GATE 2025 CY – Question 35
The expressions for the vapour pressure of solid ($p_1$) and vapour pressure of liquid ($p_2$) phases of a pure substance, respectively, are $$\ln p_1=-2000/T+5,\qquad\ln p_2=-4000/T+10.$$ The triple point temperature of this substance is ____ K (in integer).
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Correct answer: 400
Explanation
At the **triple point** the solid, liquid and vapour are in equilibrium, so the vapour pressure of the solid equals the vapour pressure of the liquid at that temperature:
$$p_1=p_2\;\Rightarrow\;\ln p_1=\ln p_2 .$$
$$-\frac{2000}{T}+5=-\frac{4000}{T}+10 .$$
**Solve:**
$$\frac{4000-2000}{T}=10-5\;\Rightarrow\;\frac{2000}{T}=5\;\Rightarrow\;T=\mathbf{400\ K}.$$