Gibbs' Phase Rule Calculator

Calculate the degrees of freedom in a thermodynamic system using Gibbs' phase rule. Enter the number of components and phases to determine how many variables can be changed independently.

Number of chemically independent constituents

Number of physically distinct, homogeneous parts

Temperature for pressure consideration

System pressure in atmospheres

Gibbs' Phase Rule Equation: F = C - P + 2 Where: • F = Degrees of freedom (independent variables) • C = Number of components (chemically independent species) • P = Number of phases (physically distinct states) • 2 = Intensive variables (Temperature and Pressure) Interpretation: • F = 0: Invariant system (fixed T and P) • F = 1: Univariant system (one variable can change) • F = 2: Bivariant system (T and P both variable) • F > 2: Multivariant system
Example 1 (Pure Water - Single Component): C = 1 (H₂O) P = 1 (liquid only) F = 1 - 1 + 2 = 2 Result: Bivariant - T and P can both vary Example 2 (Water at Triple Point): C = 1 (H₂O) P = 3 (solid + liquid + vapor) F = 1 - 3 + 2 = 0 Result: Invariant - T and P are fixed Example 3 (NaCl Water Solution): C = 2 (NaCl + H₂O) P = 2 (solid NaCl + liquid solution) F = 2 - 2 + 2 = 2 Result: Bivariant system Example 4 (Eutectic Point): C = 2 (A + B metals) P = 3 (solid A + solid B + liquid) F = 2 - 3 + 2 = 1 Result: Univariant - one variable determines the system

What is Gibbs' Phase Rule?

Gibbs' Phase Rule (F = C - P + 2) relates the number of components (C), phases (P), and degrees of freedom (F) in a system at equilibrium. It was derived by Josiah Willard Gibbs and is fundamental to understanding phase diagrams in thermodynamics.

What are components in the phase rule?

Components are the minimum number of chemically independent species needed to describe the composition of the system. For water (H₂O), C = 1. For a NaCl-water solution, C = 2. For CaCO₃ ⇌ CaO + CO₂, C = 3 even though there are 4 chemical species.

What is a phase in thermodynamics?

A phase is a physically homogeneous and distinct portion of a system with uniform chemical composition and physical state. Examples include solid, liquid, gas, or different crystal structures (e.g., graphite vs diamond). Different phases are separated by boundaries.

What do degrees of freedom mean?

Degrees of freedom (F) are the number of intensive variables (temperature, pressure, composition) that can be changed independently without altering the number of phases in equilibrium. F = 2 means both T and P can vary; F = 0 means nothing can change.

What is the triple point?

The triple point is where three phases coexist in equilibrium. For water: solid ice, liquid water, and water vapor. At the triple point: F = C - P + 2 = 1 - 3 + 2 = 0 (invariant - fixed T and P). For water triple point: 0.01°C and 0.006 atm.

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