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Charles's law From Wikipedia, the free encyclopedia (Redirected from Charles' law)

Charles' law (also known as the law of ) is an experimental law which describes how tend to expand when heated. It was first published by French natural philosopher Joseph Louis Gay-Lussac in 1802,[1] although he credited the discovery to unpublished from the by . The law was independently discovered by British natural philosopher by 1801, although Dalton's description was less thorough than Gay-Lussac's.[2] The basic principles had already been described a century earlier by . An animation demonstrating the Taylor Buchanan was the first to demonstrate that the law relationship between and applied generally to all gases, and also to the vapours of . volatile if the temperature was more than a few degrees above the point.[citation needed] His statement of the law can be expressed mathematically as:

where V100 is the volume occupied by a given sample of gas at 100 °C; V0 is the volume occupied by the same sample of gas at 0 °C; and k is a constant which is the same for all gases at constant 1 1 . Gay-Lussac's value for k was ⁄2.6666, remarkably close to the present-day value of ⁄2.7315.

A modern statement of Charles' law is:

At constant pressure, the volume of a given of an increases or decreases by the same factor as its temperature on the absolute temperature scale (i.e. the gas expands as the temperature increases).[3] which can be written as:

where V is the volume of the gas; and T is the absolute temperature. The law can also be usefully expressed as follows:

The equation shows that, as absolute temperature increases, the volume of the gas also increases in proportion.

Contents

■ 1 Limitations ■ 2 Relation to the ■ 3 Relation to

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■ 4 Relation to kinetic theory ■ 5 See also ■ 6 References ■ 7 Further reading ■ 8 External links

Limitations

In modern , Charles' Law is seen as a special case of the ideal gas equation, in which the pressure and number of are held constant. The ideal gas equation is usually derived from the , which presumes that molecules occupy negligible volume, do not attract each other and undergo elastic collisions (no loss of kinetic ); an imaginary gas with exactly these properties is termed an ideal gas. The behavior of a is close to that of an ideal gas under most circumstances, which makes the ideal gas law useful. Gases made up of polar molecules (for example, water) deviate more from this ideal, so Charles's Law is less accurate in describing the behavior of these gases.

This law of volumes implies theoretically that as a temperature reaches absolute zero the gas will shrink down to zero volume. This is not physically correct, since in fact all gases turn into liquids at a low enough temperature, and Charles's law is not applicable at low for this reason.

The fact that the gas will occupy a non-zero volume - even as the temperature approaches absolute zero - arises fundamentally from the of quantum theory. However, as the temperature is reduced, gases turn into liquids long before the limits of the uncertainty principle come into play due to the attractive between molecules which are neglected by Charles's Law. Relation to the ideal gas law

French physicist Émile Clapeyron combined Charles's law with Boyle's law in 1834 to produce a single statement which would become known as the ideal gas law.[4] Claypeyron's original statement was:

where t is the temperature; and p0, V0 and t0 are the pressure, volume and temperature of a sample of gas under some standard state. The figure of 267 came directly from Gay-Lussac's work: p0V0 the modern figure would be 273.15. For any given sample of gas, ⁄267+t0 is a constant (Clapeyron denoted this constant R, and it is closely related to the modern ); if the pressure is also constant, the equation simplifies to

as required.

The modern statement of the ideal gas law is:

where n is the of the gas sample; and R is the gas constant. The amount of substance is constant for any given gas sample so, at constant pressure, the equation rearranges to:

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nR where ⁄p is the constant of proportionality.

An ideal gas is defined as a gas which obeys the ideal gas law, so Charles's law is only expected to be followed exactly by ideal gases. Nevertheless, it is a good approximation to the behaviour of real gases at relatively high temperatures and relatively low . Relation to absolute zero

Charles' law appears to imply that the volume of a gas will descend to zero at a certain temperature (−266.66 °C according to Gay-Lussac's figures) or -273°C. Gay-Lussac was clear in his description that the law was not applicable at low temperatures:

but I may mention that this last conclusion cannot be true except so long as the compressed 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 state.[1]

Gay-Lussac had no experience of liquid air (first prepared in 1877), although he appears to believe (as did Dalton) that the "permanent gases" such as air and could be liquified. Gay-Lussac had also worked with the vapours of volatile liquids in demonstrating Charles's law, and was aware that the law does not apply just above the of the liquid:

I may however remark that when the temperature of the ether is only a little above its boiling point, its 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 state, but which is no longer sensible at temperatures a few degrees above that at which the transition occurs.[1]

The first mention of a temperature at which the volume of a gas might descend to zero was by William Thomson (later known as Lord ) in 1848:[5]

This is what we might anticipate, when we reflect that infinite must correspond to a finite number of degrees of the air- below zero; since if we push the strict principle of graduation, stated above, sufficiently far, we should arrive at a point corresponding to the volume of air being reduced to nothing, which would be marked as −273° of the scale (−100/.366, if .366 be the coefficient of expansion); and therefore −273° of the air-thermometer is a point which cannot be reached at any finite temperature, however low.

