Charles's Law - Relation To The Ideal Gas 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. Claypeyron's original statement was:

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, p0V0267+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 nRp is the constant of proportionality.

An ideal gas is defined as a gas which obeys the ideal gas law, so Charles' 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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