ON PHYSICS, OR NATURAL PHILOSOPHY. No. XXXV. (Continued from page 110.) EXPANSION AND DENSITY OF THE GASES. Laws of Expansion.-M. Gay-Lussac first proposed the two following laws on the expansion of gas, which have been, till very recently, considered as correct, and universally received. 1st, That all gases have the same co-efficient of expansion, that is, the same increase in volume in passing from 0° to 1° Centigrade, and that its numerical value is 0.00375 or 266 say gr 1 2nd. That this co-efficient is independent of the pressure, that is, of the original density of the gas. These laws are founded on the supposition that all gases expand equally under an equal increase of temperature, and that the expansion is in direct proportion to the temperature. The method adopted by Gay-Lussac in the determination of these laws was the following: the expansion of air and other gases was measured by an air-thermometer formed of a spherical bulb A, and a capillary stem A B, fig. 183. The part of the stem between B and c was divided into parts of equal capacity; and the number of these parts which the bulb A contained, was ascertained by weighing the apparatus when full of mercury at 00 Centigrade, and then heating it gently in order to force out of it a little of the mercury. By weighing it again, the weight of the mercury forced out was determined. By cooling the remainder down to 0° Centigrade, a vacuum was produced which showed the volume of the corresponding weight of the mercury which was forced out. From this, the volume of the mer diminished in volume, and the index at в was forced towards the bulb at A. The point where it became stationary was marked, and this determined the volume of the air at 0° Centigrade, since the capacity of the bulb was known. The ice was then removed and replaced by water or oil, and the box was heated over a furnace. The air in the bulb expanded, and the index advanced from A towards B. The point where it became stationary was then marked, and at the same time the temperature indicated by the two thermometers D and E was noted, so that the volume of air and its temperature were both ascertained. Now if in the first instance we suppose that the atmospheric pressure did not vary during the experiment, and neglect the expansion of the glass, which is very small, the total expansion of the air in the apparatus will be found by subtracting the volume which it had at 0° Centigrade from the volume which it had at the end of the experiment. Then, by dividing the the expansion corresponding to 1° Centigrade will be deterremainder by the number of degrees in the final temperature, units contained in the volume at 0° Centigrade, we obtain the mined; and again dividing this quotient by the number of expansion corresponding to one degree and one unit of volume, that is, the co-efficient of expansion. In the following problems, the corrections for the variations in the pressure of the atmosphere and the expansion of the glass are taken into account. Problems on the Expansion of the Gases.-1st. Given v the volume of a gas at 0° Centigrade, and the co-efficient of expansion a, what will be its volume v' at the temperature to Centigrade, the pressure remaining constant. Here, the same reasoning being employed as in the case of linear expansion given in a former lesson, we shall, at once, have v'v+avt; whence vv (1+at) (1.) 2nd. Given v' the volume of a gas at the temperature to, and the co-efficient of expansion a, what will be its volume v at 0° Centigrade, the pressure remaining constant? Here, from cury remaining in the apparatus was deduced, and consequently the volume of the bulb, by proportion, as already shown in the case of the piesometer, p. 105, vol. iv. The bulb and the stem were now filled with dry air, in the following manner: they were first filled with mercury, which was boiled in the bulb in order to dry it; a tube c, filled with drying substances, such as chloride of calcium, was then fixed to the extremity of the stem by means of a cork. Into the stem AB, through the tube, was next introduced a fine platinum wire, by means of which the interior of the tube was agitated; and it was at the same time held in an inclined position, so as to permit the mercury to flow out drop by drop, by slightly shaking the apparatus. The air then entered the bulb A, bubble by bubble, after having been dried by passing through the chloride of calcium. Lastly, there was preserved in the stem A B a small portion of mercury to serve as an index, as shown at B. The air-thermometer was then placed in a rectangular box made of tin. This box was at first filled with ice, the air was VOL. V. pressure H. Now by the law of Mariotte, we have vh dried; for the humidity which adhered to its sides is dissipated VH 1+at whence, v= VH (4.) (1+at) 5th. Given the volume v' of a glass bulb at to Centigrade to find its volume v at 0° Centigrade. In solving this problem, we suppose that the bulb will expand for a given variation of temperature, by the same quantity that it would expand were it a mass of glass of the same volume and at the same temperature. If we then represent the co-efficient of the cubic expansion of