However, the "absolute zero" on the Kelvin temperature scale was originally defined in terms of the law of thermodynamics, which Thomson himself described in 1852.[6] Thomson did not assume that this was equal to the "zero-volume point" of Charles's law, merely that Charles's law provided the minimum temperature which could be attained. The two can be shown to be equivalent by 's statistical view of (1870). Relation to kinetic theory

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The kinetic theory of gases relates the macroscopic properties of gases, such as pressure and volume, to the microscopic properties of the molecules which make up the gas, particularly the mass and of the molecules. In order to derive Charles's law from kinetic theory, it is necessary to have a microscopic definition of temperature: this can be conveniently taken as the temperature being proportional to the average of the gas molecules, Ek:

Under this definition, the demonstration of Charles's law is almost trivial. The kinetic theory equivalent of the ideal gas law relates pV to the average kinetic energy:

where N is the number of molecules in the gas sample. If the pressure is constant, the volume is directly proportional to the average kinetic energy (and hence to the temperature) for any given gas sample. ... absolute zero is in attainable in gases because most of the gases turn to liquids i.e. they leave the state of gas thus the law is not valid . This is only a theoretical limitation and thus is practically working Applications of charles's law

■ bursting of hydrogen ■ Making of chappathi See also

■ Boyle's law ■ Gay-Lussac's law ■ Avogadro's law ■ Hand boiler References

1. ^ abcGay-Lussac, J. L. (L'An X – 1802), "Recherches sur la dilatation des gaz et des vapeurs", Annales de chimie XLIII: 137. English translation (extract). (http://web.lemoyne.edu/~giunta/gaygas.html) 2. ^ http://www.chemistryexplained.com/Fe-Ge/Gay-Lussac-Joseph-Louis.html 3. ^ Fullick, P. (1994), Physics, Heinemann, pp. 141–42, ISBN 0435570781. 4. ^ Clapeyron, E. (1834), "Mémoire sur la puissance motrice de la chaleur", Journal de l'École Polytechnique XIV: 153–90. Facsimile at the Bibliothèque nationale de (pp. 153–90). (http://gallica.bnf.fr/ark:/12148/bpt6k4336791/f157.table) 5. ^ Thomson, William (1848), "On an Absolute Thermometric Scale founded on Carnot's Theory of the Motive of , and calculated from Regnault's Observations" (http://zapatopi.net/kelvin/papers/on_an_absolute_thermometric_scale.html) , Philosophical Magazine: 100–6, http://zapatopi.net/kelvin/papers/on_an_absolute_thermometric_scale.html. 6. ^ Thomson, William (1852), "On the Dynamical Theory of Heat, with numerical results deduced from Mr 's equivalent of a Thermal Unit, and M. Regnault's Observations on Steam", Philosophical Magazine 4. Extract. (http://web.lemoyne.edu/~giunta/KELVIN1.html) Further reading

■ Krönig, A. (1856), "Grundzüge einer Theorie der Gase", Annalen der Physik 99: 315–22, Bibcode 1856AnP...175..315K (http://adsabs.harvard.edu/abs/1856AnP...175..315K) , doi:10.1002/andp.18561751008 (http://dx.doi.org/10.1002%2Fandp.18561751008) .

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Facsimile at the Bibliothèque nationale de France (pp. 315–22). (http://gallica.bnf.fr/ark:/12148/bpt6k15184h/f327.table) ■ Clausius, R. (1857), "Ueber die Art der Bewegung, welche wir Wärme nennen", Annalen der Physik und Chemie 100: 353–79, Bibcode 1857AnP...176..353C (http://adsabs.harvard.edu/abs/1857AnP...176..353C) , doi:10.1002/andp.18571760302 (http://dx.doi.org/10.1002%2Fandp.18571760302) . Facsimile at the Bibliothèque nationale de France (pp. 353–79). (http://gallica.bnf.fr/ark:/12148/bpt6k15185v/f371.table) ■ Joseph Louis Gay-Lussac – Liste de ses communications (http://www.polytechnique.fr/bcx/associations/gaylussac/pages/CommunicationsGL.html) , http://www.polytechnique.fr/bcx/associations/gaylussac/pages/CommunicationsGL.html. (French) External links

■ Charles's law simulation (http://www.chm.davidson.edu/CHEMISTRYAPPLETS/GASLAWS/CharlesLaw.html) from Davidson College, Davidson, North Carolina ■ Charles's law simulation (http://www.tutorvista.com/content/chemistry/chemistry-iii/matter- states/charles-law-animation.php) from TutorVista.com ■ Charles's law demonstration (http://www.youtube.com/watch?v=IkRIKGN3i0k) by Prof. Robert Burk, Carleton University, Ottawa, Canada ■ Charles's law animation (http://video.google.com/videoplay?docid=- 4506461547173401204) from the Leonardo Project (GTEP/CCHS, UK) Retrieved from "http://en.wikipedia.org/w/index.php?title=Charles%27s_law&oldid=460008232" Categories: Volumeszww

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