(a) state the postulates of statistical mechanics (which refer to the microstates and macrostates of an isolated system in equilibrium). [2 marks] (b) a general definition of the entropy of a system can be found by considering a macroscopic system with microstates labelled 1,2, and generating an ensemble of v identical replicas of this system. if p, is the probability that our original system is in state r, the number of systems in our ensemble in state r is given by (9.1) vrvpr explain each step in the following outline of the derivation of a general expression for the entropy of our system. v! (9.2) .. s kln k in- (9.3) v,! v, in v (9.4) s kvn v- sy vk nvvk> p, lnvp, (9.5 s =-kv p, in p, (9.6) s -k р, in p, . (9.7) [9 marks (c) (write down the probability distribution for microstates in an isolated system, and show that eq. (9.7) reduces to the boltzmann definition of entropy, s k ln (ii write down the probability distribution for microstates in a system at constant temperature (the boltzmann distribution), and show that eq. (9.7) becomes: kln z + e/t s(t, v,n (iii) write down the probability distribution for microstates in an open system (the gibbs distribution), and show that eq. (9.7) becomes: e un т т +k in z