# Trouble with Gibbs free energy equation

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1. Nov 4, 2015

### Eureka99

Hi everybody! Lately I tried to overcome some problems with understanding thermodynamics laws, and unfortunately I couldn't find anything about my question and I really hope someone can help me here...
My question is:
This version of Gibbs formula dG= VdP-SdT, can be applied to any close system, in which occur only reversible processes, if I understood well, and so I was wondering, with solid or liquid systems, what is the variation of Pressure, if there is any? I mean, with gases it might be the variation of the internal pressure of the gas, but with solids and liquids, I saw my book in a example about chemical potentials of vapor and liquid in equilibrium, that as dP of the liquid, it takes the variation of the total pressure ON the liquid. But that seems to me not legit, and only confuses me more.
I apologize for eventual inaccuracies, but I would appreciate it so much, if someone helps me making this clear!

2. Nov 5, 2015

### Staff: Mentor

How many pressures do you think there are?

Chet

3. Nov 5, 2015

### Eureka99

Your question actually made me realize how silly my question was, and now I really seem and feel like a stupid...the fact that confused me is that, when I think about the pressure as a definition of any force applied on a surface, I was thinking of a system composed only for example by a liquid in a container, and so I was wondering if the pressure can be considered as the pressure that the liquid applies on the internal surfaces of the container, and so the hydrostatic pressure. Now that I see, it is actually granted that the pressure is referred to a gas (that can be the atmosphere or else), but when I thought about it for a moment, and about the motion of the particles of the system (like vibrating motion in solids and liquids) that can apply a resultant force on the surroundings, I came to a doubt, but clearly I've been confusing many different things that are not related in this case.
So, I thank you for your response.

4. Nov 5, 2015

### Staff: Mentor

Pressure is not just something that exists at surfaces. It exists throughout the gas and throughout the liquid. Plus, in the present thermodynamic context, it is assumed that hydrostatic effects are negligible.
In a system of liquid and vapor at equilibrium, the pressure within the gas is the same as the pressure within the liquid.

5. Nov 5, 2015

### Eureka99

Oh, now I see... but what about solids? I'm sorry for bothering you with trivial questions, but if for example we have a system with a solid in a vacuum, is the solid going to have a pressure, or is it going to be 0 (if there is the possibility that the solid remains in its state) ?

6. Nov 5, 2015

### Staff: Mentor

If the solid is in a perfect vacuum, it is not at equilibrium. At equilibrium, there will be molecules of the solid material in the gas phase. That is, like liquids, solids have vapor pressure also. At equilibrium, the pressure in the solid is equal to the pressure in the vapor phase. The equilibrium vapor pressure is usually very low, however.

7. Nov 5, 2015

### Eureka99

And so I can know the pressure within a liquid or a solid, only in case the total system is in equilibrium with the vapor phase ( plus eventually any other gas added to the system)? Last thing is, I need to visualize the concept of pressure because seeing it only as something applied on surfaces is clearly causing me troubles in understanding systems, and so I ask what generates exactly pressure? Is it the resultant force of particles's motion or is related to something else?
I really thank you for your time.

8. Nov 6, 2015

### Staff: Mentor

That's all you could get from Thermodynamics. Thermodynamics focuses mainly on equilibrium states. To analyze what is happening during the transition between equilibrium states, you need to study Transport Phenomena.
If you think of a small imaginary cube within a gas (away from any solid surfaces), there are gas molecules carrying momentum through the walls of the cube from outside to inside, and there are gas molecules carrying momentum through the walls of the cube from inside to outside. This is equivalent to what happens at a solid surface where gas molecules bounce off the surface. And, if you replaced one of the walls of your imaginary cube with a thin planar solid surface, you would measure pressure on each side of the surface from the molecules bouncing off its two sides, but nothing else would be any different.

Chet

9. Nov 6, 2015

### Eureka99

Now, I think I got it... for now I don't think I have anymore questions related, I have to fix some concepts, and I thank you very much for your help it has really helped me. Even if those concepts are very basic, sometimes even if I study more complex things, I realize that I kind of missed them, because I've never stopped before thinking deeply on their meaning (like in this case of pressure). So, I really appreciate your help.
Thank you very much again!