# What happens to P when a vessel of water with no headspace is heated?

1. Feb 23, 2013

Assume we have a vessel capable of withstanding infinite pressure. What happens to the pressure inside the vessel when that vessel is filled completely with water, with no air space at the top, and is then heated? Do the equations for vapor pressure still apply if there's no space for a vapor?

Also, what happens when you reach supercritical temperature/pressure combinations?

2. Feb 23, 2013

### SteamKing

Staff Emeritus
Re: What happens to P when a vessel of water with no headspace is heat

What do you think will happen?

3. Feb 23, 2013

Re: What happens to P when a vessel of water with no headspace is heat

Well I don't know precisely, which is why I'm asking for help. Obviously pressure will increase, but what I don't know is if it's predicted by a whole different equation than the equation for vapor pressure. Does it change as a function of the amount headspace (0% headspace vs. 15% vs 58%, for example)? Does it change to a whole new regime under supercritical conditions? Stuff like that.

4. Feb 23, 2013

### SteamKing

Staff Emeritus
Re: What happens to P when a vessel of water with no headspace is heat

Is liquid water compressible or incompressible? If there is no vapor, will the vapor pressure equation be valid?

5. Feb 24, 2013

Re: What happens to P when a vessel of water with no headspace is heat

I reckon not. That's what I was trying to ask with "Do the equations for vapor pressure still apply if there's no space for a vapor?" So that being said, how do you describe pressure in a heated liquid that has no room for expansion?

6. Feb 25, 2013

### Khashishi

Re: What happens to P when a vessel of water with no headspace is heat

I don't know, but I can guess. Water expands quite a bit when heated, so, given an invincible container, the pressure must get very large very fast. So no gas will form. Now either, you keep increasing the temperature beyond the critical temperature of water, and the distinction between liquid and gas disappears, or, perhaps even weirder you will get some exotic forms of ice like ice VII, X, or XI, according to the phase diagram here.
http://www.lsbu.ac.uk/water/phase.html
(Water is crazy!)

I don't think you will actually get these ice forms, because those exotic ice forms are denser than water, so the pressure would not increase beyond a certain point. Rather, you would probably move in a curved path that takes you from liquid water over the critical point, and you will have a supercritical fluid. Note that there is no sudden change from a liquid to a supercritical fluid. As you increase the temperature, the liquid just gradually transforms into a supercritical fluid.

Last edited: Feb 25, 2013
7. Feb 25, 2013

### Staff: Mentor

Re: What happens to P when a vessel of water with no headspace is heat

I think Khashishi is correct. But, why don't you do a calculation just to see? If the container does not expand, then the average density of the water in the container is constant while you heat it. See if this is consistent with the water remaining all liquid (or supercritical liquid). Almost certainly it is.