glass by d, we have according to formula (1.) v'v+ V dvt v(1+dt); whence v -I+ di 6th. Given the weight r' of a certain volume of gas at t Centigrade, what will be its weight P at 0° Centigrade, the co-efficient of expansion being a? Here, let d' be the density of the gas at to, and d its density at 0° Centigrade. The P' ď weights being proportional to the densities, we have = P d. Now representing by 1 a certain volume of a given gas at 0° Centigrade, its volume at t° will be 1+at; but the densities are inversely proportional to the volumes, therefore we have ; whence, and from the former expression, we = 1 d 1+a In the determination of the co-efficient of the expansion of gases, M. Regnault employed in succession, four different processes. In one set the pressure was constant, and the volume of the gas variable, as in the process of Gay-Lussac; in the other set, the volume remained the same, but the pressure was varied at pleasure. The following is the first process employed by M. Regnault, and in it the pressure remained constant; the same process was employed by M. Dulong and by M. Rudberg. The experiments of M. Regnault are characterised by the greatest care to avoid the possibility of error in the results. His apparatus was composed of a cylindric bulb or reservoir B, fig. 184, of a pretty large capacity, to which is cemented a bent capil in steam, and the air which filled it each time that a vacuum was made, was dried in its passage through the U-shaped tubes. When this is done, a space of time, say about half-anhour, is allowed for the air to assume the temperature of the steam; the dessiccating tubes are then removed, and the extremity of the capillary tube is hermetically sealed, the height of the barometer at the same instant being noted. The reservoir B is then cooled, and placed in the apparatus shown at fig. 185. lary tube. In order to fill this bulb with perfectly dry air, it was arranged, as shown in the figure, in a tin vessel similar to that employed in determining the boiling point of the thermometer; then by means of sheets of caoutchouc, the capillary tube is connected in a series of U-shaped india rubber tubes, filled with dessiccating substances. These tubes terminate in a small air-pump, by means of which a vacuum is made in the tubes and in the reservoir. whilst the latter is surrounded with steam. The air is then allowed to enter slowly, and a new vacuum is made; and this process is repeated a great number of times; so that at last the air in the reservoir is completely pincers, and the interior air being condensed, the mercury in the cup enters the capillary tube in consequence of the pressure of the atmosphere, and rises to a height ca, the pressure of which, added to the elastic force of the air remaining in the apparatus, makes an equilibrium with the atmospheric pressure. In order to measure the height of the column c G, which may be represented by h, a moveable rod go is lowered until the point o is level with the surface of mercury in the cup; and the difference of the height between the point g and the level of the mercury at G is then measured with the cathetometer. Adding to this difference the length of the part go, which is known, we have the height h of the column G c. The point b is then closed with a little wax, and the barometric pressure is noted. Now, if this pressure be denoted by H', the pressure in the reservoir B, is denoted by '-h. The reservoir is now withdrawn from the ice and weighed, in order to ascertain the weight of the mercury which has been introduced into it. This reservoir is then completely filled with mercury at 0° Centigrade, and the weight P' of the mercury contained both in the reservoir and the tube is ascertained. Now, if k denoted the co-efficient of the expansion of glass, a that of air, and D the density of mercury at 0° Centigrade, we find a by the following process. The volume of the reservoir and of the P' tube at 0° Centigrade is from the formula PVD formerly D P' -P D stationary. Hence the indications of the air-thermometer are influenced by the pressure of the atmosphere, and thus require to be corrected at every observation. When variations of temperature of considerable extent are to be measured, the air-thermometer is furnished with a tube similar to that employed in measuring the co-efficient of the expansion of gases in the apparatus of M. Regnault (figs. 184 and 185). Making experiments with this tube, as explained in the description of that apparatus, the quantities P, P', H, H', and h, which enter into equation (3.) are determined; and as a is known, this equation, by reduction, will give the temperature t, to which the tube has been raised. According to the researches of M. Regnault, the air-thermometer sensibly agrees with the mercurial thermometer as far as 260° Centigrade, or 500° Fahrenheit; but beyond this point the mercury expands more rapidly than the air. Density of Gases.