Question:
At composition $C_a$, the free energy curve has a minimum. Which statement is correct?
At composition $C_a$, the free energy curve has a minimum. Which statement is correct?
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Global minimum of Gibbs free energy corresponds to absolute stability.
Updated On: Jun 29, 2026
- Unstable equilibrium state
- Metastable state
- Phase boundary composition
- Stable composition of $\alpha$ phase
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The Correct Option is D
Solution and Explanation
Concept:
Gibbs free energy determines thermodynamic stability:
- Minimum $G$ → stable equilibrium
- Local minimum → metastable
- Maximum → unstable
Step 1: Interpret given condition.
At $C_a$: \[ G \text{ is minimum} \] This implies: \[ \frac{dG}{dC} = 0,\quad \frac{d^2G}{dC^2} > 0 \]
Step 2: Check stability meaning.
A minimum in Gibbs free energy indicates: - system is in equilibrium - no spontaneous tendency to change composition - thermodynamically stable state
Step 3: Evaluate options.
(A) unstable → false (B) metastable → only local minimum in constrained conditions (C) phase boundary → occurs at common tangent points (D) stable α-phase composition → correct Final Answer: \[ \boxed{\text{Stable composition of } \alpha \text{ phase}} \]
Step 1: Interpret given condition.
At $C_a$: \[ G \text{ is minimum} \] This implies: \[ \frac{dG}{dC} = 0,\quad \frac{d^2G}{dC^2} > 0 \]
Step 2: Check stability meaning.
A minimum in Gibbs free energy indicates: - system is in equilibrium - no spontaneous tendency to change composition - thermodynamically stable state
Step 3: Evaluate options.
(A) unstable → false (B) metastable → only local minimum in constrained conditions (C) phase boundary → occurs at common tangent points (D) stable α-phase composition → correct Final Answer: \[ \boxed{\text{Stable composition of } \alpha \text{ phase}} \]
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