161
Chapter 16: Kinetic Theory of Gases
Problem numbers in italics indicate that the solution is included in the
Student’s Solutions Manual.
Questions on Concepts
Q16.1)
Why is probability used to describe the velocity and speed of gas molecules?
Velocity is a measure of kinetic energy.
As with any large ensemble of particles
(~N
A
) not all of the particles will have the same energies.
Instead, the particle
energies are distributed through a range of values.
The fraction of gas particles
with a specific energy is defined by a probability.
Q16.2)
Describe pressure using gas kinetic theory. Why would one expect pressure to
depend on the inverse of volume in this theory?
Pressure arises due to collision of particles with the walls of the container.
Since
the pressure is dependent upon the number of particles striking the wall of the
container per unit area, the pressure is dependent upon the density of the gas
(number of particles per volume).
As the volume increases, the density
decreases, and the pressure will subsequently decrease.
Q16.3)
What are the inherent assumptions about gas particle interactions in gas kinetic
theory?
The assumptions made are that the particles do not interact at long distances (i.e.,
the intermolecular potential is zero when particles are separated) and) particles
interact only through elastic collisions (total conservation of kinetic energy).
Q16.4)
Provide a physical explanation as to why the Maxwell speed distribution
approaches zero at high speeds. Why is
() 0
a
t
0
f
ν
==
?
Since kinetic energy content is related to temperature, higher particle speeds
corresponds to a high inherent particle temperature.
The
ensemble of particles
demonstrates an average temperature, and we can think of the inherent particle
temperatures as distributed around this value.
We would expect this number of
particles demonstrating temperatures higher than the average temperature to
decrease as the inherent temperature increases.
Also, a nonzero distribution at
infinite inherent temperature implies that the ensemble consists of an infinite
number of particles.
The distribution must reach zero as T
→
0 and T
→
∞
in
order to preserve unit probability.
Conversely, there can be no distribution at
v = 0, due to the Uncertainty Principle since zero velocity would allow one to
know both the position and velocity to arbitrary precision.
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162
Q16.5)
How would the Maxwell speed distributions for He versus Kr compare if the
gases were at the same temperature?
The two distributions differ because of the mass difference between He and Kr.
The Kr distribution will have a most probable speed that is smaller than He, the
width of the Kr distribution will be smaller in comparison to He, and the Kr
distribution will have a larger maximum amplitude.
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 Spring '03
 Nefzi
 Physical chemistry, Mole, pH, Kinetic Energy, Mass, Velocity, Trigraph, Orders of magnitude, Kinetic theory

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