1. Kinetic Theory of Gas Da Procida: Lesson 2

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.

3. Concept Question As you raise the temperature in a gas, will the molecules move: o Faster o Slower o No speed change o Sideways.

4. Activity! What is the change in momentum when a molecule hits the side of the box?

5. Activity! What is the average force for one of these collisions? How do we relate momentum and force?

6. Activity! What is the average velocity?

7. Activity! So what is the average force for all of these molecules?

8. Activity! Let us assume that the velocity in x, y and z are the same. This means then that: v^2 = 3vx^2

9. Activity! Now re-write the average force using the average velocity.

10. Activity! What is the pressure on the wall of all of these atoms hitting the wall?

11. Activity! Finally, how do we calculate kinetic energy?

12. 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.

13. 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