What is the relationship between Charles law and the kinetic theory of gases?

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Answer 1 · 2017-06-06T07:01:04

From the kinetic theory, one derives the pressure equation,

#p = (mnv^2)/2# where #m# is mass of a molecule, #n# is no. of molecules in unit volume, and #v# is rms speed.

Thus, #n = N/V# where, #N# is total number of gas molecules.

Therefore, one may write,

#pV = (mNv^2)/3#

Now, #(mv^2)/2 = E# where #E# is the kinetic energy of a molecule.

Thus, #pV = (2NE)/3#

Now from the kinetic interpretation of temperature,

#E = (3kT)/2# where #k# is the Boltzmann constant.

Thus, #pV = NkT#

Now since, #N# and #k# are constants, then for a fixed #p#,

#V/T =# constant

This is Charles' law from kinetic theory.