Elements of Chemistry Part 27

_Calculation before Combustion._

The air in the jar before combustion was 353 cubical inches, but it was only under a barometrical pressure of 27 inches 9-1/2 lines; which, reduced to decimal fractions by Tab. I. of the Appendix, gives 27.79167 inches; and from this we must deduct the difference of 4-1/2 inches of water, which, by Tab. II. corresponds to 0.33166 inches of the barometer; hence the real pressure of the air in the jar is 27.46001. As the volume of elastic fluids diminish in the inverse ratio of the compressing weights, we have the following statement to reduce the 353 inches to the volume the air would occupy at 28 inches barometrical pressure.

353 : x, the unknown volume, :: 27.46001 : 28. Hence, x = 353 27.46001 / 28 = 346.192 cubical inches, which is the volume the same quant.i.ty of air would have occupied at 28 inches of the barometer.

The 210th part of this corrected volume is 1.65, which, for the five degrees of temperature above the standard gives 8.255 cubical inches; and, as this correction is subtractive, the real corrected volume of the air before combustion is 337.942 inches.

_Calculation after Combustion._

By a similar calculation upon the volume of air after combustion, we find its barometrical pressure 27.77083 - 0.51593 = 27.25490. Hence, to have the volume of air under the pressure of 28 inches, 295 : x :: 27.77083 : 28 inversely; or, x = 295 x 27.25490 / 28 = 287.150. The 210th part of this corrected volume is 1.368, which, multiplied by 6 degrees of thermometrical difference, gives the subtractive correction for temperature 8.208, leaving the actual corrected volume of air after combustion 278.942 inches.

_Result._

The corrected volume before combustion 337.942

Ditto remaining after combustion 278.942 -------- Volume absorbed during combustion 59.000.

SECT. VIII.

_Method of determining the Absolute Gravity of the different Ga.s.ses._

Take a large balloon A, Pl. V. Fig. 10. capable of holding 17 or 18 pints, or about half a cubical foot, having the bra.s.s cap bcde strongly cemented to its neck, and to which the tube and stop-c.o.c.k f g is fixed by a tight screw. This apparatus is connected by the double screw represented separately at Fig. 12. to the jar BCD, Fig. 10. which must be some pints larger in dimensions than the balloon. This jar is open at top, and is furnished with the bra.s.s cap h i, and stop-c.o.c.k l m. One of these slop-c.o.c.ks is represented separately at Fig. 11.

We first determine the exact capacity of the balloon by filling it with water, and weighing it both full and empty. When emptied of water, it is dried with a cloth introduced through its neck d e, and the last remains of moisture are removed by exhausting it once or twice in an air-pump.

When the weight of any gas is to be ascertained, this apparatus is used as follows: Fix the balloon A to the plate of an air-pump by means of the screw of the stop-c.o.c.k f g, which is left open; the balloon is to be exhausted as completely as possible, observing carefully the degree of exhaustion by means of the barometer attached to the air-pump. When the vacuum is formed, the stop-c.o.c.k f g is shut, and the weight of the balloon determined with the most scrupulous exact.i.tude. It is then fixed to the jar BCD, which we suppose placed in water in the shelf of the pneumato chemical apparatus Fig. 1.; the jar is to be filled with the gas we mean to weigh, and then, by opening the stop-c.o.c.ks f g and l m, the gas ascends into the balloon, whilst the water of the cistern rises at the same time into the jar. To avoid very troublesome corrections, it is necessary, during this first part of the operation, to sink the jar in the cistern till the surfaces of the water within the jar and without exactly correspond. The stop-c.o.c.ks are again shut, and the balloon being unscrewed from its connection with the jar, is to be carefully weighed; the difference between this weight and that of the exhausted balloon is the precise weight of the air or gas contained in the balloon. Multiply this weight by 1728, the number of cubical inches in a cubical foot, and divide the product by the number of cubical inches contained in the balloon, the quotient is the weight of a cubical foot of the gas or air submitted to experiment.

