The Gibbs Phase Rule
(named after J.W. Gibbs)
In classical Thermodynamics we consider only two forms of energy, namely
heat and work.
Reminder:
This is expressed in the first law of thermodynamics as:
dU =  w - PdV.
(The total change of internal Energy is equal to the change in heat content plus the work absorbed by the system).
Combined with the second law, this equation can be written (for a closed system) as:
dU = TdS - PdV.
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We can therefore change the state of a closed system only by changing the heat content or by changing the Volume
of the system.
| Variables related to heat content: | T (Temperature) and S (Entropy) |
| Variables related to work: | P (Pressure) and V (Volume) |
The Gibbs Phase Rule: P + F = C + 2
- P = Maximum number of phases in a stable assemblage
- F = Degree of freedom (Number of independent Variables that can be varied independently
without changing the assemblage)
- C = number of components in the system
- 2 = (This is the maximum number of independent variables (besides the compositional
variables) a thermodynamic system can have: one related to heat, the other to work)
Given a system with C components and list of all (Pt) possible phases, we can easily
calculate
- the maximum number of possible assemblages with C phases (assemblages with a stability
field, F=2)
- The maximum number of possible assemblages with C+1 phases (assemblages defining
a reaction, F=1)
- The maximum number of possible assemblages with C+2 phases (The maximum number of
phases that can coexist, F=0)
Fill in numbers for C and Pt:
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