Obtain expression for average energy for the canonical ensemble in terms of partition function Z.
For a canonical ensemble, the system is in thermal equilibrium at temperature (T) with a heat bath. The probability (P_i) of the system being in a microstate (i) with energy (E_i) is given by the Boltzmann factor: [ P_i = ____ _____ ___ ________ ________ ___.
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btain the phase space area enclosed by a classical harmonic oscillator for energies ranging from 0 to E.
A proton inside a nucleus
may have speed upto
. How many quantum states are available to it?
State and prove quantum Liouville equation.
Using entropy as a function of temperature and pressure, obtain the first Ehrenfest’s equation.
Show under what condition Poisson distribution tends to Normal distribution.
For the grand canonical ensemble, obtain an expression for the ensemble average energy and ensemble average particle numbers.
The Hamiltonian for the non-relativistic, non-interacting, monoatomic ideal gas is given by
where m is the mass of the particle and U(qi) is the potential energy. Obtain an expression of the phase space volume of the energy shell and hence obtain an expression of number of microstates.