Louis-Joseph Gay-Lussac (1778-1850)

excerpts from

The Expansion of Gases by Heat[1]

Annales de Chimie 43, 137 (1802) [reprinted in William Francis Magie, ed., A Source Book in Physics (New York: McGraw-Hill, 1935)].

First Section
Object of this Memoir

For many years physicists have studied the expansion of gases; but the results which they obtained showed such great differences that instead of reaching a definite result they render further examination desirable.

The expansion of vapors has been given less consideration, although we have known for many years the prodigious effects of water vapor; and although we have made most fortunate applications of these effects, Zeigler and Bettancourt are the only ones, so far as I know, who have tried to measure them. Their experiments cannot give the true expansion of this vapor; for since they always had water in their apparatus, for each new degree of heat they had the expansion of the vapor formed by the preceding degrees of heat, and an increase of volume by the formation of new vapor; two causes which manifestly conspire to raise the mercury in their manometer.

The thermometer, such as we have it to-day, cannot be used to indicate exact ratios of heat, because we still do not know what ratio there is between the degrees of the thermometer and the quantities of heat which they can indicate. It is generally believed, it is true, that equal divisions of its scale represent equal tensions of caloric; but this opinion is not based on any definite fact.

It must then be admitted that we are still very far from having certain knowledge of the expansion of gases and vapors, and of the progress of a thermometer; and nevertheless we need every day, in physics and in chemistry, to bring a given volume of a gas from one temperature to another, to measure the heat disengaged or absorbed when a body changes its state, or that disengaged or absorbed by the same body in passing from one temperature to another; in the arts, to calculate the effect of a machine moved by heat or to have a proper knowledge of the expansion of certain bodies; in meteorology, to determine the quantity of water held in solution in the air, a quantity which varies with its temperature and density, according to a law which is not yet known. Finally in constructing tables of refraction for astronomy and in the use of the barometer for measuring heights, it is indispensable to know exactly both the temperature of the air and the law of its expansion.

Although these considerations were sufficient to make it desirable that someone should take up an investigation of such general utility, yet the difficulty of the researches which it involved would have prevented me giving myself to it, if I had not been strongly urged to undertake it by Citizen Berthollet, of whom I have the honor to be a pupil. I owe to him the apparatus needed to carry out this work, in which I have often been guided by his advice and that of Citizen Laplace: such great authorities will increase the confidence with which it may be received.

The researches which I have undertaken on the law of expansion of gases and vapors, and on the progress of the thermometer, are not yet complete. In this memoir my object is only to examine the expansion of gases and vapors for a fixed rise of temperature, and to show that it is the same for all these fluids; but before giving an account of my experiments I think it will be well to give a historical sketch of what has been done in this field; and as I shall introduce at the same time some observations on the different methods which have been employed, I will before entering on the history mention one of the principal causes of uncertainty which can arise in this sort of experiment. Although it is very important and although it seems to have been unrecognized by most of the physicists who have studied the expansion of gases, it will be sufficient for me to mention it to make clear what its influence will be. What I shall say of atmospheric air applies to the other gases also.

This cause of uncertainty is the presence of water in the apparatus. Suppose, in fact, that some drops of water are left in a globe full of air, of which the temperature is raised to that of boiling water; this water will turn into vapor and will occupy a volume about 1800 times greater than its original volume, and thus will then necessarily happen that when these vapors are condensed so that they occupy a volume 1800 times smaller, there will be attributed to the air which remains in the globe much too great an expansion; because it will be assumed that it is this air which, at the temperature of boiling water, occupied the whole volume of the globe. If the temperature is not carried to this degree the same cause of uncertainty will nevertheless exist, and its importance will depend upon the temperature at which the experiment is tried: for in this case the water will not be entirely vaporized, but the air will dissolve more and more of it as its temperature rises, and will receive in consequence a greater and greater increase in volume besides that which it gets from the heat; so that when we go again into the lower temperature, the volume of air which fills the globe will diminish for two reasons, 1. because of the loss of caloric, 2. because of the loss of the water which it holds in solution. We shall then still attribute to the air too great an expansion.

In general whenever we enclose with the gas liquids or even solids, for example muriate of ammonia, which can dissolve or vaporize at the temperature to which they are exposed, there necessarily result errors in the determination of the expansion of these gases.


