Define thermodynamic probability (W) of the macrostate. Establish the relation
between entropy (S) and W.
The thermodynamic probability (denoted by W) is equal to the number of micro-states which realize a given macrostate, from which it follows that W ^ 1. The thermodynamic probability is connected with one of the basic macroscopic characteristics of the system, the entropy S, by the Boltzmann relation S = k ln W, where k is Boltzmann’s constant.
The thermodynamic probability is not a probability in a mathematical sense. It is used in statistical physics to determine the properties of systems which are in thermodynamic equilibrium (for which the thermodynamic probability attains a maximum value). Of importance in the calculation of the thermodynamic probability is whether the system’s particles
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What is Gibb’s paradox? Why does it arise? Obtain Sackur-Tetrode equation and
show that it is free from Gibb’s paradox.
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.
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.
Using the results in (i) and (ii) obtain an expression for viscosity of the gas.
Discuss its pressure and temperature dependence.
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.
A gaseous system expands from volume V1 to V2 under isobaric conditions.
Calculate the work done in this process.