Pressure on (T,P) Phase Diagram for Substance

[Big-Daddy]

On a (T,P) phase diagram, what is meant by the pressure at each phase for the substance? Chemically speaking we are only usually dealing with "gaseous" pressure (i.e. that exerted by the gases), but only when the substance is in (one of the phases in) the gaseous state or supercritical fluid state will it exert gaseous pressure, so what is meant by the value of P for the substance when in a phase that is not gaseous (or supercritical)? Perhaps, the surrounding gaseous pressure?

 

[colliflour]

There is a common misconception that only gases are compressible. Liquids and solids do change their volume with changes in pressure. If you look at a P,T,V diagram, you'll see that the slope of the V surface for a gas is much greater than for a liquid or solid, i.e. it's more compressible. See also: isobaric volumetric thermal expansion coefficient and isothermal compressibility. These are the slopes (dV/dT)_P and (dV/dP)_T respectively in the P,T,V diagram.

 

[Big-Daddy]

What I'm asking is, what is meant by "pressure" when we look at a phase diagram where the phase in question is not a gas or supercritical fluid? Is it the surrounding gaseous pressure around the phase, or is it the internal pressure (e.g. think pressure=density * g * height for a pure liquid) within the phase?

 

[colliflour]

What do you mean, what is meant by pressure? pressure means pressure- force per unit area on the substance. The substance could be pressurized in a piston cylinder with no gas around it. If the pressure on a solid is released (vacuum created around it) it may turn to liquid or gas, moving into a different region of the phase diagram. This has no relation whatsoever to hydrostatic head pressure rho*g*h. Pressure is a force per unit area of the substance, this is the same no matter if the substance is solid, liquid, gas, or supercritical. The force is not affected by the phase, the force is still just the same. The type of phase present is dependent on the force around it, not the other way around.

 

[Big-Daddy]

Maybe there's been a misunderstanding.

Let's say I've got water vapour at 450 K and 1 Pa pressure. This pressure then refers to the pressure exerted by the water vapour in its gaseous phase.

Now let's say I've instead got water at 320 K and 1 MPa pressure, thus the water is in the liquid phase (mainly). When I say the water is at 1 MPa, does that mean the vapour over the water (which is causing the pressure to be exerted on it) is at 1 MPa, or does it mean something internal within the water is causing the pressure of 1 MPa? Further clarification might be needed if it is the latter case.

I would guess that in the case of vacuum surrounding a liquid or solid phase that you pointed towards, the pressure is then 0, until a vapour comes into place to exert a force on the substance in question.

 

[colliflour]

You seem to be completely missing what the phase diagram means- if you're not on a vaporization or sublimation line or melting line on the phase diagram, there are not 2 phases present there is only 1.

There is no vapor over the liquid. The liquid water fills the container, no gas is present. Here, in the former case, with 320K and 1MPa, no water vapor is present because you are not on the liquid-vapor (saturation) line of the phase diagram. The reason it seems you keep thinking there needs to be vapor sitting on top of the liquid is that in everyday situations there is air sitting on top of the liquid. In this context, there is NO AIR, we speak here of pure water. It is not "mainly" liquid, it is ALL liquid, completely 100% liquid. No vapor (vapor meaning gaseous water) surrounds the liquid. What surrounds the liquid could be solid walls. No water vapor can be formed until the boiling temperature is reached (something like 180C at 1MPa). There is not "something internal within the water" causing pressure, this is not how pressure works, pressure is external. When we speak of pressure, we mean we are keeping the pressure constant such as with a fixed weight on top of a moving piston as part of the container that holds the water.

When water is placed in a vacuum, we mean that the pressure is maintained at zero and the water turns to water vapor and takes up significantly more volume than it would as a liquid, but pressure is still zero by means of a vacuum pump or being in space. Often solids can exist in space because they are simply not hot enough to vaporize despite being at zero pressure.

 

[Point Conception]

On a pressure- temperature liquid water / water vapor phase diagram with pressure on y axis
there is a line O A from lower left to upper right. This line shows how vapor pressure changes
with temperature. The points on the line are where liquid water and water vapor are in
equilibrium: Where the water is boiling.
A horizontal line through O A from T₁ to T₂ will show liquid on left
side, boiling on line point and vapor on right. A similar vertical line moving up from P₁ to P₂ goes from vapor to boiling on line to liquid.

 

[Big-Daddy]

Ok, let's say I have a beaker of volume V_{tot} containing water of volume V_w above which there is gas of volume V_{gas} and total gaseous pressure is P_{gas}. The gas is at temperature T_{gas} (this shouldn't really matter, given that P_{gas} is known) and the water at temperature T_w. What is the pressure, P_w, in the water?

Online videos suggest that P_w has no dependence on T_w or V_w, or on the chemical properties of water, but I don't see how this can be.