Question

Consider a schematic isobaric ternary phase diagram A-B-C, shown below, which is contoured with isopleths of liquidus temperatures (in \(^\circ C\)), reveals crystallization behaviour of melt (L) of different compositions during cooling. When a melt of composition "a" lies at a temperature of 1800\(^\circ C\), the variance (or degree of freedom) of the magmatic system is ........ 

Hint:

The variance in a phase diagram is calculated using the Gibbs phase rule. The number of phases and components must be identified first to calculate the degrees of freedom.

Answer 1

Correct Answer: 3

Step 1: Understand the Phase Diagram.
In a ternary phase diagram, the number of components is 3 (A, B, C), and the number of phases involved can vary during cooling. The variance of the system is calculated using the Gibbs phase rule, which is given by: \[ F = C - P + 2 \] Where: - \( F \) is the variance (degrees of freedom), - \( C \) is the number of components (3 for a ternary system), - \( P \) is the number of phases present.

Step 2: Identify the Phases at 1800°C.
At 1800°C, the system is in the liquid + solid phase region, where the phases are liquid (L) and one or more solid phases. At this temperature, the number of phases \( P \) is 2 (L and solid phase).

Step 3: Apply the Gibbs Phase Rule.
Since there are 3 components (A, B, C) and 2 phases (L and solid), the degree of freedom \( F \) is: \[ F = 3 - 2 + 2 = 3 \] Thus, the variance (degrees of freedom) of the magmatic system is 3.