Question

Which of the following schematic plots correctly represent(s) a first order phase transition occurring at temperature 𝑇=𝑇_c? Here 𝑔, 𝑠, 𝑣 are specific Gibbs free energy, entropy and volume, respectively

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is B, C

To solve this problem, we need to understand the characteristics of a first-order phase transition. A first-order phase transition involves a discontinuous change in a property of the substance, such as volume or entropy, at a specific temperature. At the transition temperature \(T = T_c\), these properties experience an abrupt change, while the Gibbs free energy remains continuous across the transition.

Key Characteristics of First-Order Phase Transitions: 

• Gibbs Free Energy (\(g\)): It remains continuous at the transition temperature but has a kink, indicating a discontinuity in its derivative.
• Entropy (\(s\)) and Volume (\(v\)): Both properties show a discontinuous jump, as they are first derivatives of Gibbs free energy with respect to temperature and pressure, respectively.

Examining the Options:

1. Option 1: Not shown as correct — if it shows a continuous line without sudden changes, it's incorrect for both \(s\) and \(v\).
2. Option 2: Represents entropy (\(s\)) with a discontinuity at \(T = T_c\). This is characteristic of a first-order phase transition.
3. Option 3: Represents volume (\(v\)) with a discontinuity at \(T = T_c\). Again, this is characteristic of a first-order phase transition.
4. Option 4: Not shown as correct — if it represents Gibbs free energy (\(g\)) without a kink or shows discontinuities, it's incorrect.

Based on the characteristics of a first-order phase transition, Options 2 and 3 best represent the correct schematic plots because they display the necessary discontinuities in entropy and volume, respectively, at the critical temperature \(T = T_c\).

Hence, the correct answer is Option 2 and Option 3:

•  - Entropy (\(s\)) behavior
•  - Volume (\(v\)) behavior