Two-Dimensional Diatomic Model Simulation


Description:


One the left is a model of a single diatomic molecule made up of two atoms with a mass ratio of 1 to 4. The brown bar graph shows the total kinetic energy of the two atoms and the blue graph shows the energy stored in the spring.

The table below the window shows the instantaneous kinetic energy of each mass (K1 and K2), the total kinetic energy (KE) and the total spring energy (Spring E).

 

Question 1:

Pause the simulation and add the total kinetic energy and the total spring energy. This is the internal energy of the molecule. What is the value of the internal energy?

Question 2:

Pause the simulation several times and add the total kinetic energy and total spring energy. Is the internal energy (approximately) constant over time for this diatomic molecule? (Note: There is a small amount of energy exchange when the molecule hits the walls of the container but as long as the collision is not too hard not much energy will be lost or gained.)

Question 3:

Which value of kinetic energy (K1 or K2) belongs to the red mass? (Hint: Grab one mass with the mouse and hold it still. Note: This will change the internal energy- click 'Reset' to go back to the original simulation energy.)

Question 4:

Grab one end of the molecule with the mouse, drag it just a little bit and let go so that the total internal energy is different. What is this new value of internal energy? Is it conserved? (Note: If you give it too much energy it will start losing energy to the walls.)

Question 5:

As you saw for the Brownian motion simulation, different size molecules in the same monatomic gas come into thermal equilibrium with each other so that they have the same kinetic energy (but different speeds). Are the two atoms of the diatomic molecule in thermal equilibrium with each other? (Hint: Pause the simulation 6 or 8 times, recording K1 and K2 each time and take an average.) Explain.

Question 6:

For the monatomic case when energy is added it has to appear as kinetic energy. In the diatomic case is it possible to add energy only to the spring, without adding kinetic energy to the atoms (try it using the mouse)? Explain.

Question 7:

Is it possible to add kinetic energy to the diatomic molecule without adding energy to the spring (try it using the mouse- be sure to wait until after the molecule collides with the sides before answering the question)? Explain.

Question 8:

When you add energy to a monatomic gas its kinetic energy increases which causes the temperature to increase. Explain why the temperature of a diatomic gas does not increase as rapidly for the same added energy as in the monatomic case.