 So, thus far what we've been talking about are tables and diagrams at the back of the book that you can use to get property data for solving thermodynamic problems. The tables themselves are one way of presenting data. There is a, so using the tables, so what we saw is that if you know P and T, so pressure and temperature, or some of the other properties, you can usually find the other properties and the ones that we looked at were specific volume, internal energy, enthalpy, entropy, and we also looked at quality. That was for a liquid vapor system or mixture. Now, for some substances, what we can do is we can relate pressure and temperature to the specific volume itself. The equation that we use for doing this is called an equation of state. Now, a very popular one is the ideal gas equation. So let's take a look at that. So we know the ideal gas equation PV equals MRT. Now what we can do is we can rearrange this. If we want to rearrange it in terms of specific volume, we can write it as RT over P. So the left hand side here is our specific volume we can say is equal to RT over P. Now, this equation you can use for some gases, but you have to be careful when you're dealing with liquid vapor systems or superheated vapor because you have to be quite a ways to the right, so basically high temperature and pressure in order to be able to apply this. So gases deviate, so gases deviate at states near the saturation region and also near the critical point. So this equation would not be wise to use if you are near either the critical point or near the saturation region. So let's take a look at that in terms of a PV diagram. So here's our two phase region. Our critical point is up here and remember a few minutes ago we talked about earlier in this lecture we said that that was PCR, TCR. The place where the ideal gas equation will work is way up over here. So you'll want to make sure that you're in this region out here if you're going to try to use the ideal gas equation. Typically if you're dealing with steam what I would recommend is using the steam tables and the superheated steam tables. Now if you do need to work with the ideal gas equation as you get close to the two phase region there are ways that you can account for the non-ideal behavior. What we do is we introduce what is referred to as being a compressibility factor, Z or Z depending where you are and then we have compressibility charts that we can look up if we know the critical pressure and temperature and then we can get a Z compressibility correction value and we can then adjust the ideal gas equation to look something like this where the Z compressibility factor is the actual specific volume divided by the ideal specific volume. So that's the compressibility correction factor and you use that if you're trying to apply the ideal gas equation near the two phase region again I would recommend that you use the steam charts for the majority of the problems or R134A superheated charts. Thank you that concludes today's lecture.