State the Virial theorem and prove Boyle’s law using it.
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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.
For the grand canonical ensemble, obtain an expression for the ensemble average energy and ensemble average particle numbers.
Using entropy as a function of temperature and pressure, obtain the first Ehrenfest’s equation.
What is meant by Cluster Integrals? Express B2 and B3 in terms of Cluster Integrals.
The time evolution of the quantum state, is given by the Schrödinger wave equation:
Obtain expression for average energy for the canonical ensemble in terms of partition function Z.
A monthly demand for commodity is a continuous random distribution with probability distribution function given as:
where N is normalization constant. Obtain the value of N so that the function is normalized and hence, find the mean and the variance.