The main result for grand canonical ensemble are summarized. The Planck’s law and the Stephan Boltzmann law for black body radiation are derived.
Using the grand canonical ensemble method, the Bose Einstein and Fermi Dirac distribution formula are derived. An expression for the partition function for photons is proved and result on the mean number of particles in terms of grand canonical partition function is obtained
Quantum effects in macroscopic systems appear in two ways. The first the energy levels are quantized. The quantization of energy levels does not need any modification in the framework. Secondly identical nature of particles constituting the system. This requires a new approach to enumerating the microstates. The microstates are not labeled by coordinates and momenta as is the case in classical theory. In quantum theory the microstates are specified by giving the number of particles for different levels.
In this lecture we derive law of equipartition of energy under the assumption that the energy is quadratic function of some variable such as coordinates and momenta. The classical theory of specific heat of gases is given and the Einstein model of taking quantum corrections is briefly discussed. A comparison of the classical and quantum model with experiments is given.
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