Question

The triple point \( (T_t, P_t) \) is shown in a schematic phase diagram (pressure (P) – temperature (T) plot) for one component system. \( G_S, G_L, G_V \) are the free energies of solid, liquid, and vapor, respectively. At a constant pressure, \( P_t \), the correct free energy \( G \) versus temperature \( T \) plot is:

• A.
• B.
• C.
• D.

Hint:

When dealing with phase diagrams, it is crucial to understand the behavior of the free energy as a function of temperature for each phase. The triple point occurs where all phase boundaries meet, and each phase has the same free energy at that specific temperature and pressure.

Answer 1

The Correct Option is A

At the triple point, the three phases—solid, liquid, and vapor—exist in equilibrium. This means that the free energy of each phase is equal at the temperature and pressure corresponding to the triple point, denoted by \( T_t \) and \( P_t \).
For a system held at constant pressure \( P_t \), the free energy of each phase will change with temperature. Typically:
- The solid phase has a higher free energy at higher temperatures. As temperature increases, the free energy of solid increases.
- The liquid phase has a lower free energy at higher temperatures compared to solid and vapor.
- The vapor phase has the lowest free energy as temperature increases, with the free energy decreasing at a faster rate than in the solid phase.
At the triple point temperature \( T_t \), all three phases have equal free energies. However, for temperatures greater than \( T_t \), the liquid and vapor phases show a decreasing trend in their free energies, whereas the solid phase shows an increasing trend in free energy.
The diagram in option (A) correctly shows the free energy versus temperature (\( G \)-\( T \)) plot for these phases. It features:
- A positive slope for the free energy of the solid phase, indicating that the free energy increases with temperature.
- A negative slope for both the liquid and vapor phases, showing that their free energies decrease as temperature increases.
- The free energy curves for each phase intersect at the triple point temperature \( T_t \).
This plot represents the fundamental thermodynamic behavior of the system at constant pressure \( P_t \), where the phases transition based on temperature.