Define Fermi energy. Show that the expression of Fermi-energy is given by
How it is related with Fermi-temperature.
The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature. In a Fermi gas, the lowest occupied state is taken to have zero kinetic energy, whereas in a metal, the lowest occupied state is typically taken to mean the bottom of the conduction band.
The Fermi temperature 
, is defined as the temperature corresponding to the Fermi energy such that :
With the Fermi energy of the order of a few eV, the Fermi temperature works out to be of the order of several thousand Kelvin (approximately 10,000
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Using the results in (i) and (ii) obtain an expression for viscosity of the gas.
Consider a classical linear oscillator with
ε = p2/2m + bx2
where b is a constant. Assuming that the oscillator is in thermal equilibrium with a
heat reservoir at temperature T, calculate (i) the mean kinetic energy, (ii) the mean
potential energy for an assembly of N such oscillators.
Discuss its pressure and temperature dependence.
Write the first law of thermodynamics for a gaseous system. Show that the
expression of difference of heat capacities of a gas at constant pressure and at
constant volume is given by
b) 2 kg of water is heated from 0°C to 100°C and converted into steam at the same temperature. Calculate the increase in entropy, given that specific heat of water is
4.18 × 103 J kg−1 K−1 and Latent heat of vaporisation is 2.27 × 107 J kg−1.
Define Fermi energy. Show that the expression of Fermi-energy is given by
How it is related with Fermi-temperature.
Write Mayer’s formula. The molar heat capacities of a gas at constant pressure
and constant volume are 28.8 J mol−1 K−1 and 20.5 J mol−1 K−1 respectively.
Calculate the gas constant.
Write Onne’s equation. Using van der Waals’ equation, obtain an expression of
Boyle temperature (TB) in terms of van der Waals’ constants and hence show that the
Boyle’s temperature is related to critical temperature (TC) through the relation
TB = 3.375TC