-The specific weight or density of a gas is the ratio of the weight of a certain volume of the gas to that of the same volume of air, the gas and the air being both at the same temperature and pressure; and in the use of the Centigrade thermometer, this temperature and pressure are 0° Centigrade and 29.922 inches, which we shall call the standard temperature and pressure. According to this definition, the density of a gas is found by determining the weight of a certain volume of the gas at the standard temperature and pressure; next, the weight of the same volume of air at the standard temperature and pressure; and then by dividing the former weight by the latter. In determining the density of gases, a glass vessel or at the temperature 0° Centigrade and at the pressure uh. At the same pressure, but at to, this volume is there-globe, whose capacity is about that of two imperial gallons, is (P′ − r) (1 + a t) (H′ — H); (2.) h D But the volumes represented by the formulæ (1.) and (2.) are the volume of the reservoir and the tube at the pressure h; they are therefore equal. Whence, by suppressing the common denominator, we have the equation P' (1 + kt) H= : (r′ —P) (1 + a t) (н — h); (3.) from which may be deduced the value of a. By experiments and calculations of this kind, M. Regnault found that from 0° to 100° Centigrade, and for barometric pressures between 11.8 inches and 59·1 inches, the co-efficients of expansion for certain gases were as follows: employed, having a stop-cock at the neck or aperture, which TABLE OF THE CO-EFFICIENTS OF EXPANSION FOR corrections are effected by means of the formulæ which we have given in this lesson for the solution of problems of this description, but most of these may be avoided by the following method: M. Regnault has applied to the preceding process some modifications, which dispense with part of the corrections. For this purpose, the globe, which is employed to weigh the given gas, is hung on the one scale of a balance, and it is brought into equilibrium with another globe of the same volume herThese two metically sealed and hung on the other scale. globes expanding equally under the same degree of temperature, always displace the same quantity of air, whence the variations in the temperature and pressure of the atmosphere have no influence on their weights. Now, when the first globe is successively filled with the air and with the gas whose density is required, it is placed in a zinc vessel, and surrounded with ice. By this means it is brought to the standard temperature; and by shutting the stop-cock when the gas introduced into it is at the same temperature, the corrections for temperature are avoided. Lastly, the two gases can be easily brought to the standard pressure by referring the pressure under which the experiment is made to the law that the weights are proportional to the pressures. These numbers show that the co-efficients of the expansion of gases differ only by quantities which are extremely small. M. Regnault has proved, also, that at the same temperature the expansion of any gas is greater in proportion to the increase of pressure; and that the co-efficients of the expansion of two gases differ more when they are subjected to greater pressures. The Air Thermometer.-This thermometer, as its name indicates, is founded on the principle of the expansion of air. When it is intended to measure small variations of temperature, the same form is given to it as that employed by Gay-Lussac in order to measure the co-efficient of the expansion of the gases (fig. 183); that is, it is composed of a glass bulb, to which is cemented a long capillary tube or stem. The bulb is filled In the case of gases which act upon brass, as chlorine for with air perfectly dry; and there is introduced into the stem, a example, a brass stop-cock cannot be employed. It is then small quantity of sulphuric acid, coloured red, to serve as an necessary to employ a glass bottle with a ground stopper, and index; the instrument is then graduated by comparing its in- to introduce the gas by a bent tube which reaches to the botdications with those of a mercurial thermometer. The ex- tom; the bottle being held upright or inverted, according as tremity of the stem of this thermometer must be allowed to the gas introduced into it is heavier or lighter than the air. remain open; otherwise, the contraction or expansion of When all the air is expelled from the bottle, the tube is rethe air above the index would take place at the same time as moved, and it is closed by the stopper. If the bottle be then that of the air in the bulb, and the index would remain | weighed full of gas, the weight obtained will include the weight of the bottle, plus the weight of the gas, minus the weight of the air displaced, according to principles formerly explained. Now, the weight of the bottle is easily determined; and if it be gauged by finding the volume of water which it contains, its volume will thus be found, and consequently the weight of the air which it displaces. If, then, we subtract the weight of the bottle itself from the weight obtained by weighing it when full of gas, and add to the remainder the weight of the air displaced, we have the required weight of the gas. It now only remains to divide the weight of the gas by the weight of the same volume of air, care being taken to make the necessary corrections for temperature and pressure in