قانون شارل

تحريك يوضح العلاقة بين الحجم ودرجة الحرارة.

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قانون شارل Charles's law (ويُعرف أيضاً بإسم قانون الحجوم) هو قانون تجريبي للغازات يصف كيف تنحى الغازات للتمدد حين تـُسخـَّن. والصياغة العصرية لقانون شارل هي

حين يتم الحفاظ على الضغط على عينة من الغاز الجاف ثابتاً، فإن درجة الحرارة بالكلڤن والحجم سيكونا مرتبطين مباشرةً.

علاقة التناسب الطردي المباشر هذه يمكن أن تُكتَب كالتالي:

$V\propto T\,$

أو

${\frac {V}{T}}=k$

حيث:

V هي حجم الغاز

T هي درجة حرارة الغاز (مقاسة بـكلڤن).

k هو ثابت.

هذا القانون يصف كيف يتمدد الغاز بارتفاع درجة الحرارة؛ وبالعكس، فإن انخفاض درجة الحرارة يؤدي إلى نقصان الحجم. فلمقارنة نفس المادة تحت ظرفين مختلفين، يمكن كتابة القانون كالتالي:

${\frac {V_{1}}{T_{1}}}={\frac {V_{2}}{T_{2}}}\qquad \mathrm {or} \qquad {\frac {V_{2}}{V_{1}}}={\frac {T_{2}}{T_{1}}}\qquad \mathrm {or} \qquad V_{1}T_{2}=V_{2}T_{1}.$

وتبين المعادلة أنه، كلما ارتفعت درجة الحرارة المطلقة، فإن حجم الغاز يزداد هو الآخر باضطراد. سُمِّي القانون على اسم العالم جاك شارل، الذي صاغ القانون الأصلي في عمله غير المنشور من ع1780.

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 تاريخ

في سلسلتين من أربع مقالات تم تقديمهم بين 2 و 30 أكتوبر 1801، بيَّن جون دالتون بالتجربة أن كل الغازات والأبخرة التي درسها، تتمدد بنفس القدر بين نقطتين ثابتتين من درجات الحرارة. أكـّد الفيلسوف الطبيعي الفرنسي جوزيف لوي گاي-لوساك الاكتشاف في محاضرة في المعهد الوطني الفرنسي في 31 يناير 1802، إلا أنه أعزى فضل الاكتشاف إلى العمل غير المنشور من عقد 1780 للعالم جاك شارل. المبادئ الأساسية had already been described a century earlier by Guillaume Amontons.

Dalton was the first to demonstrate that the law applied generally to all gases, and to the vapours of volatile liquids if the temperature was well above the boiling point. Gay-Lussac concurred. With measurements only at the two thermometric fixed points of water, 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:

$V_{100}-V_{0}=kV_{0}\,$

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 pressure. This equation does not contain the temperature and so has nothing to do with what became known as Charles's Law. Gay-Lussac's value for “k” (¹⁄_2.6666), was indentical to Dalton's earlier value for vapours and remarkably close to the present-day value of ¹⁄_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 named after 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. His conclusion for vapours is a clear statement of what became become known wrongly as Charles's Law, then even more wrongly as Gay-Lussaac's law, but never correctly as Dalton's 2nd law. His 1st law was that of partial pressures.

 علاقته بالصفر المطلق

Charles's 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 −273.15 °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 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.

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 hydrogen 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 boiling point of the liquid:

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.

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 Kelvin) in 1848:

This is what we might anticipate, when we reflect that infinite cold must correspond to a finite number of degrees of the air-thermometer 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 second law of thermodynamics, which Thomson himself described in 1852. 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 Ludwig Boltzmann's statistical view of entropy (1870).

 علاقته بالنظرية الحركية

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 speed 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 kinetic energy of the gas molecules, E_k:

$T\propto {\bar {E_{\rm {k}}}}.\,$

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:

$pV={\frac {2}{3}}N{\bar {E_{\rm {k}}}}\,$

 انظر أيضاً

• قانون بويل
• Combined gas law
• قانون گاي-لوساك
• قانون أڤوگادرو
• قانون الغازات المثالية
• Hand boiler

 للاستزادة

• Krönig, A. (1856), "Grundzüge einer Theorie der Gase", Annalen der Physik 99: 315–22, doi:10.1002/andp.18561751008, Bibcode: 1856AnP...175..315K . Facsimile at the Bibliothèque nationale de France (pp. 315–22).
• Clausius, R. (1857), "Ueber die Art der Bewegung, welche wir Wärme nennen", Annalen der Physik und Chemie 176: 353–79, doi:10.1002/andp.18571760302, Bibcode: 1857AnP...176..353C . Facsimile at the Bibliothèque nationale de France (pp. 353–79).
• Joseph Louis Gay-Lussac – Liste de ses communications, http://www.polytechnique.fr/bcx/associations/gaylussac/pages/CommunicationsGL.html . (بالفرنسية)

 وصلات خارجية

• Charles's law simulation from Davidson College, Davidson, North Carolina
• Charles's law demonstration by Prof. Robert Burk, Carleton University, Ottawa, Canada
• Charles's law animation from the Leonardo Project (GTEP/CCHS, UK)