All Problems

Phase Transformations

Problem 2.204

Demonstrate that the straight line 151-5 corresponding to the isothermal-isobaric phase transition cuts the Van der Waals isotherm so that areas II and III I are equal (Fig. 2.5).

Reveal Answer
2.204. Let us apply Eq. (2.4e) to the reversible isothermic cycle 1234531:1-2-3-4-5-3-1: TdS=dU+pdV T \oint d S=\oint d U+\oint p d V Since the first two integrals are equal to zero, pdV=0\oint p d V=0 as well. The latter equality is possible only when areas II and III I are equal. Note that this reasoning is inapplicable to the cycle 1231,1-2-3-1, for example. It is irreversible since it involves the irreversible transition at point 3 from a single-phase to a diphase state.