1. Having discussed the need for the modification of the perfect gas equation, establish the van der Waals’ equation of state for a real gas. With the help of this equation, derive an expression for one of the critical constants. [7+3]
OR
Write down the postulates regarding to
Fermi-Dirac statistics. Derive an expression for the probability distribution
of particles obeying Fermi-Dirac statistics. Explain electron gas in a metal.
[2+6+2]
2.
Establish Clausius-Clapeyron’s latent heat
equation starting from Maxwell’s thermodynamic relation. Explain the
significance of this equation. [5+3]
3.
Answer any one question. [3]
(a)
What is Gibbs free energy? Show that Gibbs free
energy remains constant in an isothermal-isobaric process.
(b)
The change in temperature for the van der Waals’
gas due to Joule-Thomson effect is given by
$dT=\frac{p_1-p_2}{c_p}(\frac{2a}{RT}-b)$ where the symbols carry their usual
meanings. Explain its consequences.
4.
Attempt all questions. [2.5+2.5]
(a)
What do you mean by the third law of
thermodynamics?
(b)
Define Fermions, Fermi energy and Fermi level.
5.
Calculate the change in entropy when 1 gram atom
of solid mercury at its melting point is raised to a temperature of $40^oC$.
Given for mercury: melting point = $-39^oC$, latent heat of fusion=3.0 cal/g,
mean specific heat= 0.0335 cal/g.K and one gram atom of mercury= 200 g. [5]
6.
The molecular diameter of nitrogen is 3.5 $A^o$.
Calculate the mean free path at temperature $27^oC$ and pressure 1 atmosphere.
(Boltzmann constant= $1.38*10^{-23}$ J/K.) [5}