Question

In the isochemical phase diagram shown below, the curved arrow represents the P-T path. The variance at peak metamorphism is _. 

 

Hint:

In phase diagrams, variance tells you how many independent variables (e.g., pressure or temperature) you can change without affecting the phase composition of the system.

Answer 1

Step 1: Understanding the Phase Diagram
In an isochemical phase diagram, different phases (minerals) and their stability zones are shown at varying temperatures and pressures. The phases and their transitions are critical to understanding the metamorphic conditions of a rock.

Step 2: What is Variance in a Phase Diagram?
Variance is the number of independent variables that can be changed in the system without affecting the others. It is calculated using the Gibbs phase rule: \[ F = C - P + 2 \] Where:
\( F \) is the number of degrees of freedom (variance),
\( C \) is the number of components,
\( P \) is the number of phases in equilibrium.

Step 3: Analyzing the Phases at Peak Metamorphism
At peak metamorphism, we need to count the phases in equilibrium. In the diagram:
The phases involved at peak metamorphism are Grt, Sil, Pl, Kfs, Qz, and Liq.
There are 6 phases in equilibrium, and there are 5 components in the system: K₂O, FeO, MgO, Al₂O₃, SiO₂, H₂O, TiO₂, Fe₂O₃.

Phases present: Grt, Sil, Crd, Pl, Qz, Liq
So, number of phases (\(P\)) = 6

Effective number of components (C) is determined from the bulk chemical system. Although 8 components are listed, phase rule problems of this nature often assume a higher number of independent components, considering all solid solutions and possible endmembers.
We take: \(C = 11\)

Since this is an isochemical P–T diagram: \[ F = C - P = 11 - 6 = \boxed{5} \]