Question

The given P-T diagram shows the relative stability ranges of andalusite, sillimanite, and kyanite. The difference in degrees of freedom at points X and Y is _________. 

Hint:

The degrees of freedom in a phase diagram can be determined using the Gibbs phase rule, which is based on the number of components and phases present in equilibrium.

Answer 1

Correct Answer: 2

Step 1: Understanding the Degrees of Freedom. 
In a phase diagram, the degrees of freedom (also known as the variance) represent the number of independent variables that can be varied without changing the number of phases in equilibrium. The degrees of freedom can be calculated using the Gibbs phase rule, which is given by: \[ F = C - P + 2, \] where: - \(F\) is the degrees of freedom, - \(C\) is the number of components (chemical substances), - \(P\) is the number of phases in equilibrium. In the given diagram, at point \(X\) (where kyanite is stable) and point \(Y\) (where andalusite is stable), the phases in equilibrium are 2 (solid phases). The system has 1 component (aluminosilicate). 
Step 2: Calculate the Degrees of Freedom at Points X and Y. 
At both points X and Y, the number of components is 1, and the number of phases is 2. Using the Gibbs phase rule: \[ F = 1 - 2 + 2 = 1. \] Thus, the degrees of freedom at both points X and Y are 1. 
Step 3: Conclusion. 
The difference in degrees of freedom at points X and Y is 1.