Phase Transition
المؤلف:
Sidney B. Cahn, Gerald D. Mahan And Boris E. Nadgorny
المصدر:
A GUIDE TO PHYSICS PROBLEMS
الجزء والصفحة:
part 2 , p 30
30-8-2016
1529
Phase Transition
The curve separating the liquid and gas phases ends in the critical point Vc, τc, where (∂P/∂V)τ = τc = 0. Using arguments based on thermodynamic stability, determine
at the critical point.
SOLUTION
For a system at equilibrium with an external reservoir, the Gibbs free energy G = F + P0V is a minimum. Any deviation from equilibrium will raise G:
(1)
where P0 is the pressure of the reservoir. Expanding δF in δV, we have
(2)
Since ∂F/∂V = -P, we may rewrite (2) as
(3)
At the critical point, ∂P/∂V = 0, so (3) becomes
(4)
For (4) to hold for arbitrary δV, we have
(5)
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