Exact account must be kept of the barometrical height and temperature of the thermometer during the above experiment; and from these the resulting weight of a cubical foot is easily corrected to the standard of 28 inches and 10, as directed in the preceding section. The small portion of air remaining in the balloon after forming the vacuum must likewise be attended to, which is easily determined by the barometer attached to the air-pump. If that barometer, for instance, remains at the hundredth part of the height it stood at before the vacuum was formed, we conclude that one hundredth part of the air originally contained remained in the balloon, and consequently that only 99/100 of gas was introduced from the jar into the balloon.

FOOTNOTES:

[58] According to the proportion of 114 to 107, given between the French and English foot, 28 inches of the French barometer are equal to 29.83 inches of the English. Directions will be found in the appendix for converting all the French weights and measures used in this work into corresponding English denominations.--E.

[59] When Fahrenheit's thermometer is employed, the dilatation by each degree must be smaller, in the proportion of 1 to 2.25, because each degree of Reaumur's scale contains 2.25 degrees of Fahrenheit; hence we must divide by 472.5, and finish the rest of the calculation as above.--E.

CHAP. III.

_Description of the Calorimeter, or Apparatus for measuring Caloric._

The calorimeter, or apparatus for measuring the relative quant.i.ties of heat contained in bodies, was described by Mr de la Place and me in the Memoirs of the Academy for 1780, p. 355. and from that Essay the materials of this chapter are extracted.

If, after having cooled any body to the freezing point, it be exposed in an atmosphere of 25 (88.25), the body will gradually become heated, from the surface inwards, till at last it acquire the same temperature with the surrounding air. But, if a piece of ice be placed in the same situation, the circ.u.mstances are quite different; it does not approach in the smallest degree towards the temperature of the circ.u.mambient air, but remains constantly at Zero (32), or the temperature of melting ice, till the last portion of ice be completely melted.

This phenomenon is readily explained; as, to melt ice, or reduce it to water, it requires to be combined with a certain portion of caloric; the whole caloric attracted from the surrounding bodies, is arrested or fixed at the surface or external layer of ice which it is employed to dissolve, and combines with it to form water; the next quant.i.ty of caloric combines with the second layer to dissolve it into water, and so on successively till the whole ice be dissolved or converted into water by combination with caloric, the very last atom still remaining at its former temperature, because the caloric has never penetrated so far as long as any intermediate ice remained to melt.

Upon these principles, if we conceive a hollow sphere of ice at the temperature of Zero (32) placed in an atmosphere 10 (54.5), and containing a substance at any degree of temperature above freezing, it follows, 1st, That the heat of the external atmosphere cannot penetrate into the internal hollow of the sphere of ice; 2dly, That the heat of the body placed in the hollow of the sphere cannot penetrate outwards beyond it, but will be stopped at the internal surface, and continually employed to melt successive layers of ice, until the temperature of the body be reduced to Zero (32), by having all its superabundant caloric above that temperature carried off by the ice. If the whole water, formed within the sphere of ice during the reduction of the temperature of the included body to Zero, be carefully collected, the weight of the water will be exactly proportional to the quant.i.ty of caloric lost by the body in pa.s.sing from its original temperature to that of melting ice; for it is evident that a double quant.i.ty of caloric would have melted twice the quant.i.ty of ice; hence the quant.i.ty of ice melted is a very exact measure of the quant.i.ty of caloric employed to produce that effect, and consequently of the quant.i.ty lost by the only substance that could possibly have supplied it.

I have made this supposition of what would take place in a hollow sphere of ice, for the purpose of more readily explaining the method used in this species of experiment, which was first conceived by Mr de la Place.

