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Lecture 4:
Kinetic Theory of Gases and some math
We have derived the
Barometric formula
From the point of individual molecules, the formula tells us what
the probability is that a molecule is at the height
z
.
It relates the
potential energy
of the molecule
in the gravitational field to the average
thermal energy
k
b
T.
The same kind of distribution holds for all other energy contributions,
in particular, for the kinetic energy. So their probability
distributions are
where
E
v
is the kinetic energy of the molecule or its internal rotational
and vibrational energy.
The above probability
f(v)
is called the
Boltzmann distribution
(its 3D integral over all
v
is normalized to 1, which gives C=(1/2
π
m
mol
k
b
T)
3/2
).
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it relates statistical theory to thermodynamics (chem
346).
Let us try to calculate the pressure that the molecules exert on the walls.
The number of molecules with velocities in the interval
v
and
v+dv
, which
collide with the surface element
dS
in time
dt
is (without all the details)
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 Spring '08
 PRESTONSNEE
 Physical chemistry, Mole, pH

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