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GATE 2025 MT – Question 37

Metallurgical Thermodynamics · Phase equilibria and phase diagrams · 2 marks · Multiple choice

Consider the phase diagram of a one-component system. $V_\alpha$, $V_\beta$, and $V_{Liquid}$ are the molar volumes of the α, β, and liquid phases, respectively. Which statement is true? Given: both molar enthalpy changes $\Delta H_{\alpha\to\beta}$ and $\Delta H_{\beta\to Liquid}$ are positive.

Diagram for GATE 2025 MT question 37
  1. $V_\alpha<V_\beta$ and $V_\beta<V_{Liquid}$
  2. $V_\alpha>V_\beta$ and $V_\beta<V_{Liquid}$
  3. $V_\alpha<V_\beta$ and $V_\beta>V_{Liquid}$
  4. $V_\alpha>V_\beta$ and $V_\beta>V_{Liquid}$

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Correct answer: (B) $V_\alpha>V_\beta$ and $V_\beta<V_{Liquid}$

Explanation

Clapeyron’s equation is dP/dT=ΔH/(TΔV). Both enthalpy changes are positive. The α→β boundary slopes negatively, so Vβ−Vα<0. The β→liquid boundary slopes positively, so Vliquid−Vβ>0. Hence **Vα>Vβ and Vβ<Vliquid, B**.