ABSTRACT
The first postulate of Statistical Mechanics, the time average equals the ensemble average, was made in the understanding that, at least for equilibrium properties, ensemble averages will be easier to perform than the time averages. Ensembles allow formulation of equilibrium probability distribution functions in terms of averages over the well-known Boltzmann distribution. In the process we develop expressions for partition functions under different thermodynamic conditions. These partition functions give a quantitative measure of the weight of the system under given thermodynamic conditions and are equivalent to free energies under appropriate conditions that are employed to specify the state of the system. For example, partition function under constant (N, V, T) is different from that under constant (N, P, T). In this chapter we study various ensembles and their partition functions. The relationship between free energy and partition function is also discussed in each case. This is an important chapter, as it describes how Statistical Mechanics makes the transition from postulates to quantitative expressions of various thermodynamic functions.
