[2003SM/LNP-10] Lecture-10--Internal Energy of a System in Contact with Heat Reservoir

In this lecture we continue our discussion of canonical partition function. An expression for internal energy is obtained in terms of the partition function. The parameter β is identified with 1/kT by noting that the parameter β in the partition function depends only on the heat bath and not on the system in equilibrium with the heat bath. The partition function is used to compute the energy of an ideal gas and comparing the same with the expression given by the equipartition theorem. The expression for other thermodynamic functions, entropy, free energy, enthalpy and variance of energy are derived in terms of the canonical partition function. Comparing the average energy with its variance gives a criterion so that the average energy may approximately represent the state of the system.