9.5 The Pressure of a Dilute Gas
413
x
z
y
v y ␶
Velocity
vector
Prism
volume
Area Ꮽ
Wall
v
Figure 9.14 The Prism That Contains Molecules of a Certain Velocity That Will Strike
Area A in Time τ.
The particles that are no farther from the wall in the y direction than a distance
equal to v y τ will strike the wall during the time interval τ (from the familiar relation,
distance rate × time). The distance in the y direction, not the distance along the surface of the prism, must be used because we are considering v y , not the speed. The
volume of the prism is equal to the area of its base times its altitude:
V prism A v y τ
(9.5-7)
We assume that our system is uniform. The number density, N , in any part of the
system is equal to N/V where N is the number of particles and V is the volume of the
system. The number of particles in the prism is
(number in prism)
N
V
A v y τ NA v y τ
(9.5-8)
The number in the prism with velocities in the specified range is
⎛
⎝
number in prism
with velocities in d 3 v
striking A in time τ
⎞
⎠ NA v y τg(v) dv x dv y dv z
(9.5-9)