(a) the partition function for a closed system at temperature tmay be written -σ -be (1) e = z σε ε.) -be and (2) = z explain what is meant by the partition function and why it is useful, and discuss the difference between equations (1) and (2) [4 marks] (b) a simple system consists of 3 indistinguishable spin-zero bosons, each of which can be in one of three possible energy levels, with energies 81 0, e2 2 e and e3 4. the system is in thermal equilibrium at temperature t. (1) how many states do you expect this system to have? justify your answer (ii make a table showing, for each state of the system, the energy of the state, the number of particles with each energy value and the degeneracy (iii)write down the partition function for the system