In this video we are going to talk about two physical properties of a species. That
will be critical temperature, and critical pressure, and these two physical properties
when compared to the actual system temperature and pressure will give us an idea of how well
we can use the ideal gas equation of state to model that system or whether or not we should
look into other equations of state. Now recall that the ideal gas equation of state relates
the pressure and volume to the amount of moles, some gas constant R and the temperature of that
system. Now the nice thing about the equation of state it is relative easy to use no matter
what the unknown is given the other conditions you should be able to calculate it. Another attractive
feature, that the gas equation of state is that we can use this regardless of what the species
of the gas is. So that basically assumes that all gas species regardless of their molecular
structure will behave the same. Lastly it does not matter if it is a single species
or a mixture we can use the ideal gas equation of state to model that. Now our problem happens
when we start getting to temperatures that start decreasing and get pretty low or pressures
that start getting pretty high, at this point sometimes again depending on the gas species
the ideal gas equation of state maybe pretty far off from modeling the PVT data. So the idea is
to use the critical temperature and pressure to give us an idea on how close we
may be to an ideal state where we can use the ideal gas equation. So let's start with a little
analogy on how we determine the critical temperature and pressure. Let's say we have a piston full
of ethanol vapor and we are going to heat this ethanol and lower the pressure so that
all the ethanol is a vapor, and what we are going to do is condense that vapor to a liquid
at some specific pressure, and so we will just say that at some temperature 1,
we have a pressure 1 that results in condensation. So now what we are going to do is increase
the temperature a little higher. Which will result in a needing a higher pressure to reach
condensation. So now we have increased. We will go increase to temperature 2, which is
going to result in a pressure 2, again condensation occurs, and we have both liquid and vapor.
Eventually we are going to get a temperature that we are going to call the critical temperature,
were no matter what the pressure is there is no condensation, and right before this
occurs the density if the liquid is virtually the same same as the density in the vapor.
So the last recordings that we can measure the density of the liquid and the vapor and
eventually they are the same. We are going to take that pressure as the critical pressure,
and as I mentioned that critical temperature and those are the two physical properties
of that species. When the temperature and the pressure is greater then the critical
temperature and critical pressure of the species we are are said to have a super critical
fluid meaning that it does not necessarily behave like a liquid or a gas, and these values
of the critical temperature and critical pressure could typically be looked up in any physical
properties hand book in the material and energy balances textbook. We can see that ethanol critical
temperature is around 516.3 Kelvin, which correlates with 243 degree Celsius approximately
and the critical pressure reported in atmospheres is 63 atm. So go through a little
bit more and test what we have just gone through let's go ahead and take a look at a a conceptual
problem that deals with this critical state. Let's take a look at the following question.
As the temperature of water decreases from its critical temperature of 374 degrees Celsius,
which of the following is true? We are given 4 answers. At this point I will say pause
the video and try to answer this on your own. Alright, so now let's go through each of these
to see whether or not A, B,C, or D is true. Since we are decreasing from its critical temperature
of 374 we do not form a super critical fluid. If we increase above the critical temperature
we possibly could form a super critical fluid if we also increase the pressure of the system
above the critical pressure. So C is false. Now as the temperature decreases for the system
the saturation of pressure also decreases, meaning it is going to take a lower pressure
of the system to reach condensation. So thus lower pressures are needed for condensation,
and B is false. So that leaves us with A or D. Now if we think of the density of
liquid water or the density of the vapor phase of the water, we should know that as temperature decreases
the density of the liquid water is going to increase not decrease, and the density of
the vapor phase also decreases. Since there is a lower temperature we need a lower volume
for that same amount of fluid. So A is false in this case. That leaves us with 1 answer,
which is D none of the above. So hopefully this gives you a good idea of these two parameters
and further videos using different equations of state will definitely use these parameters
to help go through those calculations.