It would be difficult to procure such spheres of ices and inconvenient to make use of them when got; but, by means of the following apparatus, we have remedied that defect. I acknowledge the name of Calorimeter, which I have given it, as derived partly from Greek and partly from Latin, is in some degree open to criticism; but, in matters of science, a slight deviation from strict etymology, for the sake of giving distinctness of idea, is excusable; and I could not derive the name entirely from Greek without approaching too near to the names of known instruments employed for other purposes.

The calorimeter is represented in Pl. VI. It is shown in perspective at Fig. 1. and its interior structure is engraved in Fig. 2. and 3.; the former being a horizontal, and the latter a perpendicular section. Its capacity or cavity is divided into three parts, which, for better distinction, I shall name the interior, middle, and external cavities.

The interior cavity f f f f, Fig. 4. into which the substances submitted to experiment are put, is composed of a grating or cage of iron wire, supported by several iron bars; its opening or mouth LM, is covered by the lid HG, of the same materials. The middle cavity b b b b, Fig. 2. and 3. is intended to contain the ice which surrounds the interior cavity, and which is to be melted by the caloric of the substance employed in the experiment. The ice is supported by the grate m m at the bottom of the cavity, under which is placed the sieve n n. These two are represented separately in Fig. 5. and 6.

In proportion as the ice contained in the middle cavity is melted, by the caloric disengaged from the body placed in the interior cavity, the water runs through the grate and sieve, and falls through the conical funnel c c d, Fig. 3. and tube x y, into the receiver F, Fig. 1.

This water may be retained or let out at pleasure, by means of the stop-c.o.c.k u. The external cavity a a a a, Fig. 2. and 3. is filled with ice, to prevent any effect upon the ice in the middle cavity from the heat of the surrounding air, and the water produced from it is carried off through the pipe ST, which shuts by means of the stop-c.o.c.k r. The whole machine is covered by the lid FF, Fig. 7. made of tin painted with oil colour, to prevent rust.

When this machine is to be employed, the middle cavity b b b b, Fig.

2. and 3., the lid GH, Fig. 4. of the interior cavity, the external cavity a a a a, Fig. 2. and 3. and the general lid FF, Fig. 7. are all filled with pounded ice, well rammed, so that no void s.p.a.ces remain, and the ice of the middle cavity is allowed to drain. The machine is then opened, and the substance submitted to experiment being placed in the interior cavity, it is instantly closed. After waiting till the included body is completely cooled to the freezing point, and the whole melted ice has drained from the middle cavity, the water collected in the vessel F, Fig. 1. is accurately weighed. The weight of the water produced during the experiment is an exact measure of the caloric disengaged during the cooling of the included body, as this substance is evidently in a similar situation with the one formerly mentioned as included in a hollow sphere of ice; the whole caloric disengaged is stopped by the ice in the middle cavity, and that ice is preserved from being affected by any other heat by means of the ice contained in the general lid, Fig. 7. and in the external cavity. Experiments of this kind last from fifteen to twenty hours; they are sometimes accelerated by covering up the substance in the interior cavity with well drained ice, which hastens its cooling.

The substances to be operated upon are placed in the thin iron bucket, Fig. 8. the cover of which has an opening fitted with a cork, into which a small thermometer is fixed. When we use acids, or other fluids capable of injuring the metal of the instruments, they are contained in the matras, Fig. 10. which has a similar thermometer in a cork fitted to its mouth, and which stands in the interior cavity upon the small cylindrical support RS, Fig. 10.

It is absolutely requisite that there be no communication between the external and middle cavities of the calorimeter, otherwise the ice melted by the influence of the surrounding air, in the external cavity, would mix with the water produced from the ice of the middle cavity, which would no longer be a measure of the caloric lost by the substance submitted to experiment.

When the temperature of the atmosphere is only a few degrees above the freezing point, its heat can hardly reach the middle cavity, being arrested by the ice of the cover, Fig. 7. and of the external cavity; but, if the temperature of the air be under the degree of freezing, it might cool the ice contained in the middle cavity, by causing the ice in the external cavity to fall, in the first place, below zero (32). It is therefore essential that this experiment be carried on in a temperature somewhat above freezing: Hence, in time of frost, the calorimeter must be kept in an apartment carefully heated. It is likewise necessary that the ice employed be not under zero (32); for which purpose it must be pounded, and spread out thin for some time, in a place of a higher temperature.

