Question

A hypothetical rock contains the assemblage kyanite, sillimanite and quartz. The variance (degree of freedom) of the assemblage is_____. (In integer)

Answer 1

Correct Answer: 1

To solve the problem of finding the variance (degree of freedom) of a mineral assemblage containing kyanite, sillimanite, and quartz, we will use the phase rule formula in thermodynamics of geology. The phase rule is expressed as:

F = C - P + 2

 

Where:

• F is the variance or the degree of freedom.
• C is the number of components.
• P is the number of phases.

In this context, the components typically refer to the chemical components necessary to describe the minerals. For kyanite, sillimanite, and quartz, the principal components are usually aluminum (Al) and silicon dioxide (SiO₂), which implies:

• C = 2 (representing Al₂SiO₅ and SiO₂ as simplified representations).
• P = 3 (the phases are kyanite, sillimanite, and quartz).

Substituting into the phase rule formula:

F = 2 - 3 + 2

 

= 1

 

The degree of freedom F is 1.