GATE 2024 PH – Question 33
Solid ammonia vapor pressure obeys $\ln P=23.03-3754/T$, and liquid ammonia obeys $\ln P=19.49-3063/T$, with T in kelvin. The triple-point temperature in K (two decimal places) is _____
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Correct answer: 194.22 to 196.18
Explanation
At the **triple point** the solid, liquid and vapour phases coexist, so the vapour pressure of the solid equals the vapour pressure of the liquid:
$$\ln P_{solid}=\ln P_{liquid}\;\Rightarrow\;23.03-\frac{3754}{T}=19.49-\frac{3063}{T}.$$
**Solve:**
$$23.03-19.49=\frac{3754-3063}{T}\;\Rightarrow\;3.54=\frac{691}{T}\;\Rightarrow\;T=\frac{691}{3.54}=\mathbf{195.2\ K}.$$