Editing Charles's law (section)

==History==

The law was named after scientist [[Jacques Charles]], who formulated the original law in his unpublished work from the 1780s.

In two of a series of four essays presented between 2 and 30 October 1801,<ref>J. Dalton (1802), [https://books.google.com/books?id=3qdJAAAAYAAJ&pg=PA595 "Essay II. On the force of steam or vapour from water and various other liquids, both in vacuum and in air"  and Essay IV.  "On the expansion of elastic fluids by heat," ] ''Memoirs of the Literary and Philosophical Society of Manchester'', vol. 8, pt. 2, pp. 550–74, 595–602.</ref> [[John Dalton]] demonstrated by experiment that all the gases and vapours that he studied expanded by the same amount between two fixed points of temperature.  The [[France|French]] [[natural philosopher]] [[Joseph Louis Gay-Lussac]] confirmed the discovery in a presentation to the French National Institute on 31 Jan 1802,<ref name="GL02">{{citation | author = Gay-Lussac, J. L. | author-link = Joseph Louis Gay-Lussac | year = 1802 | title = Recherches sur la dilatation des gaz et des vapeurs |trans-title=Researches on the expansion of gases and vapors | journal = Annales de Chimie | volume = 43 | pages = 137–75 | url = https://books.google.com/books?id=Z6ctSn3TIeYC&pg=PA137}}. [http://web.lemoyne.edu/~giunta/gaygas.html English translation (extract).]<br>
On page 157, Gay-Lussac mentions the unpublished findings of Charles: "''Avant d'aller plus loin, je dois prévenir que quoique j'eusse reconnu un grand nombre de fois que les gaz oxigène, azote, hydrogène et acide carbonique, et l'air atmosphérique se dilatent également depuis 0° jusqu'a 80°, le cit. Charles avait remarqué depuis 15 ans la même propriété dans ces gaz; mais n'avant jamais publié ses résultats, c'est par le plus grand hasard que je les ai connus''." (Before going further, I should inform [you] that although I had recognized many times that the gases oxygen, nitrogen, hydrogen, and carbonic acid [i.e., carbon dioxide], and atmospheric air also expand from 0° to 80°, citizen Charles had noticed 15 years ago the same property in these gases; but having never published his results, it is by the merest chance that I knew of them.)</ref> although he credited the discovery to unpublished work from the 1780s by [[Jacques Charles]]. The basic principles had already been described by [[Guillaume Amontons]]<ref name=Amontons>See:
*  Amontons, G. (presented 1699, published 1732) [https://books.google.com/books?id=_czOAAAAMAAJ&pg=RA1-PA114 "Moyens de substituer commodément l'action du feu à la force des hommes et des chevaux pour mouvoir les machines"] (Ways to conveniently substitute the action of fire for the force of men and horses to power machines), ''Mémoires de l’Académie des sciences de Paris'' (presented 1699, published 1732), 112–26; see especially pp. 113–17.
*  Amontons, G. (presented 1702, published 1743) [https://books.google.com/books?id=P_Wgj2sMY-4C&pg=PA155 "Discours sur quelques propriétés de l'Air, & le moyen d'en connoître la température dans tous les climats de la Terre"] (Discourse on some properties of air and on the means of knowing the temperature in all climates of the Earth), ''Mémoires de l’Académie des sciences de Paris'', 155–74.
*  Review of Amontons' findings:  [https://books.google.com/books?id=P_Wgj2sMY-4C&pg=PA1 "Sur une nouvelle proprieté de l'air, et une nouvelle construction de Thermométre"] (On a new property of the air and a new construction of thermometer), ''Histoire de l'Académie Royale des Sciences'', 1–8 (submitted: 1702; published: 1743).</ref> and [[Francis Hauksbee]]<ref name=Hauksbee>*  Englishman [[Francis Hauksbee]] (1660–1713) independently also discovered Charles's law:  Francis Hauksbee (1708) [http://rstl.royalsocietypublishing.org/content/26/313-324/93.full.pdf+html "An account of an experiment touching the different densities of air, from the greatest natural heat to the greatest natural cold in this climate,"] {{Webarchive|url=https://web.archive.org/web/20151214093602/http://rstl.royalsocietypublishing.org/content/26/313-324/93.full.pdf+html# |date=2015-12-14 }} ''Philosophical Transactions of the Royal Society of London'' '''26'''(315): 93–96.</ref>  a century earlier.

Dalton was the first to demonstrate that the law applied generally to all gases, and to the [[vapour]]s of volatile liquids if the temperature was well above the boiling point. Gay-Lussac concurred.<ref>Gay-Lussac (1802), from [https://books.google.com/books?id=Z6ctSn3TIeYC&pg=PA166 p. 166]:<br>
"''Si l'on divise l'augmentation totale de volume par le nombre de degrés qui l'ont produite ou par 80, on trouvera, en faisant le volume à la température 0 égal à l'unité, que l'augmentation de volume pour chaque degré est de 1 / 223.33 ou bien de 1 / 266.66 pour chaque degré du thermomètre centrigrade.''"<br>
If one divides the total increase in volume by the number of degrees that produce it or by 80, one will find, by making the volume at the temperature 0 equal to unity (1), that the increase in volume for each degree is 1 / 223.33 or 1 / 266.66 for each degree of the centigrade thermometer.<br> 
From [https://books.google.com/books?id=Z6ctSn3TIeYC&pg=PA174 p. 174]:<br>
"'' … elle nous porte, par conséquent, à conclure que tous les gaz et toutes les vapeurs se dilatent également par les mêmes degrés de chaleur.''"<br>
 … it leads us, consequently, to conclude that all gases and all vapors expand equally [when subjected to] the same degrees of heat.</ref> With measurements only at the two thermometric fixed points of water (0°C and 100°C), Gay-Lussac was unable to show that the equation relating volume to temperature was a linear function.   On mathematical grounds alone,  Gay-Lussac's paper  does not permit the assignment of any law stating the linear relation.   Both Dalton's and Gay-Lussac's main conclusions can be expressed mathematically as:
:<math>V_{100} - V_0 = kV_0\,</math>
where {{mvar|V}}<sub>100</sub> is the volume occupied by a given sample of gas at 100&nbsp;°C; {{mvar|V}}<sub>0</sub> is the volume occupied by the same sample of gas at 0&nbsp;°C; and {{mvar|k}} is a constant which is the same for all gases at constant pressure. This equation does not contain the temperature and so is not what became known as Charles's Law. Gay-Lussac's value for {{mvar|k}} ({{frac|2.6666}}), was identical to Dalton's earlier value for vapours and remarkably close to the present-day value of {{frac|2.7315}}. Gay-Lussac gave credit for this equation to unpublished statements by his fellow Republican citizen J. Charles in 1787.  In the absence of a firm record, the gas law relating volume to temperature cannot be attributed to Charles.
Dalton's measurements had much more scope regarding temperature than Gay-Lussac, not only measuring the volume at the fixed points of water but also at two intermediate points.  Unaware of the inaccuracies of mercury thermometers at the time, which were divided into equal portions between the fixed points, Dalton, after concluding in Essay II that in the case of vapours, “any elastic fluid expands nearly in a uniform manner into 1370 or 1380 parts by 180 degrees (Fahrenheit) of heat”, was unable to confirm it for gases.