Discuss the concept of thermodynamic fluctuations in the canonical ensemble. Define energy fluctuations and derive an expression for the mean square fluctuation of energy. Using a classical ideal gas, show that the relative fluctuation in energy varies as and hence, justify why thermodynamic calculations are valid for ordinary macroscopic systems.
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What is meant by Cluster Integrals? Express B2 and B3 in terms of Cluster Integrals.
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The time evolution of the quantum state, is given by the Schrödinger wave equation:
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. If the equilibrium energy of the system is approximately 3000kBT, calculate the total number of particles.