Gibbs Phase Rule Calculator
A binary eutectic with liquid and two solids in equilibrium at constant pressure has 0 degrees of freedom: an invariant point.
0
- Equilibrium is
- invariant (a point: eutectic, peritectic, triple point)
Step-by-step solution
- F = C − P + 1 = 2 − 3 + 1 = 0
Gibbs Phase Rule Formula
F = C − P + 2 (or + 1 at fixed pressure)
C components, P phases in equilibrium, F independent intensive variables
Worked Example
A binary alloy at a eutectic, with three phases at constant pressure:
- F = C − P + 1 = 2 − 3 + 1 = 0
GATE tip
Invariant reactions in binary systems (eutectic, eutectoid, peritectic, monotectic) always involve three phases, because F = 2 − 3 + 1 = 0.
More Thermodynamics and Electrochemistry Calculators
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Gibbs Free Energy Calculator
ΔG = ΔH − TΔS, K = exp(−ΔG/RT)
R = 8.314 J/(mol·K); ΔG = 0 at T = ΔH/ΔS
Example: A reaction with ΔH = −200 kJ/mol and ΔS = −100 J/(mol·K) at 1000 K: Gibbs free energy ΔG = -100 kJ/mol.
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Lever Rule Calculator
Wα = (Cβ − C₀) / (Cβ − Cα)
Fe–C: eutectoid 0.76 wt% C, ferrite 0.022, cementite 6.7 wt% C
Example: An alloy of 35 wt% B between α at 20 wt% and β at 60 wt%: Fraction of α, Wα = 62.5 %.
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Free Energy of Mixing Calculator
ΔG_mix = Ωx_Ax_B + RT(x_A ln x_A + x_B ln x_B)
Ω interaction parameter (0 for ideal); critical temperature T_c = Ω/(2R)
Example: A solution with x_B = 0.3 at 1000 K and Ω = 10 kJ/mol: Free energy of mixing ΔG_mix = -2.97901 kJ/mol.
-
Faraday's Law Electrolysis Calculator
m = I t M η / (z F)
F = 96,485 C/mol, z electrons per ion, η current efficiency
Example: Copper electrowinning at 1000 A for 24 h with 95 % current efficiency: Mass deposited = 27.0293 kg.
Frequently asked questions
Why +1 for metallurgical phase diagrams?
Binary diagrams are drawn at one atmosphere, removing pressure as a variable.
What is the triple point of water?
One component, three phases with variable pressure: F = 1 − 3 + 2 = 0, a single temperature and pressure.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Gibbs Phase Rule Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/gibbs-phase-rule-calculator/
IEEE
Scientific Converters, "Gibbs Phase Rule Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/gibbs-phase-rule-calculator/