View source for Gay-Lussac's law

{{short description| Relationship between pressure and temperature of a gas at constant volume. }}
{{Continuum mechanics|fluid}}
'''Gay-Lussac's law''' states that the pressure of a given mass of gas varies directly with the absolute temperature of the gas, when the volume is kept constant.<ref>{{cite web |title=Gay-Lussac's Law |url=https://chem.libretexts.org/Textbook_Maps/Introductory_Chemistry/Book%3A_Introductory_Chemistry_(CK-12)/14%3A_The_Behavior_of_Gases/14.05%3A_Gay-Lussac%27s_Law |website=LibreTexts |accessdate=5 December 2018|date=2016-06-27 }}</ref>

Mathematically, it can be written as: <math>\frac{P}{T} = k</math>.

Gay-Lussac is most often recognized for the Pressure Law which established that the pressure of an enclosed gas is directly proportional to its temperature and which he was the first to formulate (c. 1808).<ref name=ColumbiaLussac>{{citation|chapter=Joseph Louis Gay-Lussac|title=Columbia Electronic Encyclopedia|edition=6th Edition, Q2|year=2016|isbn=978-0787650155|last=Lagassé|first=Paul|publisher=Columbia University|page=|url=https://archive.org/details/columbiaencyclop00laga}}{{page?|date=July 2019}}</ref> He is also sometimes credited<ref name=Palmer>{{citation|last=Palmer|first=WP|year=1991|title=Philately, Science Teaching and the History of Science|journal=Lab Talk|volume=35|issue=1|pages=30–31|url=http://files.eric.ed.gov/fulltext/ED511749.pdf}}</ref><ref name=Holbrow/><ref name=Spurgin>{{citation|first=CB|last=Spurgin|title=Gay-Lussac's gas-expansivity experiments and the traditional mis-teaching of 'Charles's Law'|journal=Annals of Science|volume=44|issue=5|pages=489–505|year=1987|doi=10.1080/00033798700200321|url=}}</ref> with being the first to publish convincing evidence that shows the relationship between the pressure and temperature of a fixed mass of gas kept at a constant volume.<ref name="Holbrow">{{citation|title=What Gay-Lussac didn't tell us|last1=Holbrow|first1=CH|last2=Amato|first2=JC|journal=Am. J. Phys. |volume=79|issue=1|pages=17|year=2011 |doi=10.1119/1.3485034|bibcode=2011AmJPh..79...17H}}</ref>

These laws are also known variously as the Pressure Law or [[Guillaume Amontons|Amontons's law]] and [[Dalton's law]] respectively.<ref name=Palmer/><ref name=Holbrow/><ref name="Spurgin"/><ref name=Crosland>{{citation|title=The Origins of Gay-Lussac's Law of Combining Volumes of Gases|vauthors=Crosland MP|year=1961|journal=Annals of Science|volume=17|issue=1|page=1|doi=10.1080/00033796100202521}}</ref>

== Law of combining volumes ==
[[Image:Law of combining volumes.svg|thumb|150px|right|Under [[Standard conditions for temperature and pressure|STP]], a reaction between three cubic meters of hydrogen gas and one cubic meter of nitrogen gas will produce about two cubic meters of [[ammonia]].]]
The law of combining volumes states that, when gases react together to form other gases, and when all volumes are measured at the same temperature and pressure

'''The ratio between the volumes of the reactant gases and the gaseous products can be expressed in simple [[Natural number|whole number]]s.'''

For example, Gay-Lussac found that 2 volumes of hydrogen and 1 volume of oxygen would react to form 2 volumes of gaseous water. Based on Gay-Lussac's results, [[Amedeo Avogadro]] hypothesized that, at the same temperature and pressure, equal volumes of gas contain equal numbers of molecules ([[Avogadro's law]]). This hypothesis meant that the previously stated result
:2 volumes of hydrogen + 1 volume of oxygen = 2 volume of gaseous water
could also be expressed as
:2 molecules of hydrogen + 1 molecule of oxygen = 2 molecule of water.

