Kinetic Theory of Gases
Pressure is caused by the constant bombardment of the many individual molecules of a gas.
The ideal gas law can be explained by the constant bombardment of the many individual molecules of a gas.
Pressure is caused by the collisions of gas molecules with the walls of the container holding the gas.
Assume one-third of the molecules move along the x-axis at constant speed v.
This is the average force exerted by each single molecule. But we have N/3 molecules hitting this wall. Therefore, the total force on the wall is
Now, to get the pressure. Remember, in our simplified model, we are looking at a cube with edge length L,
P V = (1/3) N m v2
The kinetic energy of each molecule is KE = (1/2) m v2 so we can rewrite this as
P V = (2/3) N (1/2) m v2
We already know that
P V = N k T
so this means
(2/3) N (1/2) m v2 = N k T
(1/2) m v2 = (3/2) k T
Let us replace our constant speed v with an average speed <v>,
(1/2) m <v>2 = (3/2) k T
(1/2) m <v>2 = Eint
Eint, tot = N (3/2) k T
Eint, tot = (3/2) N k T = (3/2) n R T
(c) 2005, Doug Davis; all rights reserved
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