“Kinetic Theory of Gases”
MQ Chapter 27
Prof. GianluigiVeglia

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Let’s recall the definition of an ideal gas:
The gas molecules which have mass m and diameter d are
in constant motion
The molecules are small compared to the distances they
travel between collisions
The molecules do not interact except when they collide
and then the collisions are perfectly elastic.

Physical interpretation of gas pressure
In this vessel, the velocity of a molecule of
mass m has components: u
1x
, u
1y,
u
1z
. The
particle moves along the direction of the
vector and collides with the surface of
the box.
Assuming an elastic collision:
The time elapsed between the collision is
(the molecule needs to travel a distance
2a)
x
x
x
x
mu
mu
mu
mu
1
1
1
1
2
)
(
)
(
=
−
−
=
∆
The momentum is conserved
x
u
a
t
1
/
2
=
∆

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Applying Newton’s law:
Where F is the force that the molecule exerts on the wall. From the force
it is possible to calculate the pressure:
Where V=abc is the volume of the box. The total
pressure is given by
The average value of u
2
is
F
a
mu
u
a
mu
t
mu
x
x
x
x
=
=
=
∆
∆
2
1
1
1
1
/
2
2
)
(
V
mu
abc
mu
bc
F
P
x
x
2
1
2
1
1
=
=
=
∑
∑
∑
=
=
=
=
=
=
N
j
jx
N
j
x
N
j
j
u
V
m
V
mu
P
P
1
2
1
2
1
1
∑
=
=
N
j
jx
x
u
N
u
1
2
2
1