I'm going to describe on a pressure-temperature phase diagram, and this is for water. How
we can go from a liquid to a vapor phase without exhibiting a phase change by circumnavigating
the critical point which is this point here is the highest temperature and pressure where
we can have two distinct phases that exist in equilibrium. So two phases coexisting given
the values of the critical point of water. So in this diagram we're plotting the log
of pressure versus absolute temperature and then on the right side we have a piston and
cylinder and this is representing the volume of our system, but on the log scale because
we have large volume changes, and so right now the drawing, dark blue represents a liquid
and corresponds to this point, our starting point in the simulation and the idea is first
that we have a region that we label as a liquid phase, a region we label as a vapor phase,
and a region we label as a supercritical fluid but we don't have a boundary between
these phases, in other words this is a continuous transition if we go around the critical point,
and so what I want to show in the simulation is that I can start with a liquid at this
point here, I could raise the pressure at constant temperature till I'm above the critical
pressure I could then raise the temperature at constant pressure until I'm above the critical
temperature, now I can lower the pressure at constant temperature back below the critical
temperature, I could then lower the temperature till I'm near this phase envelope at constant
pressure and so I've gone from a label in the liquid region to something we'd label
in the vapor region without a phase change, now this vapor I could condense back to liquid
at constant pressure by lowering the temperature and now I would see the phase change and so
the interactive simulation will demonstrate this a little more clearly. This is a simulation
you can look at on your own online its on the wolfram demonstration project and it uses
Mathematica to create the simulation, so lets look at this simulation now. So here's the
interactive Mathematica simulation, I'm starting in the liquid phase with the green point,
and as I raise the pressure you don't see really any significant change in the volume,
one: because remember we're looking at a log scale and two: because liquid is fairly in-compressible,
and now I'm going to raise the temperature at constant pressure as best I can do, the
main point is that I'm above the critical pressure, then we start to see some increase
in volume, colored slightly lighter now I'm going to lower the pressure, and now we see
the volume increase quite a bit more somewhere between what we would call supercritical or
vapor, remember there is no boundary I said in the first part of the screencast that as
the fluid gets less dense and becomes a vapor it becomes green but actually its just lighter
blue, and so I'm going to lower the pressure and of course a fairly significant volume
change. Now I'm going to lower the temperature so we're in the vapor region, the volume decreases
slightly but remember its on a log scale so now I've gone from the liquid, small volume,
to clearly much larger volume in the vapor because this is a log scale so the volume
is much larger, and I can take this vapor now and I can go through a transition and
now we see a sharp transition, a phase change, to get back to my original liquid phase. So
in one direction, this direction I went around the critical point and in doing that the transition
is continuous but now if I instead cross this phase boundary we see abrupt transition, we
have two phases in equilibrium, here we just see the transition to go from the vapor phase
to the liquid phase. So this is important for understanding the properties of fluid's
critical point, its a very important property of a fluid we have to keep in mind these phase
boundaries between the regions are relatively arbitrary.