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The canonical partition function for an ideal gas is computed and ideal gas equation is derived. A measurement of the Boltzmann constant k is discussed using effusion of gas molecules through a hole. Distribution function of molecules in presence of gravity is as function of height is derived.

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.

Statistical mechanics is based on the fundamental assumption that all microstates of an isolated system are equally

We begin with scope of thermodynamics and emphasize wide range of its applications. Thermodynamics takes a macroscopic view of a physical system. It laws are based on experience. Statistical mechanics is a microscopic view of physical systems and is based on established laws of classical and quantum mechanics.

In this lecture the binomial distribution, the random walk problem and the Poisson distributions are introduced and their interconnections and important properties are discussed.

For an experiment whose outcomes of simple events 1,...n have probabilities \(p_1, p_2, ...p_n\), the uncertainty, \(H(p)\) ,is defined a

$$ H(p_1, p_2, .., p_n) = − \sum_n   p_n \ln p_n $$

Some important properties of uncertainty are Taking several examples, several properties of the uncertainty are brought out. The uncertainty is maximum when all probabilities are equal. It is zero when one of the events has probability1 and all other events have zero probability. The uncertainty for case of two independent random variables is the sum of individual uncertainties. By means of examples, it is shown that increase (decrease) in uncertainty is associated with decrease (increase) in information.