Phase Change question?

[Trufflehog]

Hi,

I am having trouble understanding this question. The answer in the back of the worksheet is (A). I understand that the ΔG = 0 but why is pressure > pt?

Consider a pressure – temperature phase diagram with the triple point at a pressure of pt and a temperature of Tt. If a system is on the phase boundary between solid and liquid phases, which of the following statements is always true for the system?

(A) ΔG = 0, pressure > pt
(B) ΔG ≠ 0, temperature > Tt
© ΔG = 0, pressure < pt
(D) ΔG = 0, temperature < Tt
(E) ΔG ≠ 0, pressure > pt

 

Thank you

 

 

[studiot]

Since you have the answer and seek deeper explanation for it I think offer a fuller discussion than would be allowed initially for homework.

 

The question discusses G so I am guessing this is a Chemistry question. Chemists and physicists use P as the vertical axis and T as the horizontal axis in a PT diagram, unlike engineers who tend to do it the other way round.

You say that you are interested in nanotechnology so I assume that includes computing and have constructed a truth table.

 

Now the question is about understanding two things and has presented two statements about the state of the system.

This is because it is about two separate things, the phase rules and the general form of a PT diagram.

 

Firstly the phase rule, from which we can deduce that for equilibrium across a phase boundary G₁=G_{2 ;} P₁=P₂ ; T₁=T₂ where 1 and 2 refer to the phases.

The equilibrium is important because even if the question did not explicitly state this you need to assume this and not that the system point is just passing through the liquid/solid phase line.

If it is just passing through and not in equilibrium we cannot apply most of the equations and cannot even determine the 'state' of the system.

 

OK so the system state is in equilibrium on the solid liquid phase boundary.

 

You say you understand why [math]\Delta G = 0[/math] so making the [math]\Delta G[/math] statement in A, C and D true.

 

Do you also understand why the [math]\Delta G \ne 0[/math] statements in B and E are false?

 

The second statement made in the question concerns the systems state pressure/temperature relative to the triple point pressure/temperature.

 

I have drawn a PT general diagram but this is where you need to do some work, to become familiar with the characteristics of these diagrams.

 

The triple point is marked TRP on my diagram but I have not identified the lines, although I have divided the diagram into regions where the pressure/temperature is greater or less than the triple point temperature/pressure.

 

Can you identify the solid. liquid and gas regions on the diagram. As a result on which line does the system state position lie A, B or C?

 

Once you have the answers to the above you should be able to check off all the truth/falsity values in the last column of my truth table.

 

You answer is then the only one with True in both columns.

 

Edited June 13, 2014 by studiot

[Trufflehog]

Thank you so much for your detailed explanation, you have really helped me out allot!

 

Do you also understand why the statements in B and E are false?

 

Is this because both phases are on the boundary so the rate of change from solid to liquid and liquid to solid are equal. If both phases have the same amount of energy than the difference between ΔG for the phases is 0.

 

One other thing, how did you know to draw that type of phase diagram? Off the top of my head I probably would have drawn a water phase diagram which would mean (D) is also correct.

[studiot]

You are asked about a single state and is for a change from one state to another.

The only available change is from/to solid and liquid and for an equilibrium state G_solid = G_liquid so =0 always.

 

The diagram I drew is followed by most substances, and results in my truth table.

It is true that water is anomalous and line B leans back for water so your T_system may be < T_t ; thus making D may be correct for water.

However it still goes upwards (on the P axis) from T_t so P_system > P_t always, even for water.

But you were asked which was always correct and D is only correct sometimes, but incorrect most times.

 

It was nice to see someone thinking about it.

 

Edited June 13, 2014 by studiot

[Trufflehog]

Wow, that has pretty much cleared away all my confusion about phase diagrams.

 

Once again, thank you.