The vibrational energy levels of an HBr molecule are EK = C (K + ½), where C = 5 · 10–20 Joules and K = 0, 1, 2,… Each level is singly degenerate: gK = 1. Consider four HBr molecules trapped in a solid matrix such that they are able to undergo vibrational motion, but not translational or rotational motion. The total vibrational energy of the four molecules is 25 · 10–20 Joules.
(a) How many microstates are in this system?
(b) Suppose another 5 · 10–20 Joules worth of enegry is added to the system, so the total energy is now 30 · 10–20 Joules. Calculate the change in the entropy of the system.
(c) Is application of the equipartition theorem to this system justified? Why or why not?