Phase rule application — For a single-component (pure) substance at its triple point, the number of thermodynamic degrees of freedom (F) is:

Introduction:
The Gibbs phase rule quantifies how many independent intensive variables must be specified to fix the state of a multiphase, multicomponent system at equilibrium. The triple point is a classic test case.

Given Data / Assumptions:

• Single-component system (C = 1).
• Three phases (P = 3): solid, liquid, and vapor coexist.
• Thermodynamic equilibrium.

Concept / Approach:
The phase rule for non-reacting systems is F = C − P + 2. Substituting C = 1 and P = 3 gives F = 1 − 3 + 2 = 0. Hence neither temperature nor pressure can be varied independently without destroying the three-phase coexistence; both are fixed by the substance’s nature.

Step-by-Step Solution:
Write the phase rule: F = C − P + 2.Insert values: C = 1, P = 3.Compute: F = 0 → state is invariant at the triple point.

Verification / Alternative check:
Phase diagrams show a unique triple-point temperature and pressure for each pure substance, confirming zero degrees of freedom at that point.

Why Other Options Are Wrong:

• Any positive F would imply a range of T or P allows three-phase coexistence, which is false.
• Container volume (an extensive property) does not affect F.

Common Pitfalls:
Confusing degrees of freedom with number of phases; misapplying the rule to reactive systems without modification.

Final Answer:
0