STATISTICAL AND THERMAL PHYSICS PLEASE HELP ANSWER ALL QUESTIONS (a) Calculate the number of possible microstates for each macrostate n for N = 8 particles. What is the probability that n= 8? What is the probability that n = 4? It is possible to count the number of microstates for each n by hand if you have enough patience, but because there are a total of 2° = 256 microstates, this counting would be very tedious. An alternative is to obtain an expression for the number of ways that n particles out of N can be in the left half of the box. Motivate such an expression by enumerating the possible microstates for smaller values of N until you see a pattern. (b) The macrostate with n = N/2 is much more probable than the macrostate withn = N. Why?

STATISTICAL AND THERMAL PHYSICS PLEASE HELP ANSWER ALL QUESTIONS (a) Calculate the number of possible microstates for each macrostate n for N = 8 particles. What is the probability that n= 8? What is the probability that n = 4? It is possible to count the number of microstates for each n by hand if you have enough patience, but because there are a total of 2° = 256 microstates, this counting would be very tedious. An alternative is to obtain an expression for the number of ways that n particles out of N can be in the left half of the box. Motivate such an expression by enumerating the possible microstates for smaller values of N until you see a pattern. (b) The macrostate with n = N/2 is much more probable than the macrostate withn = N. Why?