Chapter 21 The kinetic theory of gas

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• Chapter 21 The kinetic theory of gas
• September 19, 22 Ideal gas model
• 21.1 Molecular model of an ideal gas
• Assumptions of the molecular model of an ideal
  gas
• The number of molecules is large. The average
  distance between them is large comparing to their
  size.
• Each molecules obeys Newtons law of motion, but
  as a whole the molecules move randomly.
• The molecules interact only during elastic
  collisions.
• The molecules collide with the walls elastically.
• All molecules are identical.
• Application pressure of an ideal gas caused by
  the collisions of the gas with the walls.

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Momentum change per collision Impulse on
molecule Time interval of collision Let
be the average force within one collision
period which is also the long-term average force
on the molecule.
Total average force on wall
Large number of molecules results in a constant
force on wall
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Total pressure exerted on the wall

• This equation relates the macroscopic quantity of
  pressure with a microscopic quantity of the
  average value of the square of the molecular
  speed.
• The pressure of an ideal gas is proportional to
  the number density and the average translational
  kinetic energy of the molecule.

Molecular interpretation of temperature Temperatu
re is a direct measure of average molecular
kinetic energy.
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Theorem of equipartition of energy Each degree
of freedom contributes ½ kBT to the energy of a
system.
Degree of freedom Independent means a molecule
can move. Translation, vibration (kinetic and
potential energies), rotation.
Total translational kinetic energy ?The
internal energy of an ideal gas depends only on
the temperature.
Root-mean-square (rms) speed Table 21.1 Example
21.1 Quiz 21.1
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Read Ch21 1 Homework Ch21 (1-11) 6,8,9 Due
September 26
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September 26 Molar specific heat 21.2 Molar
specific heat of an ideal gas In gases Q DEint-
W The heat absorbed with a given change in
temperature is not a unique value. Molar specific
heat at constant volume CV, and Molar specific
heat at constant pressure CP
CP gt CV for a give DT.
For a monatomic ideal gas
In general, the internal energy of an ideal gas
is a function of T only.
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For a constant-volume process W 0, Q DEint,
DEint n CVDT. If CV is a constant? Eint n CVT
(applies to all ideal gases). For infinitesimal
changes
for monatomic ideal gases.
For a constant-pressure process
This relation applies to all ideal gases. For
monatomic ideal gases For solids and liquids,
CP and CV are approximately the same.
Table 21.2
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21.3 Adiabatic processes for an ideal gas The
relationship between P and V for an adiabatic
process involving an ideal gas
That is, for an adiabatic process,
.
Example 21.3
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21.4 The equipartition of energy For diatomic
ideal gases, including rotation (
)
Including vibration ( )
The figure shows the rotation and vibration
excitation of molecules at higher temperatures.
Quiz 21.3
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Read Ch21 2-4 Homework Ch21 (12-30)13,16,24,26
Due October 3
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• September 29 Boltzmann distribution
• 21.5 The Boltzmann distribution law
• The motion of molecules is extremely chaotic.
• Any individual molecule is colliding with others
  at an enormous rate.
• Distribution function nV(E) nV(E)dE is the
  number of molecules per unit volume with energy
  between E and EdE.
• Boltzmann distribution law
• The probability of finding the molecule in a
  particular
• energy state (E) varies exponentially as
  exp(-E/kBT).
• n0 N/kBT for the purpose of normalization.

Example 21.4
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21.6 Distribution of molecular speeds Maxwell-Bolt
zmann speed distribution function Nv The number
of molecules with speed between v and vdv is
dNNvdv.
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Root-mean-square speed vrms, average speed ,
and most probable speed vmp
Table B.6
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Read Ch21 5-7 Homework Ch21 (31-)33,36,57,58 D
ue October 10