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GATE 2023 MT – Question 11

Metallurgical Thermodynamics · Phase equilibria and phase diagrams · 1 mark · Multiple choice

At one atmosphere, $\alpha$-Fe transforms to $\gamma$-Fe above 912 °C. The density of $\gamma$-Fe exceeds that of $\alpha$-Fe. Choose the correct statement.

  1. Increasing the pressure above one atmosphere lowers the α-Fe to γ-Fe transformation temperature.
  2. Increasing the pressure above one atmosphere raises the α-Fe to γ-Fe transformation temperature.
  3. Molar volume of γ-Fe is higher than the molar volume of α-Fe.
  4. Pressure change will not have any effect on the α-Fe to γ-Fe transformation temperature.

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Show answer and explanation

Correct answer: (A) Increasing the pressure above one atmosphere lowers the α-Fe to γ-Fe transformation temperature.

Explanation

The denser gamma phase has smaller molar volume, so $\Delta V=V_\gamma-V_\alpha<0$. Heating favours gamma, giving $\Delta S>0$. Clapeyron gives $dT/dP=\Delta V/\Delta S<0$. Higher pressure therefore lowers the transition temperature, **A**.