complete the posted #1 (20%). Using the given notes "Entropy_statistical_definition", given template "Entropy_statistical_TEMPLATE" that illustrates the statistical (Boltzmann's) definition of entropy and then do and comment on the following: (i) Show that (thermal) equilibrium is reached when the total entropy (of the system plus surroundings) reaches its maximum value, which coincides with the state of highest probability. (ii) (iii) To verify the observed trends, extend the templates to represent boxes of vastly different sizes. Does the shift of thermal equilibrium with increasing size of the 'surroundings' agree with your intuitive expectations? For example, if the 'universe' is 20x20 and the system is 11x11, does your graph look like the one in "Entropy_Universe_20x20_System_11x11" file? And why does it make sense that the thermal equilibrium shifts to the right (i.e., closer to the system's temperature) w/r to the posted graphs? And, of course, if the size of the surroundings is equal to the size of the system, does your result agree with the one in "Entropy_Equal_surroundings_and_system_size"?

Fig: 1