The law of combining gases was made public by [[Joseph Louis Gay-Lussac]] in 1808.<ref>Gay-Lussac (1809) [https://books.google.com/books?id=hnJKAAAAYAAJ&pg=PA207#v=onepage&q&f=false "Mémoire sur la combinaison des substances gazeuses, les unes avec les autres"] (Memoir on the combination of gaseous substances with each other), ''Mémoires de la Société d'Arcueil'' '''2''': 207–234.  Available in English at:  [http://web.lemoyne.edu/~giunta/gaylussac.html Le Moyne College].</ref><ref>{{cite web|url=http://www.chemistryexplained.com/Fe-Ge/Gay-Lussac-Joseph-Louis.html|title=Joseph-Louis Gay-Lussac|work=chemistryexplained.com}}</ref> Avogadro's hypothesis, however, was not initially accepted by chemists until the Italian chemist [[Stanislao Cannizzaro]] was able to convince the First International Chemical Congress in 1860.<ref>{{cite journal | author = Hartley Harold | year = 1966 | title = Stanislao Cannizzaro, F.R.S. (1826–1910) and the First International Chemical Conference at Karlsruhe | url = | journal = Notes and Records of the Royal Society of London | volume = 21 | issue = 1| pages = 56–63 | doi = 10.1098/rsnr.1966.0006 }}</ref>

== Pressure-temperature law ==
This law is often referred to as '''Gay-Lussac's law of pressure–temperature,''' between 1800 and 1802, discovered the relationship between the pressure and temperature of a fixed mass of gas kept at a constant volume.<ref>{{citation | author = Barnett, Martin K. | date = Aug 1941 | title = A brief history of thermometry | journal = Journal of Chemical Education | volume = 18 | issue = 8 | page = 358|bibcode = 1941JChEd..18..358B |doi = 10.1021/ed018p358 }}. [http://pubs.acs.org/doi/abs/10.1021/ed018p358 Extract.]</ref><ref>{{cite web |url=http://web.fccj.org/~ethall/gaslaw/gaslaw.htm |title=Thall's History of Gas Laws |accessdate=2010-07-16 |url-status=dead |archiveurl=https://web.archive.org/web/20100908095718/http://web.fccj.org/~ethall/gaslaw/gaslaw.htm |archivedate=2010-09-08 }}</ref><ref>See:
*  Amontons, G. (presented 1699, published 1732) [https://books.google.com/books?id=_czOAAAAMAAJ&pg=RA1-PA114#v=onepage&q&f=false "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 in order to power machines), ''Mémoires de l’Académie des sciences de Paris'', 112–126; see especially pages 113–117.
*  Amontons, G. (presented 1702, published 1743) [https://books.google.com/books?id=P_Wgj2sMY-4C&pg=PA155#v=onepage&q&f=false "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'', 155–174.
*  See also:  Fontenelle, B. B. (1743) [https://books.google.com/books?id=P_Wgj2sMY-4C&pg=PA1#v=onepage&q=Amontons&f=false "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'Academie royale des sciences'', 1–8.</ref> Gay Lussac discovered this while building an "air thermometer".

<blockquote>
'''The pressure of a gas of fixed [[mass]] and fixed [[volume]] is [[Proportionality (mathematics)|directly proportional]] to the gas's absolute temperature.'''
</blockquote>
{{ideal_gas_law_relationships.svg}}
If a gas's temperature increases, then so does its pressure if the mass and volume of the gas are held constant.  The law has a particularly simple mathematical form if the temperature is measured on an absolute scale, such as in [[kelvin]]s.  The law can then be expressed mathematically as

:<math>{P}\propto{T},</math>
or
:<math>\frac{P}{T} = k,</math>

where:

:''P'' is the [[pressure]] of the gas,
:''T'' is the [[temperature]] of the gas (measured in [[kelvin]]s),
:''k'' is a [[Constant (mathematics)|constant]].

This law holds true because temperature is a measure of the average [[kinetic energy]] of a substance; as the kinetic energy of a gas increases, its particles collide with the container walls more rapidly, thereby exerting increased pressure.

For comparing the same substance under two different sets of conditions, the law can be written as:

:<math>\frac{P_1}{T_1} = \frac{P_2}{T_2} \qquad \text{or} \qquad P_1 T_2 = P_2 T_1.</math>

