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' 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' 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.
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