For the system described in exercises 4.15 and 4.16 we have the canonical partition function                                                               Show that...

For the system described in exercises 4.15 and 4.16 we have the canonical partition function

Show that

Use this result and the analogous formula for {N_B} to show that {N_A} / {N_B} = q_A/q_B. Next consider the fluctuations from these mean values. Express the average of the square fluctua-tion, (N_A}/ {N_A} )2 , as appropriately weighted sums over states, and show that

Derive a similar expression for the fluctuations in N_B.