What is Gibb’s paradox? Why does it arise? Obtain Sackur-Tetrode equation and
show that it is free from Gibb’s paradox.
a semi-classical derivation of the entropy that does not take into account the indistinguishability of particles, yields an expression for the entropy which is not extensive (is not proportional to the amount of substance in question). This leads to a paradox known as the Gibbs paradox, after Josiah Willard Gibbs. The paradox allows for the entropy of closed systems to decrease, violating the second law of thermodynamics. A related paradox is the "mixing paradox". If one takes the perspective that the definition of entropy must be changed so as to ignore particle permutation, the paradox is averted.
The Sackur–Tetrode equation is an expression for the entropy of a monatomic classical ideal gas which incorporates quantum considerations which
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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.
Define first order phase transition. Derive the Clausius-Clapeyron equation. Plot
(a) entropy, and (b) Gibbs function as a function of temperature for a first order phase transition.
A gaseous system expands from volume V1 to V2 under isobaric conditions.
Calculate the work done in this process.
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.
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
Represent the following processes on the p-V diagrams: i) isobaric, ii) isochoric,
iii) isothermal, iv) cyclic.
Define thermodynamic probability (W) of the macrostate. Establish the relation
between entropy (S) and W.