Abstract
The Maxwell–Boltzmann method of thermodynamics is used solely for exploring systems that only hold independent particles. Unlike Maxwell–Boltzmann method, Gibbs ensemble method has been employed to explore systems composed of dependent particles. Principles, types, and essential assumptions of Gibbs ensembles have been introduced paying special attention to the canonical ensemble. Maxwell–Boltzmann and canonical ensemble methods are linked. Restricting conditions, required constraints and Lagrange multipliers are identified. Next, we probed the canonical distribution, probability of finding, and the most parable distribution of any member to be in specific quantum state. Like Maxwell–Boltzmann method, equilibrium expressions of the thermodynamic quantities are determined using canonical partition function. We derived expressions for canonical partition function for independent, distinguishable, and indistinguishable particles in dilute limit. These enable us to obtain thermodynamic expressions that duplicate the results obtained by implementing Maxwell–Boltzmann method. Finally, the canonical ensemble method used to determine the equilibrium constant, to show that the most probable distribution is the only significant distribution, and to obtain the thermodynamic expressions for the crystalline solid according to Einstein's model.
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