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GATE 2025 PH – Question 26

Thermodynamics and Statistical Mechanics · first and second order phase transitions, phase equilibria, critical phenomena. · 1 mark · Multiple select

A schematic Pressure-Temperature diagram of water is shown in the figure. Which of the following option(s) is/are correct?

Pressure–temperature phase diagram of water.
  1. Clausius-Clapeyron equation is valid across the melting curve and the vaporization curve
  2. Melting curve has the highest slope
  3. The critical point exists only for the vaporization curve
  4. Clausius-Clapeyron equation is not valid across the melting curve and the vaporization curve

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Show answer and explanation

Correct answer: (A) Clausius-Clapeyron equation is valid across the melting curve and the vaporization curve; (B) Melting curve has the highest slope; (C) The critical point exists only for the vaporization curve

Explanation

A, B and C are accepted. The coexistence curves obey the Clapeyron relation $dP/dT=\Delta S/\Delta V$. The melting curve is very steep in magnitude; its negative sign for water does not mean a small absolute slope. The ordinary critical point terminates the liquid–vapour curve. The key uses “highest slope” in this magnitude sense.

Official GATE 2025 answer key: https://gate2026.iitg.ac.in/doc/download/2025_Key/PH_Keys.pdf