Problem 2.9
For this problem, we were given a table and graph which contained data for two Einstein solids, each containing three harmonic oscillators, with a total of six units of energy, that we needed to reproduce. I used Google Sheets, and recreated the table and graph for the original data. The assignment was to then modify the table and graph to show the case where one Einstein solid contains six harmonic oscillators and the other contains four harmonic oscillators. With these changes I had to calculate the new multiplicity for each Einstein solid, and then the new total multiplicity, with this formula.
Ω(N, q) = q + N − 1
q
= (q + N − 1)!
q!(N − 1)!
Problem 2.10:
For this problem, we are to produce a table and graph, where one Einstein solid contains 200 oscillators, the other contains 100 oscillators, and there were 100 units of energy in total. The assignment was then to find the most probable macrostate, the least probable macrostate, and their corresponding probabilities. I found the most probable macrostate by finding the state that had the highest multiplicity, and the least probable macrostate by finding the state that had the smallest multiplicity. I then created the graph from the table I made.
I then found the corresponding probabilities with the ratio of the number of its microstates to the total number of possible microstates. The most probable macrostate is qA = 67 and qB = 33. The least probable macrostate is qA = 0 and qB = 100.
