Dalvoy Logo
Dalvoy
UPSC MainsGEOLOGY-PAPER-II201910 Marks
Q4.

Define thermodynamic phase rule and state its mathematical expression. Determine the degree of freedom for a system under equilibrium with 8 components and 5 mineral phases. Briefly discuss the principle of ACF diagram.

How to Approach

This question requires a demonstration of understanding of fundamental principles in petrology and geochemistry. The approach should begin with a clear definition of the thermodynamic phase rule, followed by its mathematical expression. Then, apply the rule to the given system (8 components, 5 phases) to calculate the degree of freedom. Finally, explain the principle behind the ACF diagram, highlighting its utility in understanding ternary systems. A structured response with clear definitions and calculations is crucial.

Model Answer

0 min read

Introduction

The study of rocks and minerals necessitates understanding the conditions under which they form and remain stable. Thermodynamic principles, particularly the phase rule, provide a framework for predicting the number of coexisting phases in a system at equilibrium. Developed by J. Willard Gibbs, the phase rule is a powerful tool in petrology and geochemistry, allowing us to interpret mineral assemblages and infer the physical conditions (temperature, pressure, composition) of rock formation. The ACF diagram, a graphical representation of ternary systems, is a direct application of the phase rule and is widely used in understanding the stability of minerals in metamorphic rocks.

Thermodynamic Phase Rule: Definition and Mathematical Expression

The thermodynamic phase rule describes the relationship between the number of phases (P), components (C), and degrees of freedom (F) in a system at equilibrium. A phase is a physically distinct and homogeneous portion of a system, such as a solid mineral, a liquid melt, or a gas. A component is the minimum number of chemically independent constituents required to define the composition of all phases in the system. The degree of freedom represents the number of intensive variables (like temperature, pressure, or composition) that can be changed independently without altering the number of phases present.

The mathematical expression of the phase rule is:

F = C - P + 2

Where:

  • F = Degrees of freedom
  • C = Number of components
  • P = Number of phases
  • 2 represents the intensive variables – temperature and pressure.

Degree of Freedom Calculation for the Given System

For a system under equilibrium with 8 components (C = 8) and 5 mineral phases (P = 5), the degree of freedom can be calculated as follows:

F = C - P + 2

F = 8 - 5 + 2

F = 5

Therefore, the system has 5 degrees of freedom. This means that five intensive variables (temperature, pressure, and three compositional variables) can be independently varied without changing the number of phases present.

Principle of the ACF Diagram

The ACF diagram is a triangular diagram used to represent the compositions of ternary systems – systems with three components. In petrology, it is commonly used to represent the compositions of metamorphic rocks and their constituent minerals. The vertices of the triangle represent the end-member components, typically:

  • A – Anorthite (CaAl2Si2O8)
  • C – Albite (NaAlSi3O8)
  • F – Feldspar (KAlSi3O8)

The diagram is based on the principle that the composition of any point within the triangle can be expressed as a combination of the three end-member components. The phase rule dictates the number of degrees of freedom within the diagram. For example:

  • If three phases coexist (P=3), then F = 3 - 3 + 2 = 2. This means that temperature and pressure can be varied independently.
  • If two phases coexist (P=2), then F = 3 - 2 + 2 = 3. This means that temperature, pressure, and one compositional variable can be varied independently.
  • If one phase exists (P=1), then F = 3 - 1 + 2 = 4. All four variables can be varied independently.

The ACF diagram is used to determine the stability fields of different mineral assemblages under varying conditions. By plotting the compositions of rocks and minerals on the diagram, petrologists can infer the P-T conditions under which those rocks and minerals formed. It’s a powerful tool for interpreting metamorphic petrology and understanding the evolution of rocks within the Earth’s crust.

The diagram is particularly useful in understanding the reactions involving plagioclase feldspars and alkali feldspars, and helps in interpreting the metamorphic history of rocks.

Conclusion

The thermodynamic phase rule is a fundamental principle in geology, providing a quantitative framework for understanding phase equilibria. Applying this rule to systems with varying components and phases allows us to predict the degrees of freedom and interpret the conditions of rock formation. The ACF diagram, a graphical application of the phase rule, is an invaluable tool for petrologists in deciphering the complex histories of metamorphic rocks and understanding the interplay between composition, temperature, and pressure.

Answer Length

This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.

Evaluate your handwritten answer in under a minute

Free trial available • Trusted by 1,00,000+ aspirants

Additional Resources

Key Definitions

Equilibrium
A state in which opposing forces or processes are balanced, resulting in no net change. In geology, it refers to the state where phases are stable and do not spontaneously change.
Component
In the context of the phase rule, a component is a chemically independent species that is necessary to define the composition of all phases in the system. It represents the minimum number of chemical constituents needed.

Key Statistics

The Earth's crust is composed of approximately 98.5% silicate minerals (as of 2023 data from the US Geological Survey).

Source: US Geological Survey

Approximately 3,800 known minerals exist, each with a unique chemical composition and crystal structure (Mindat.org, as of November 2023).

Source: Mindat.org

Examples

Granite Formation

The formation of granite, a common igneous rock, exemplifies the phase rule. The coexistence of quartz, feldspar, and mica (phases) within a system of defined components (SiO2, Al2O3, Na2O, K2O, CaO) is governed by temperature, pressure, and composition, as predicted by the phase rule.

Frequently Asked Questions

▶How does pressure affect phase diagrams?

Increasing pressure generally favors denser phases and can shift phase boundaries, leading to the formation of different mineral assemblages. High-pressure metamorphism, for example, results in the formation of minerals like eclogite.

Topics Covered

GeologyPetrologyGeochemistryPhase EquilibriaMineralogyThermodynamics
Back to all GEOLOGY-PAPER-II 2019 questions