Fugacity: It is derived from Latin, expressed as fleetness or escaping ...

Phase Equilibrium
Criteria for phase equilibrium: If a system says to be in thermodynamic equilibrium,
Temperature, pressure must be constant and there should not be any mass transfer.
The different criteria for phase equilibrium are
At Constant U and V: An isolated system do not exchange mass or heat or work with
surroundings. Therefore dQ=0, dW=0 hence dU=0. A perfectly insulated vessel at
constant volume dU=0 and dV=0.
dS
U , V
0
At Constant T and V: Helmoltz free energy is given by the expression
A U TS
U A TS
on differentiating
dU dA TdS SdT
we know that
dU TdS PdV
TdS PdV dA TdS SdT
dA PdV
SdT
Under the restriction of constant temperature and volume the equation simplifies to
dAT
, V
0
At Constant P and T
The equation defines Gibbs free energy
G H TS
G U PV TS
dG dU PdV VdP TdS SdT
dU dG PdV VdP
TdS SdT
dU dG dG PdV TdS
Under the restriction of constant Pressure and Temperature the equation simplifies to
dGT
, P
0
This means the Gibbs free energy decreases or remains un altered depending on the
reversibility and the irreversibility of the process. It implies that for a system at
equilibrium at given temperature and pressure the free energy must be minimum.