Free · Chemical thermodynamics calculators 🌡️

Gibbs Phase Rule with Fixed Conditions

Calculate equilibrium degrees of freedom from independent components and phases, with zero, one or two fixed temperature/pressure constraints.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

For one component in three coexisting phases, leaving temperature and pressure unconstrained gives F = 1 − 3 + 2 = 0: the invariant triple-point case.

Degrees of freedom = independent components − equilibrium phases + unfixed temperature/pressure variables

Worked example

Enter these known values and leave the other values blank.

Independent chemical components
1
Coexisting equilibrium phases
3
Fixed independent conditions
Neither are constant
Remaining degrees of freedom
0

Assumptions and limitations

  • Components and phases are positive whole numbers. Components mean the minimum independent chemical constituents, which may differ from the number of species when reactions or constraints exist.
  • The unconstrained Gibbs rule has two temperature/pressure variables. Fixing one independent condition subtracts one degree of freedom; fixing two subtracts two.
  • The rule assumes equilibrium and the usual thermodynamic variables. Electrical, magnetic, surface and other additional constraints are not counted automatically.
  • A negative result is rejected as inconsistent with the specified independent constraints. At an invariant point, do not subtract a supposedly fixed variable that is already determined by phase coexistence.

Common questions

Does a zero result mean no system exists?

No. Zero means the equilibrium is invariant under the counted independent variables. Negative values instead indicate inconsistent counting or constraints.

References

Bookify requires at least one component and one phase for the equilibrium system.

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