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Charles’s law
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• Charles's law is an experimental gas law which
describes how gases tend to expand when heated.
• It was first published by French natural philosopher
Joseph Louis Gay-Lussac in 1802 although he credits
the discovery to unpublished work from the 1780s
by Jacques Charles.
• where V is the volume of the gas; and T is the
absolute temperature. The law can also be usefully
expressed as follows:
Limitation
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In modern physics, Charles's Law is seen as a special case of the ideal gas
equation, in which the pressure and number of molecules are held constant.
The ideal gas equation is usually derived from the kinetic theory of gases,
which presumes that molecules occupy negligible volume, do not attract
each other and undergo elastic collisions (no loss of kinetic energy); an
imaginary gas with exactly these properties is termed an ideal gas. The
behavior of a real gas is close to that of an ideal gas under most
circumstances, which makes the ideal gas law useful.
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 temperatures 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
uncertainty principle 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 forces between molecules
which are neglected by Charles's Law.
Relation to the ideal gas law
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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:
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where t is the Celsius 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: the modern figure would be 273.15. For any given
sample of gas, p0V0⁄267+t0 is a constant (Clapeyron denoted this constant R, and it is
closely related to the modern gas constant); 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 amount of substance 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:
where nR⁄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
pressures
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Relation to absolute zero
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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°C. GayLussac 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.[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
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.[1]
Relation to absolute zero
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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:[5]
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.[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 Ludwig Boltzmann's
statistical view of entropy (1870).
Relation to kinetic theory
• 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, 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.