The most probable configuration is characterized by a parameter we know as the 'temperature'. The temperatures of the system specified in Problems 16.13 and 16.14 must be such as to give a mean value of E forth energy of each molecule and a total energy NE for the system.
(a) Show that the temperature can be obtained by plotting against j, where Pi is the (most probable) fraction of molecules in the state with energy i.e. Apply the procedure to the system in Problem 16.14. What is the temperature of the system when E corresponds to 50 cm-3?
(b) Choose configurations other than the most probable, and show that the same procedure gives a worse straight line, indicating that a temperature is not well-defined for them.