order to refer them to the same capacity, and the standard temperature and pressure. The following table shows the density of some gases which have been thus determined at the standard temperature and pressure above mentioned : TABLE OF THE DENSITY of gases, CHANGE OF STATE IN BODIES. The Laws of Fusion. Of the various phenomena which are presented by bodies under the influence of caloric, we have only hitherto considered those of expansion. Now, if we first turn our attention to solid bodies, it is evident that this expansion has a limit. For, in proportion as a solid body absorbs a greater quantity of caloric, the repulsive force of its particles is increased; and a period may arrive when the molecular attraction is insufficient to preserve the body in the solid state. A new phenomenon then takes place; viz. that of fusion (melting), or the passage of a body from the solid to the liquid state. Yet a great number of substances, as paper, wood, wool, and certain salts, do not melt under the action of an elevated temperature, but are decomposed. Of all the simple bodies, one only has not hitherto been fused by the action of the most intense sources of heat, and this is carbon. Latent Caloric.-When the temperature remains constant during the period of fusion, while a body passes from the solid to the liquid state, whatever may be the intensity of the fire, it is evident that in order to change its state, the body absorbs a considerable quantity of heat, of which the sole effect is to keep it in the liquid state. This quantity of heat, which does not act on the thermometer, and which is combined in some way with the particles of the body, is denominated latent caloric, or the caloric of fusion. The following experiment will give a clear idea of what is to be understood by latent caloric: if we mix a pound of water at 09 Centigrade with a pound of water at 79° Centigrade, we shall have immediately two pounds of water at 39.5 Centigrade, that is, at the mean temperature of the two quantities mixed; this result was to be expected, because they are of the same nature, and of an equal quantity. But if we mix a pound of water at 79° Centigrade with an equal weight of pounded ice at 0° Centigrade, the ice will instantly melt, and we shall have two pounds of water at 0o Centigrade. Thus we see that, without changing its temperature, and solely to effect its fusion, one pound of ice absorbs the quantity of heat necessary to raise one pound of water from the freezing point to 79° Čentigrade, or 164°.4 Fahrenheit. This quantity of heat, therefore, represents the caloric of fusion, or the latent caloric of ice. Each body has its own particular quantity of latent caloric, which may be determined by calculation. Solution.-A body is said to be dissolved, or put into a state of solution, when it is liquified by the effect of the mutual attraction of its particles and those of a liquid. Thus, gum arabic, sugar, and the greater number of salts, are soluble in water. During solution, as well as during fusion, a greater or less quantity of heat is absorbed. This is the reason why the solution of a salt, in general, occasions a lowering of temperature. Yet it happens that in certain solutions the temperature does not vary, and in others that it even rises. This will be understood by observing how these two simultaneous and contrary effects are produced. The first is the passage from the solid to the liquid state, an effect which produces a lowering of temperature; the second is the combination of the dissolved body and the liquid. Now, every chemical combination takes place with the development of heat; consequently, according as one of these effects predominates over the other, or as one is equal to the other, so is cold or heat the result, or the temperature remains constant. The following are the two general laws of fusion to which bodies are subjected, as discovered by experiment. 1. Every body enters into a state of fusion at a certain temperature, which is invariable for each individual substance. 2. What-is exactly that of fusion. 2. From the moment when solidifiever may be the intensity of the source of heat at the moment when fusion commences, the temperature ceases to rise, and remains constant until the fusion be completed. The following table exhibits the temperatures at which fusion commences in different substances : Solidification.-Solidification, or congelation, is the passage from the liquid state to the solid. This phenomenon takes place according to the following laws, which are the converse of those of fusion, and are proved by experiment: 1. Solidification is produced in every body at a fixed temperature, which cation commences until it be completed, the temperature of the liquid remains constant. This second law is the consequence of the fact that the latent caloric absorbed during fusion is set free at the moment of solidification. Many liquids, as alcohol and ether, are not solidifiable by the greatest lowering of temperature to which they have been exposed. In general, bodies which pass slowly from the liquid to the solid state assume determinate geometrical forms called crystals; such as those of the tetrahedron, the cube, the prism, and the rhombohedron. If the body which solidifies be in a state of fusion, its crystallisation is said to take place by the dry method; but if the body be held in solution in a liquid, its crystallisation is said to take place by the humid method. It is by allowing the liquids which hold salts in solution to evaporate slowly, that salts are made to crystallise. Snow, ice newly formed, and salts, exhibit fine examples of crystallisation. We shall take the first opportunity to bring under the notice of our students the subject of crystallisation. The Formation of Ice.