The ice of the interior cavity always retains a certain quant.i.ty of water adhering to its surface, which may be supposed to belong to the result of the experiment; but as, at the beginning of each experiment, the ice is already saturated with as much water as it can contain, if any of the water produced by the caloric should remain attached to the ice, it is evident, that very nearly an equal quant.i.ty of what adhered to it before the experiment must have run down into the vessel F in its stead; for the inner surface of the ice in the middle cavity is very little changed during the experiment.

By any contrivance that could be devised, we could not prevent the access of the external air into the interior cavity when the atmosphere was 9 or 10 (52 or 54) above zero. The air confined in the cavity being in that case specifically heavier than the external air, escapes downwards through the pipe x y, Fig. 3, and is replaced by the warmer external air, which, giving out its caloric to the ice, becomes heavier, and sinks in its turn; thus a current of air is formed through the machine, which is the more rapid in proportion as the external air exceeds the internal in temperature. This current of warm air must melt a part of the ice, and injure the accuracy of the experiment: We may, in a great degree, guard against this source of error by keeping the stop-c.o.c.k u continually shut; but it is better to operate only when the temperature of the external air does not exceed 3, or at most 4, (39 to 41); for we have observed, that, in this case, the melting of the interior ice by the atmospheric air is perfectly insensible; so that we may answer for the accuracy of our experiments upon the specific heat of bodies to a fortieth part.

We have caused make two of the above described machines; one, which is intended for such experiments as do not require the interior air to be renewed, is precisely formed according to the description here given; the other, which answers for experiments upon combustion, respiration, &c. in which fresh quant.i.ties of air are indispensibly necessary, differs from the former in having two small tubes in the two lids, by which a current of atmospheric air may be blown into the interior cavity of the machine.

It is extremely easy, with this apparatus, to determine the phenomena which occur in operations where caloric is either disengaged or absorbed. If we wish, for instance, to ascertain the quant.i.ty of caloric which is disengaged from a solid body in cooling a certain number of degrees, let its temperature be raised to 80 (212); it is then placed in the interior cavity f f f f, Fig. 2. and 3. of the calorimeter, and allowed to remain till we are certain that its temperature is reduced to zero (32); the water produced by melting the ice during its cooling is collected, and carefully weighed; and this weight, divided by the volume of the body submitted to experiment, multiplied into the degrees of temperature which it had above zero at the commencement of the experiment, gives the proportion of what the English philosophers call specific heat.

Fluids are contained in proper vessels, whose specific heat has been previously ascertained, and operated upon in the machine in the same manner as directed for solids, taking care to deduct, from the quant.i.ty of water melted during the experiment, the proportion which belongs to the containing vessel.

If the quant.i.ty of caloric disengaged during the combination of different substances is to be determined, these substances are to be previously reduced to the freezing degree by keeping them a sufficient time surrounded with pounded ice; the mixture is then to be made in the inner cavity of the calorimeter, in a proper vessel likewise reduced to zero (32); and they are kept inclosed till the temperature of the combination has returned to the same degree: The quant.i.ty of water produced is a measure of the caloric disengaged during the combination.

To determine the quant.i.ty of caloric disengaged during combustion, and during animal respiration, the combustible bodies are burnt, or the animals are made to breathe in the interior cavity, and the water produced is carefully collected. Guinea pigs, which resist the effects of cold extremely well, are well adapted for this experiment. As the continual renewal of air is absolutely necessary in such experiments, we blow fresh air into the interior cavity of the calorimeter by means of a pipe destined for that purpose, and allow it to escape through another pipe of the same kind; and that the heat of this air may not produce errors in the results of the experiments, the tube which conveys it into the machine is made to pa.s.s through pounded ice, that it may be reduced to zero (32) before it arrives at the calorimeter. The air which escapes must likewise be made to pa.s.s through a tube surrounded with ice, included in the interior cavity of the machine, and the water which is produced must make a part of what is collected, because the caloric disengaged from this air is part of the product of the experiment.

