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Derivative the kinetic molecular theory of gases according to the gas laws?

Derivative the kinetic molecular theory of gases according to the gas laws?

Grade:11

1 Answers

Vikas TU
14148 Points
4 years ago
Comsidering a cube of side x in which an atom is in motion with velocity v.
Hence 
Change in momentum = mv – (-mv) => 2mv..............(1)
time to cover the 2x distnace,
t = 2x/v.................(2)
From Newtons law,
F = dP/dt => from eqns. (1) and  (2)
we get,
F = 2mv/(2x/v) = > 2K/x
Other assumtion that let there be N molecules in cube 1/3 are travelling in  x 1/3 in y and 1/3 in z direction.
Hence the 
Pressure along one of the axes => (1/3)NF/A => 2NK/3xyz => 2NK/3v
Hence 
PV = (2/3)NK
or
K = (3/2)kT
wher k is the Boltzman’s contant.

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