Exploration 20.4

    # of Atoms=    and/or   # of Molecules=

Please wait for the animation to completely load.

The kinetic energy of a particle can be due to motion in the x direction, y direction, z direction, as well as rotations.  The equiparition of energy theorem says that the kinetic energy of an atom or particle is, on average, equally distributed between the different modes available or different degrees of freedom.  An atom free to move in a room has three degrees of freedom because it can move in x, y and z directions.  The energy per particle has an average kinetic energy of (f/2)kBT where f is the number of degrees of freedom, kB is the Boltzmann constant and T is the temperature. Restart.

  1. In this animation of atoms in a box, why do the atoms only have 2 degrees of freedom?  The table shows the total kinetic energy of all particles in the box as well as the average kinetic energy of atoms and molecules in the box (the animation averages over a 10-second period so you need to wait 10 seconds to read the averages). 
  2. Record the total energy. 
  3. What is the energy per particle?
  4. If the energy is given in Joules/kB, what is the temperature inside the box?

Try this animation with 20 diatomic molecules.  Notice that the graph shows the total kinetic energy of the molecules and the kinetic energy of translation (motion in x, y direction) and rotation. 

  1. Why is the translational energy, on average, about two times the rotational kinetic energy? (The animation averages over a 10-second interval so you need to wait for the animation to run for at least 10 seconds to read the average values of kinetic energy). 
  2. For the total energy, what is the energy per particle? 
  3. If the energy is given in Joules/kB, what is the temperature in the box? (Remember that <KE>/particle = (f/2)kBT and in this case, f = 3 (why?).)

Now, try a mixture of 20 atoms and 20 molecules. 

  1. Why is the temperature of the gas in the box a set value (not one value for atoms and another for molecules)?  (Hint: think about the air surrounding you at essentially a constant temperature (unless the heater or air-conditioner just turned on and made one section of the air a different temperature).  Air is made up of atoms: helium and molecules: water, oxygen, nitrogen). 
  2. After waiting at least 10 seconds, compare average values.   What value is the average atomic kinetic energy close to? 
  3. Why should those two values (the two averages that you found in part (i)), averaged over a long period of time, be equal and greater than the rotational kinetic energy of the molecule? 
  4. Explain why the total energy should be equal to (2/2)20kBT + (3/2)20kBT. 
  5. From the total energy (given in Joules/kB), what is the temperature?
  6. In this animation, if a mixture has 15 atoms, how many diatomic molecules should it have so that the average kinetic energies of both particles is the same?  Try setting the number of atoms and molecules to check your answer.

 

 

Exploration by Anne J. Cox
Script by Wolfgang Christian modified by Anne J. Cox
© 2003 by Prentice-Hall, Inc. A Pearson Company