Before going further, I must jump ahead. Although I had recognized on many occasions that the gases oxygen, nitrogen, hydrogen, carbonic acid, and atmospheric air all expand identically from 0° to 80°, citizen Charles had noticed the same property in these gases 15 years ago; however, since he never published his results, it is only by great luck that I knew it. He had also sought to determine the expansion of water-soluble gas, and he had found for each a particular dilation different from that of other gases. In this respect, my experiments differ strongly from his.[3]


The experiments which I have now reported and which have all been made with great care prove incontestably that atmospheric air and the gases oxygen, hydrogen, nitrogen, nitrous oxide, ammonia, muriatic acid, sulphurous acid and carbonic acid all have the same expansion between the same degrees of heat; and thus consequently their greater or less density at the same pressure and temperature, their greater or less solubility in water, and their particular character have no influence on their expansion. On this basis I conclude that all gases in general expand equally between the same degrees of heat provided that they are all brought under the same conditions.

These investigations of the expansion of gases led me naturally to examine the expansion of vapors; but since I expected from the preceding results that they would expand like gases I decided to make my experiments only with one vapor, and I chose by preference the vapor of sulphuric ether as being the easiest to manage.

To determine the expansion of the vapor of ether I used the two tubes of which I have already spoken, taking atmospheric air for comparison. This apparatus was kept for some time in a vessel at the temperature of about 60°. I then introduced ether vapor into one of the tubes and atmospheric air into the other, in such a way that each of them corresponded to the same division. I then raised the temperature of the vessel from 60° to 100°, and I had the satisfaction of seeing that, whether rising or falling, the ether vapor and the atmospheric air always corresponded at the same time to the same divisions. This experiment, which was shown to Citizen Berthollet, was repeated several times, and I never was able to observe any difference in the expansion of the ether compared with that of atmospheric air. I may however remark that when the temperature of the ether is only a little above its boiling point, its condensation is a little more rapid than that of atmospheric air. This fact is related to a phenomenon which is exhibited by a great many bodies when passing from the liquid to the solid state, but which is no longer sensible at temperatures a few degrees above that at which the transition occurs.

This experiment, by showing that ether vapor and the gases expand equally, shows that this property depends in no way on the particular nature of gases and vapors, but only on their elastic state, and leads us in consequence to the conclusion that all gases and all vapors expand equally between the same degrees of heat.

Since all gases are equally expansible by heat and equally compressible, and since these two properties depend on each other, as I shall show in another place, the vapors which are equally expansible with the gases should also be equally compressible; but I may mention that this last conclusion cannot be true except so long as the compressed vapors remain entirely in the elastic state; and this requires that their temperature shall be sufficiently elevated to enable them to resist the pressure which tends to make them assume the liquid state.

I have reported from Saussure and my experiments confirm him, that very dry air and air carrying more or less water in solution are equally expansible; I am therefore authorized to draw from all that I have said the following conclusions.

1. All gases, whatever may be their density and the quantity of water which they hold in solution, and all vapors expand equally between the same degrees of heat.

2. For the permanent gases the increase of volume received by each of them between the temperature of melting ice and that of boiling water is equal to 80/213.33 of the original volume for the thermometer divided into 80 parts, or to 100/266.66[4] of the same volume for the centigrade thermometer.

To complete this work I must determine the law of the expansion of gases and vapors, so as to establish the true progress of a thermometer. I shall occupy myself with these new investigations; and when they are finished I shall have the honor of presenting them to the Institute.

[1]A literal translation of the whole title includes a reminder that this work was done during the first French republic: "On the expansion of gases and vapors, read at the National Institute on 11 pluviôse, year 10, by citizen Gay-Lussac" (Pluviôse was one of the nature-descriptive names of months used in the republican calendar. It is the "rainy" month corresponding to late January and early February.) --CJG

[2]Magee omits sections Two (a review of earlier work on the subject) and Three (a description of the experiments and apparatus) and the beginning of section Four (experimental results). --CJG

[3]I include these sentences from section 2 because they are relevant to the fact that Gay-Lussac's results are known to many as "Charles' Law". Charles is Jacques Charles (1746-1823), a French natural philosopher and balloonist. --CJG

[4]The figures given in Magie, 80/21333 and 100/26666 respectively, are clearly erroneous. --CJG

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