### Thermodynamics

# Triple Point Temperature and Pressure

In the vicinity of the triple point, the vapor pressures of liquid and solid ammonia are respectively given by

ln p = 15.16 - 3063/T and ln p = 18.70 - 3754/T

where p is in atmospheres and T is in Kelvin. What is the temperature at the triple point? Also calculate the triple point pressure.

Calculations:

At the triple point, all the phases (solid, liquid and vapor) exist in equilibrium.

Therefore, vapor pressure of liquid ammonia = vapor pressure of solid ammonia

15.16 - 3063/T = 18.7 - 3754/T

3754/T - 3063/T = 18.7 - 15.16

3754 - 3063 = T(18.7 - 15.16)

691 = 3.54T

T = 691/3.54 = 195.2 K

Triple point temperature = 195.2 K

Triple point pressure can be obtained from any of the vapor pressure to temperature relation.

By the vapor pressure to temperature relation of liquid ammonia,

ln p = 15.16 - 3063/195.2

p = 0.588 atm

Similarly, by the vapor pressure to temperature relation of solid ammonia,

ln p = 18.7 - 3754/195.2

p = 0.588 atm

Triple point pressure = 0.588 atm