It is somewhat more difficult to determine the specific caloric contained in the different ga.s.ses, on account of their small degree of density; for, if they are only placed in the calorimeter in vessels like other fluids, the quant.i.ty of ice melted is so small, that the result of the experiment becomes at best very uncertain. For this species of experiment we have contrived to make the air pa.s.s through two metallic worms, or spiral tubes; one of these, through which the air pa.s.ses, and becomes heated in its way to the calorimeter, is contained in a vessel full of boiling water, and the other, through which the air circulates within the calorimeter to disengage its caloric, is placed in the interior cavity, f f f f, of that machine. By means of a small thermometer placed at one end of the second worm, the temperature of the air, as it enters the calorimeter, is determined, and its temperature in getting out of the interior cavity is found by another thermometer placed at the other end of the worm. By this contrivance we are enabled to ascertain the quant.i.ty of ice melted by determinate quant.i.ties of air or gas, while losing a certain number of degrees of temperature, and, consequently, to determine their several degrees of specific caloric.

The same apparatus, with some particular precautions, may be employed to ascertain the quant.i.ty of caloric disengaged by the condensation of the vapours of different liquids.

The various experiments which may be made with the calorimeter do not afford absolute conclusions, but only give us the measure of relative quant.i.ties; we have therefore to fix a unit, or standard point, from whence to form a scale of the several results. The quant.i.ty of caloric necessary to melt a pound of ice has been chosen as this unit; and, as it requires a pound of water of the temperature of 60 (167) to melt a pound of ice, the quant.i.ty of caloric expressed by our unit or standard point is what raises a pound of water from zero (32) to 60 (167).

When this unit is once determined, we have only to express the quant.i.ties of caloric disengaged from different bodies by cooling a certain number of degrees, in a.n.a.logous values: The following is an easy mode of calculation for this purpose, applied to one of our earliest experiments.

We took 7 lib. 11 oz. 2 gros 36 grs. of plate-iron, cut into narrow slips, and rolled up, or expressing the quant.i.ty in decimals, 7.7070319. These, being heated in a bath of boiling water to about 78 (207.5), were quickly introduced into the interior cavity of the calorimeter: At the end of eleven hours, when the whole quant.i.ty of water melted from the ice had thoroughly drained off, we found that 1.109795 pounds of ice were melted. Hence, the caloric disengaged from the iron by cooling 78 (175.5) having melted 1.109795 pounds of ice, how much would have been melted by cooling 60 (135)? This question gives the following statement in direct proportion, 78 : 1.109795 :: 60 : x = 0.85369. Dividing this quant.i.ty by the weight of the whole iron employed, viz. 7.7070319, the quotient 0.110770 is the quant.i.ty of ice which would have been melted by one pound of iron whilst cooling through 60 (135) of temperature.

Fluid substances, such as sulphuric and nitric acids, &c. are contained in a matras, Pl. VI. Fig. 9. having a thermometer adapted to the cork, with its bulb immersed in the liquid. The matras is placed in a bath of boiling water, and when, from the thermometer, we judge the liquid is raised to a proper temperature, the matras is placed in the calorimeter.

The calculation of the products, to determine the specific caloric of these fluids, is made as above directed, taking care to deduct from the water obtained the quant.i.ty which would have been produced by the matras alone, which must be ascertained by a previous experiment. The table of the results obtained by these experiments is omitted, because not yet sufficiently complete, different circ.u.mstances having occasioned the series to be interrupted; it is not, however, lost sight of; and we are less or more employed upon the subject every winter.