^x — 1/, which, 

 when ttie density is doubled or"'haIved, becomes 131.2°. 

 A compression of |ig 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 densities 

 the most various, tha,t the correction of the velocity of 

 sound is nearly the same in all ; hence it may be inferred 

 that the heat produced by condensation follows nearly the 

 same law with respect to all gase?. This principle may 

 therefore probably be extended to steam. Supposing the 

 conversion of water into steam to absorb as much heat as 

 would raise its temperature 940', we may call its capacity 

 at 212° 1. 00, and may calculate a table for other tempe- 

 ratures, assuming, with Mr. Dalton, that its simple ex- 

 pansion by heat is equal to tlia,t of air. Mr. Watt' has 



VOL. II. 



shown, by direct experiment, that steam has a greater ca- 

 pacity as its temperature is lower. 



Specific Capacity. 



gravity. 



Isa'F. .50 1.72 



103 .OS i.oa 



303 .S3 1.04 



313 1.00 1.00 



332 1.21 . 1.50 



333 1.44 1.53 

 342 1.71 1.50 

 352 2.03 1.47 

 303 3.38 1.44 

 373 3.S0 1.41 



Hence, if a steam engine work with double atmo- 

 spheres, the heat being about 247°, it will require 1.87 

 times as much water, of which the capacity is 1.4 8, its 

 excess above that of water i 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 -f 940, or nearly as 8 to 5, while the effect is 

 doubled. 



Robison says, that four ounces of water at 100°, will 

 condense 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 with 

 which rarefied air is found to carry off heat, which would 

 induce us to suppose that the capacity of a given bulk of 

 air is nmch less affected by its density than this calculation 

 appears 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 from experiments on the mixture of sul- 

 furic acid and water, it might be inferred that the natural 

 zert) is 7292° below the zero of Fahrenheit, but from 

 Kirwan's experiments on ice only 1350°. Other experi- 

 ments on ice give 1401°, Dalton 1547°. 



Dalton on the iiatuial zero. Gilb. XIV. 287. 



Gay Lussac's experiments on Dalton's supposition give 

 IbiO^. Gilb. 



Heat denominated latent. 



Landriarii. Opusc. fisicoch. viii. Roz, 

 • -XXVI. 88, 197. 



3g 