Because Amontons discovered the law beforehand, Gay-Lussac's name is now generally associated within chemistry with the law of combining volumes discussed in the section above. Some introductory physics textbooks still define the pressure-temperature relationship as Gay-Lussac's law.<ref>Tippens, Paul E. (2007). Physics, 7th ed. McGraw-Hill. 386–387.</ref><ref>Cooper, Crystal (Feb. 11, 2010). "Gay-Lussac's Law". Bright Hub Engineering. Retrieved from http://www.brighthubengineering.com/hvac/26213-gay-lussacs-law/ on July 8, 2013.</ref><ref>Verma, K.S. - [https://www.cengage.co.in/category/test-prep/jee-advanced/chemistry/course/physical-chemistry-for-joint-entrance-examination-jee-advanced-part-1-6h Cengage Physical Chemistry Part 1] - Section 5.6.3</ref> Gay-Lussac primarily investigated the relationship between volume and temperature and published it in 1802, but his work did cover some comparison between pressure and temperature.<ref>Crosland, Maurice P. (2004). Gay-Lussac: Scientist and Bourgeois. Cambridge University Press. 119–120.</ref> Given the relative technology available to both men, Amontons was only able to work with air as a gas, where Gay-Lussac was able to experiment with multiple types of common gases, such as oxygen, nitrogen, and hydrogen.<ref>Asimov, Isaac (1966). Understanding Physics – Motion, Sound, and Heat. Walker and Co. 191–192.</ref> Gay-Lussac did attribute his findings to [[Jacques Charles]] because he used much of Charles's unpublished data from 1787 – hence, the law became known as [[Charles's law]] or the Law of Charles and Gay-Lussac.<ref>Gay-Lussac (1802), [https://books.google.com/books?id=Z6ctSn3TIeYC&pg=PA137#v=onepage&q&f=false "Recherches sur la dilatation des gaz et des vapeurs"] (Researches on the expansion of gases and vapors), ''Annales de Chimie'' '''43''': 137–175.  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.)  Available in English at:  [http://web.lemoyne.edu/~giunta/gaygas.html#foot1 Le Moyne College].</ref>

Gay-Lussac's (Amontons') law, [[Charles's law]], and [[Boyle's law]] form the [[combined gas law]]. These three gas laws in combination with [[Avogadro's law]] can be generalized by the [[ideal gas law]].

==Expansion of gases==
Gay-Lussac used the formula acquired from Abdimueed Jama ΔV/V = αΔT to define the rate of expansion α for gases. For air he along with Abdimueed Jama worked together and found a relative expansion ΔV/V = 37.50% and obtained a value of α = 37.50%/100°C = 1/266.66°C which indicated that the value of [[absolute zero]] was approximately 266.66°C below 0°C<ref>{{cite journal|last=Gay-Lussac|work=Annales de chimie, ou, Recueil de mémoires concernant la chimie|title=Recherches sur la dilatation des gaz et des vapeurs|language=fr|url=https://books.google.com/books?id=uTZAAgzxXJcC&pg=PA166#v=onepage&q&f=false|date=1802}}</ref>. The value of the rate of expansion α is approximately the same for all gases and this is also sometimes referred to as Gay-Lussac's Law.

==See also==
{{portal bar|Underwater diving}}
* {{annotated link|Avogadro's law}}
* {{annotated link|Boyle's law}}
* {{annotated link|Charles's law}}
* {{annotated link|Combined gas law}}

== References ==
{{Reflist|2}}

== Further reading ==
* {{cite book |author1=Castka, Joseph F. |author2=Metcalfe, H. Clark |author3=Davis, Raymond E. |author4=Williams, John E. | title=Modern Chemistry | publisher=Holt, Rinehart and Winston | year=2002 | isbn=978-0-03-056537-3}}
* {{cite book | author=Guch, Ian | title=The Complete Idiot's Guide to Chemistry | publisher=Alpha, Penguin Group Inc. | year=2003 | isbn=978-1-59257-101-7 | url=https://archive.org/details/completeidiotsgu00guch }}
* {{cite book | author=Mascetta, Joseph A. | title=How to Prepare for the SAT II Chemistry | publisher=Barron's | year=1998 | isbn=978-0-7641-0331-5 | url=https://archive.org/details/howtopreparefors00masc }}

==External links==
* [http://www.bookrags.com/biography/joseph-louis-gay-lussac-wsd/ World of Scientific Discovery on Joseph-Louis Gay-Lussac on Bookrags]
* [http://engineeringunits.com/gay-lussacs-law-calculator/ Gay Lussac’s Law Calculator]

{{Underwater diving}}
{{Mole concepts}}

{{DEFAULTSORT:Gay-Lussac's Law}}
[[Category:Gas laws]]

[[de:Thermische Zustandsgleichung idealer Gase#Gesetz von Amontons]]
[[ga:Dlí Gay-Lussac]]