-Distilled water becomes solid at the temperature of 0 Centigrade, and is then called ice; but the congelation takes place but slowly, because that the frozen part gives out its latent caloric to the rest of the liquid mass. Ice presents this remarkable phenomenon, that it possesses less density than water. We have already shown that, by cooling or lowering the temperature, water only contracts in volume as far as 40 Centigrade, but that beyond this point it expands. Now, this increase of volume remains and increases still more at the moment of congelation; and we find that the volume of ice is 1.075 times that of water at 4° Centigrade. Hence, the density of ice is only about 0.930, that of water being 1; consequently, ice always floats on the surface of water. The increase of volume which ice assumes in its formation is accompanied with a considerable expansive force, which frequently bursts the vessels which contain it. The rending of stones after a frost is due to the effect of the water which has penetrated their pores and become frozen. It is the same increase of volume which renders the action of frost so injurious to plants, because their sap, when frozen, breaks their tissues. M. Williams, in England, in order to demonstrate the expansive force of ice, placed in an atmosphere several degrees below zero, a bomb-shell filled with water, after he had firmly closed the orifice with a wooden stopper. At the instant of congelation, this stopper was forcibly thrown to a great distance, and an icy border was formed round the edges of the orifice. Retardation of the Freezing of Water.-The temperature of the congelation of water is retarded by salts or other substances which it holds in solution. Sea-water, for instance, does not solidify till it be lowered to the temperature of -2° 5 Centigrade, or 27°.5 Fahrenheit. The point of the solidification of pure water may be retarded several degrees, if it be deprived of the air which it generally contains, and if it be kept entirely free from all agitation. Thus, in a vessel surrounded with a frigorific mixture, and placed under an exhausted receiver, the water may be made to fall to -12° Centigrade, or 10°4 Fahrenheit, and even lower than this before congelation. But if then a slight motion be given to the mass, a part of the liquid will be instantly frozen; and this remarkable phenomenon will be observed, that the remaining part of the liquid will suddenly rise to 0 Centigrade, or 32° Fahrenheit. This rise in the temperature is owing to the latent caloric, which is freed by the formation of the ice. LESSONS IN GREEK.-No. XXXI. CONTRACTED Pure Verbs are those which have for their characteristic either a, e, or o, and blend those vowels with the immediately following mood-vowel. The mixing of the vowels takes place in only the Present and Imperfect of the active and middle (or passive), since only in those two is the characteristic vowel followed by the modal vowel. The v EpλKUOTIKOV in the third person singular, Imperfect, active, is not employed with the contraction. The blending of two vowels produces various vowels or diphthongs, as appears in the following table, where +, the sign of plus in Mathematics, denotes that the two vowels between which it is placed, melt together to produce another or a diphthong, and, the sign of equality, is prefixed to the result, showing that the latter is equivalent to the former. εἄω, εάσω, μειδιάω, φωρά-ω, aorist ειᾶσα I smile, fut. μειδιά-σομαι 1 catch, φωρά-σω αλοᾶ-σω ακροάσομαι Observe that lovw, I wash, forms from the simpler verb dow, the Middle Present λοῦται, λούμενος, λοῦ, λοῦσθαι ; the the other parts are Imperfect Xovμny, eλov, εlovтo, etc.: regularly formed from Xovw. Contracted Verbs are conjugated. In committing the ensuing I must now lay before you an example of the way in which forms to memory, you should repeat first the uncontracted form, and then the contracted form. The uncontracted form, to take an instance from the table, is raw, the contracted Tu: the uncontracted form is appended to the common stem in parentheses thus, ru(a-w); the contracted form stands immediately after the second parenthesis. This, then, is the way in which I advise you to repeat every part, in order to commit the whole to memory; namely, Τιμαω, τιμῶ; τιμαεις, τιμᾷς; τιμαει, τιμᾷ, τιμαετον, τιμᾶτον ; τιμαετόν, τιμᾶτον ; τιμαομεν, τιμῶμεν ; τιμαετε, τιμᾶτε; τιμαουσι, τιμῶσι, Τιμαομαι, τιμῶμαι; τιμαέσθω, τιμασθω; μισθοεσθων, μισθου σθων; φιλεομενος, φιλούμενος; εφιλεόμεθον, εφιλουμεθον ; ετιμαεσθε, ετιμᾶσθε; εφιλέοντο, εφιλοῦντο, etc.. |