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UPSC MainsGEOGRAPHY-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 answer with clear explanations and relevant examples is crucial.

Model Answer

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Introduction

The study of rocks and minerals necessitates understanding the conditions under which they form and remain stable. Thermodynamic principles play a vital role in deciphering these conditions. The Gibbs Phase Rule, a cornerstone of physical chemistry, provides a quantitative relationship between the number of components, phases, and degrees of freedom in a system at equilibrium. This rule is fundamental to interpreting mineral assemblages and understanding the evolution of geological systems. The ACF diagram, a graphical representation derived from the phase rule, is particularly useful in visualizing and interpreting the compositions of igneous and metamorphic rocks.

Thermodynamic Phase Rule: Definition and Mathematical Expression

The Gibbs Phase Rule states the number of independent variables (degrees of freedom, F) that describe the state of a system at equilibrium. It is mathematically expressed as:

F = C - P + 2

Where:

  • F = Degrees of freedom (number of independent variables)
  • C = Number of components
  • P = Number of phases
  • The '+2' represents temperature and pressure, which are considered intensive variables.

The rule applies to systems in chemical equilibrium, meaning that the chemical potential of each component is the same in all phases.

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 independent variables (e.g., temperature, pressure, and the compositions of the components) can be varied without changing the number of phases present in the system.

Principle of the ACF Diagram

The ACF diagram (Alkali – Calcium – Feldspar diagram) is a triangular diagram used to represent the compositions of igneous and metamorphic rocks, specifically focusing on the alkali feldspar (A), plagioclase feldspar (C), and foid (F) mineral phases. It’s a special application of the Gibbs Phase Rule to a three-component system.

Key Principles:

  • Ternary System: The ACF diagram represents a ternary system, meaning it considers three components. In this case, the components are Na2O, CaO, and K2O.
  • Phase Rule Application: For a ternary system (C=3) at fixed temperature and pressure, the phase rule simplifies to F = 3 - P. The diagram shows the stable phase assemblages as a function of composition.
  • Phase Boundaries: The boundaries of the different fields on the ACF diagram represent the conditions under which two or three phases coexist in equilibrium.
  • Univariant Fields: Within each field, the system is univariant (F=1), meaning that only one variable (e.g., temperature) can be changed independently without altering the number of phases.
  • Invariant Points: The points where three phase boundaries intersect represent invariant points (F=0), where the system is completely defined and no variables can be changed without altering the phase assemblage.

The ACF diagram is particularly useful in interpreting the crystallization history of igneous rocks and the metamorphic reactions that have occurred in metamorphic rocks. By plotting the composition of a rock on the ACF diagram, geologists can infer the conditions under which it formed and the mineral assemblages that are stable under those conditions.

Conclusion

The Gibbs Phase Rule is a powerful tool for understanding the stability of mineral assemblages and the conditions under which rocks form. Applying this rule, we determined that a system with 8 components and 5 phases possesses 5 degrees of freedom. The ACF diagram, a graphical representation derived from the phase rule, provides a visual framework for interpreting the compositions of rocks and understanding their petrogenetic history. These principles are fundamental to the broader field of petrology and geochemistry, enabling us to decipher the complex processes that shape our planet.

Answer Length

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Additional Resources

Key Definitions

Phase
A phase is a physically distinct, chemically homogeneous, and mechanically separable portion of a system. Examples include solid minerals, liquids, and gases.
Component
A component is the smallest number of chemically independent species necessary to define the composition of all phases in the system. For example, in a system containing calcite (CaCO3) and dolomite (CaMg(CO3)2), the components are CaO, MgO, and CO2.

Key Statistics

The Earth's crust is composed of approximately 98.5% silicate minerals, highlighting the importance of understanding their phase equilibria. (Source: Mason, B. (1979). Principles of Geochemistry. John Wiley & Sons)

Source: Mason, B. (1979)

Approximately 3,500 different minerals have been identified on Earth, each with its unique chemical composition and physical properties. (Source: Mineralogical Society of America, as of 2023)

Source: Mineralogical Society of America (2023)

Examples

Granite Formation

The formation of granite, a common igneous rock, involves the crystallization of quartz, feldspar, and mica from a magma. The phase rule helps predict which minerals will crystallize at different temperatures and pressures, and the ACF diagram can be used to understand the relative proportions of alkali and plagioclase feldspars.

Frequently Asked Questions

▶What is the significance of the '+2' in the Gibbs Phase Rule?

The '+2' accounts for the two intensive variables, temperature and pressure, which are always considered when describing the state of a system at equilibrium. These variables are independent of the amount of substance present.

Topics Covered

GeologyPetrologyGeochemistryPhase EquilibriaMineralogyThermodynamics
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