StatMech 2.7 (August 2007)

Author: Thomas A. Moore

This program automates the construction of macropartition tables for two Einstein solids in thermal contact (as discussed in chapters T4 and T5 in unit T of Six Ideas That Shaped Physics text, McGraw-Hill, 2003). Students should first thoroughly understand how to construct such tables before using this program.

Using the Program

Using the text entry boxes, enter the number of atoms in Einstein solids A and B and the combined system's total internal energy U (in units of ε, the separation between oscillator energy levels). Then press the Calculate button (or hit Enter on the keyboard), and the macropartition table should shortly appear. For small values of U, there will be one table row for every possible macropartition (i.e. way of distributing energy between the two subsystems). If you press the Graph radio button, the program will (by default) display the macropartition’s total multiplicity (which is proportional to its long-term probability) versus the fraction of the system's total energy U that is in solid A (i.e. U(A)/U).

If the system's total internal energy U (in units of ε) is larger than the number specified by the Max Row popup menu, the program automatically groups sets of macropartitions into "bins" each containing the same integer number of macropartitions. Each table line then corresponds to one bin, and specifies the mean values of U(A)/U and U(B)/U and total multiplicities for all the macropartitions in that bin. This enables handling very large values of U without generating enormously many table rows.

Indeed, the program can handle very large numbers of atoms and total energy units (up into the millions), but the calculation of the table will proceed more slowly as U increases. There is a progress bar under the Calculate button that gives a rough indication of how a calculation is progressing. Exponents over ten million cannot be displayed within the available space in the table and will be displayed as "#######" instead. But it is hard to get exponents this high without waiting a very long time.