Fugacity Based Phase Equilibrium Criterion for Pure Component System Civil Engineering (CE) Notes | EduRev

Thermodynamics

Civil Engineering (CE) : Fugacity Based Phase Equilibrium Criterion for Pure Component System Civil Engineering (CE) Notes | EduRev

The document Fugacity Based Phase Equilibrium Criterion for Pure Component System Civil Engineering (CE) Notes | EduRev is a part of the Civil Engineering (CE) Course Thermodynamics.
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Fugacity-based phase equilibrium criterion for pure component system

The general criterion of thermodynamic equilibrium has been defined by eqn. 6.38. Applying it to, for example, a vapour (V) and liquid (L) system of a pure component ‘i’ we have:

Fugacity Based Phase Equilibrium Criterion for Pure Component System Civil Engineering (CE) Notes | EduRev             ......(6.91)

However, for a pure component system:  Fugacity Based Phase Equilibrium Criterion for Pure Component System Civil Engineering (CE) Notes | EduRev

Thus:Fugacity Based Phase Equilibrium Criterion for Pure Component System Civil Engineering (CE) Notes | EduRev             ......(6.92)

Thus, using eqn. 6.91 and 6.92 we have: 

Fugacity Based Phase Equilibrium Criterion for Pure Component System Civil Engineering (CE) Notes | EduRev             ......(6.93)

The above equation may be generalized for any other types of phases. However, the eqn. 6.93 is rendered more easily applicable if the chemical potential is replaced by fugacity. Thus integrating eqn. 6.86 between vapour and liquid states of a pure component:  

Fugacity Based Phase Equilibrium Criterion for Pure Component System Civil Engineering (CE) Notes | EduRev             ......(6.94 & 6.95)

Now applying  eqn. 6.93 to 6.95 it follows   Fugacity Based Phase Equilibrium Criterion for Pure Component System Civil Engineering (CE) Notes | EduRev

Or:

Fugacity Based Phase Equilibrium Criterion for Pure Component System Civil Engineering (CE) Notes | EduRev             ......(6.96)

In eqn. 6.86 Fugacity Based Phase Equilibrium Criterion for Pure Component System Civil Engineering (CE) Notes | EduRev  indicates the value for either saturated liquid or saturated vapor, this is because the coexisting phases of saturated liquid and saturated vapor are in equilibrium. Since under such condition the pressure is Fugacity Based Phase Equilibrium Criterion for Pure Component System Civil Engineering (CE) Notes | EduRev we can write:

Fugacity Based Phase Equilibrium Criterion for Pure Component System Civil Engineering (CE) Notes | EduRev
Thus, employing eqn. 6.86 again, it follows:

Fugacity Based Phase Equilibrium Criterion for Pure Component System Civil Engineering (CE) Notes | EduRev               ......(6.97)

Both eqns. 6.93, 6.96 and 6.97 represent equivalent criterion of vapor/liquid equilibrium for pure species.

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