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.
The ï¬rst-order phase transition can be deï¬ned more systematically by considering the
Gibbs thermodynamic potential. In a ”ï¬rst-order phase transition”, the ï¬rst derivative of
the Gibbs potential is discontinuous across the phase boundary. Also, according to the
relations:
Clausius-Clapeyron equation:- This is again a result for first-order phiLse transitions. Suppose two phLses of a one- «»lnponent system coexist on a coexistence line (e.g. liquid and gas on the condensation line). We have If we move along the coexistence line by differential amounts dp and dT, we will have , since we are still at coexistence. Then:
But using the Gibbs-Dtlhem equation, we have
(where s is the entropy per particle), so that we arrivv at the Clausius-Clapeyron equation:
where v l/p V/ N is the specific volume (volume per particle), pa and
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A gaseous system expands from volume V1 to V2 under isobaric conditions.
Calculate the work done in this process.
The average energy of helium molecules is ¯E = 2.89 ×10−21J. Calculate their average speed (¯v).
Write principal merits of a Pt-resistance thermometer.
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
Define thermodynamic probability (W) of the macrostate. Establish the relation
between entropy (S) and W.
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.
What is Gibb’s paradox? Why does it arise? Obtain Sackur-Tetrode equation and
show that it is free from Gibb’s paradox.