# Why isn't the nature of the container mentioned in thermo?

1. Apr 12, 2015

### davidbenari

This question has been bugging me for long. Specifically I'm wondering about it in the context of Pressure-Tempreature phase diagrams.

With these diagrams you can deduce stuff like the Clausius-Clapeyron equation and stuff like that. But certain things confuse me, e.g.:

There is this mental picture that after placing a liquid inside a container and sealing it (the liquid has a vacuum on top), after a long time a vapor pressure will form because of dynamic equilibrium and its value is given by the Clausius-Clapeyron equation as a function of temperature. But I don't get this.

Suppose I have a GIGANTIC container, and I dropped only a litre of water. It seems unlikely to me that a vapor phase with a pressure will form on top of it because of dynamic equilibrium. Namely because it implies that on top of the liquid a vapor phase micro-atmosphere will form. Why isn't this micro-atmosphere dissipating into the surrounding vacuum?

What exactly is supposed when you say that there is some substance in a container and that its phases will be given by the P-T diagram?

Also:

I interpret P-T diagrams as if I am the one exerting the pressure. Why is that the L-G line indicates the pressure of the vapor pressure alone and not the pressure I am exerting to the system? Or are both implied?

Last edited: Apr 12, 2015
2. Apr 12, 2015

### jfizzix

The water vapor would dissipate throughout the vacuum at a constant pressure equal to the vapor pressure of the water at that temperature (assuming there's enough liquid water to begin with). If there's not enough liquid to begin with, then all of it will evaporate into water vapor.

However, evaporation also can cool the water enough to freeze, so it may take awhile for things to truly come to equilibrium. Incidentally, you can freeze liquid nitrogen by putting it into a vacuum for the same reason.

In a P-T diagram (i.e., a phase diagram), you are describing the equilibrium phase of the fluid/gas in question, for a given temperature and pressure of that fluid.
If the fluid is not in thermal equilibrium (like if it was just poured into a vacuum and sealed), then you have to wait until the system comes to equilibrium before you can use the phase diagram to describe it.

3. Apr 12, 2015

### Staff: Mentor

Not only are both implied, but they are both the same. Also, the pressure of the liquid is the same. You cannot exert more pressure at equilibrium than the vapor pressure, unless you force all the vapor to condense.

Chet

4. Apr 14, 2015

### davidbenari

$dV=\frac{\partial V}{\partial n_i} dn_i + \frac{\partial V}{\partial n_j} dn_j$

If relative composition is held constant then

$V=V_i n_i + V_j n_j$

They do this when they want to construct the system and we could have been talking about volume or gibbs energy here. They are also assuming the partial molar quantities are the same as the ones in the final state.

I think what I said about a gigantic container in this thread applies here because if you start from scratch, you start considering your system after you add $dn_i$ and $dn_j$. And then you establish a relative composition identical to the one in the final state, however the environment is completely distinct (they have so much more space)! Why would the partial molar quantities be equal?

5. Apr 14, 2015

### Staff: Mentor

I'm not able to figure out how this relates to your questions in the previous posts.

Chet