Question

According to the Gibbs Phase Rule (F = C - P + 2), at the triple point of a pure metal (e.g., where solid, liquid, and vapour coexist), the degrees of freedom F is

• A. 1 (P can be varied)
• B. 2 (Both T and P can be varied)
• C. 0 (neither T nor P can be varied)
• D. 3

Hint:

At a triple point, $F = 0$ (invariant).
Along a phase boundary line, $P = 2 \implies F = 1$ (univariant).
Inside a single-phase region, $P = 1 \implies F = 2$ (bivariant).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks to find the degrees of freedom ($F$) at the triple point of a pure metal using the Gibbs Phase Rule.

Step 2: Key Formula or Approach:

• Gibbs Phase Rule: \[ F = C - P + 2 \] where:
$F$ is the degrees of freedom (independent intensive variables like temperature and pressure),
$C$ is the number of chemical components in the system,
$P$ is the number of phases coexisting in equilibrium.

Step 3: Detailed Explanation:

• Identify the parameters for the triple point of a pure metal:
1. Since it is a "pure metal", there is only one chemical species present. Thus, the number of components is: \[ C = 1 \] 2. At the "triple point", three phases (solid, liquid, and vapour) coexist in thermodynamic equilibrium. Thus, the number of coexisting phases is: \[ P = 3 \]
• Substitute $C = 1$ and $P = 3$ into the Gibbs Phase Rule:
\[ F = 1 - 3 + 2 = 0 \]
• A system with $F = 0$ is called "invariant".
This means that the triple point occurs at a unique, fixed temperature and pressure.
Neither temperature ($T$) nor pressure ($P$) can be varied. If we attempt to change either of these variables, the equilibrium is disrupted, and one or more phases will disappear.

Step 4: Final Answer:
The degrees of freedom $F$ is 0, which means neither temperature nor pressure can be varied.