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Kinetic Theory of Gas
Da Procida: Lesson 2
•Kinetic Theory tells us that matter is made up of
atoms that are continually moving.
•Today, we are going to think about gases and how
we can further describe the behavior.
•Specifically, we are going to examine the
relationship between kinetic energy of the
molecules of a gas and the temperature.
Concept Question
•As you raise the temperature in a gas, will
the molecules move:
•oFaster
•oSlower
•oNo speed change
•oSideways.
Activity!
• What is the change in momentum when
a molecule hits the side of the box?
Activity!
• What is the average force for one of
these collisions?
• How do we relate momentum and
force?
Activity!
• What is the average velocity?
Activity!
• So what is the average force for all of
these molecules?
Activity!
• Let us assume that the velocity in x, y
and z are the same. This means then
that:
• v^2 = 3vx^2
Activity!
• Now re-write the average force using
the average velocity.
Activity!
• What is the pressure on the wall of all of
these atoms hitting the wall?
Activity!
• Finally, how do we calculate kinetic
energy?
•
Conclusions
Our equation basically tells us that
the average kinetic energy of molecules in
a gas is proportional to the temperature.
Molecules move faster at higher
temperatures.
•
The root-mean-square velocity (vrms
= sqrt(v) = sqrt(3kT/m)) is the square root
of the average velocity – often called the
rms speed.
Practice Problems
•
•
1) The rms speed of molecules in a gas at
20C is to be increased by 2 percent. To what
temperature must it be raised? Giancoli,
13.51
2) If the temperature of an ideal gas is
raised from 25C to 100C, how many times
faster is the rms speed of the gas molecules?
Wilson, 10.77