Question

In the vicinity of the triple point, the equation of liquid-vapor boundary in the \(P - T\) phase diagram for ammonia is \( \ln P = 24.38 - \frac{3063}{T} \), where \(P\) is pressure (in Pa) and \(T\) is temperature (in K). Similarly, the solid-vapor boundary is given by \( \ln P = 27.92 - \frac{3754}{T} \). The temperature at the triple point is ________ K (round off to one decimal place).

Hint:

At the triple point, the pressure and temperature are equal for all phases of the substance. Use the boundary equations for liquid-vapor and solid-vapor to find the triple point temperature.

Answer 1

Correct Answer: 195.1

At the triple point, the pressure and temperature are the same for both the liquid-vapor and solid-vapor boundaries. Thus, we set the two equations equal to each other at the triple point: \[ 24.38 - \frac{3063}{T} = 27.92 - \frac{3754}{T}. \] Solving for \(T\): \[ \frac{3754}{T} - \frac{3063}{T} = 27.92 - 24.38, \] \[ \frac{691}{T} = 3.54, \] \[ T = \frac{691}{3.54} \approx 195.2 \, \text{K}. \] Thus, the temperature at the triple point is: \[ \boxed{195.1 \, \text{to} \, 195.3 \, \text{K}}. \]