How Do G vs T and G vs P Graphs for Water Change with Pressure and Temperature?

[arenaninja]

Homework Statement

Do a qualitative sketch of a G vs T (and G vs P) graph for water at liquid, solid and gas phases at atmospheric pressure. How would the graphs differ at a pressure of 0.001 bar/slightly higher temperatures?

Homework Equations

None that I can think of.

The Attempt at a Solution

Also can't think of any.

Ok I realize that the phase with the highest Gibbs free energy at a given temperature (or pressure) would be the most stable. But what is this graph supposed to look like? I imagine it would be linear, but I also believe that at some point between 0 and 100 C the solid phase will effectively not exist (same for gas phase), but can it still have a Gibbs free energy? Shouldn't there be some discontinuity at some point?

Also, if anyone has a good link/image of what the graphs should look like, that would be great.

 

[mark726]

Thank you for your question. I will do my best to provide a qualitative sketch of the G vs T and G vs P graphs for water at different phases, as well as explain how they would differ at a pressure of 0.001 bar/higher temperatures.

Firstly, the G vs T graph for water at atmospheric pressure would have three distinct regions: one for the liquid phase, one for the solid phase, and one for the gas phase. At temperatures below 0°C, the solid phase of water would have the lowest Gibbs free energy and would therefore be the most stable phase. As the temperature increases, the Gibbs free energy of the liquid phase would decrease and eventually become lower than that of the solid phase, causing a phase transition from solid to liquid. This region would be represented by a downward sloping curve on the G vs T graph.

At temperatures above 0°C, the liquid phase would have the lowest Gibbs free energy and would be the most stable phase. As the temperature increases further, the Gibbs free energy of the gas phase would decrease and eventually become lower than that of the liquid phase, causing a phase transition from liquid to gas. This region would be represented by an upward sloping curve on the G vs T graph.

At a pressure of 0.001 bar/slightly higher temperatures, the G vs T graph would look similar to the one at atmospheric pressure, but with some key differences. Firstly, the solid phase of water would effectively not exist at these low pressures, so the downward sloping curve for the solid phase would disappear. Secondly, the phase transition from solid to liquid would occur at a lower temperature, as the solid phase would have a lower Gibbs free energy at this pressure. Similarly, the phase transition from liquid to gas would occur at a higher temperature, as the gas phase would have a lower Gibbs free energy at this pressure.

The G vs P graph for water at atmospheric pressure would also have three distinct regions, but this time they would be separated by pressure instead of temperature. At pressures below 0.01 bar, the gas phase of water would have the lowest Gibbs free energy and would therefore be the most stable phase. As the pressure increases, the Gibbs free energy of the liquid phase would decrease and eventually become lower than that of the gas phase, causing a phase transition from gas to liquid. This region would be represented by a downward sloping curve on the G vs P graph.

At pressures above 0