In this example, we're going to take a look at a model of a non ideal gas known as the Vanda balls model, which is an experimentally based model. Um and we're going to compare it to the ideal gas, which assumes that the gas particles Have zero volume or or points and that they do not interact other than somehow kind of bouncing off of each other. So pressure times the volume of the guess is the number of moles in the gas times, the gas constant times the temperature is true for the ideal gas in the Van der balls model. The left hand side of the equation is um yeah, uh, changed a little bit. So the pressure is raised. Um bye. A small amount supposedly and the volume is lowered by a small amount supposedly. And that right hand side has not changed any. So you'll notice in this model there are two parameters, there's an A and B parameter and is still the number of moles and the V is still the volume and he is still the pressure. But what are these parameters? Well, they have a physical meaning. The B is probably a little bit easier to understand. It comes from the size of the particles, the actual physical size. Over on the left here, I have some data on some real gases. So there are three noble gases for comparison and then three gases that are molecules occurring in our atmosphere. And basically you see the trend that the B parameter that's used in the Van der Waals model increases as the number of um nucleons in the nucleus of the particle or the particles atoms if it's a molecule uh that as that mass number increases, so does the B parameter. Now mass is not the same as physical diameter, but it is true that the more particles you have in the nucleus of your atoms um that the electron cloud around the nucleus grows in size as well. Um Now the other parameter, the a parameter is related to the inter atomic attractions um which are typically considered to be weak uh in a gas, even though there there and how you see those inter atomic forces operating is with the boiling point. So I've written down the boiling points of these various gases, the temperature at one atmosphere basically at which they transition from the liquid to the gaseous face. And you can clearly see that the pattern is that the larger A. Is uh the higher the boiling points are meaning that the inter atomic forces harder to break apart to turn the substance into a gas. So for our example here, we're going to take nitrogen and two. And I'm going to go ahead and write down it's A and it's B. And the proper unit for the A. C. System. So it's a parameter Is a .14. If we convert the parameters above into pascal's for pressure, m3 for volume and we still have moles of gas, which is kind of unit list, but not really. We have to remember that a mole is a large number of particles and we have a B parameter that again converts nicely into the metric units. Yes, I standard. Um and that would be in cubic meters per mole and we're going to take our gas. It will be at 10 atmospheres of pressure And I'll go ahead and write that 10 atmospheres in terms of past gals. So that would be one oh 13 Times 10 to the 6th Pascal's So 10 atmospheres. Um the volume, we're going to Uh start off with leaders 2.0 leaders. It's easier to imagine that as a volume, but we do want to convert it to cubic meters and that's easy enough to do Factor of 1000. So to Times 10 to the -3 m3 and we're going to try to compare the temperature of the ideal gas to what the vander balls prediction would be for these same conditions. Um And let's see, I'm not going to put all the calculations in there, but the left hand side on the ideal gas model Gives us 2.026 1000 jules and 8.31 jules per kelvin on the other side times temperature. So we can definitely solve that for temperature. Um and we get about 244 Kelvin roughly to 43.8 kelvin. And notice that this is a fairly high temperature. It is well, maybe not a room that you would like to be in um but you know, certainly within the realm of human survivability, but this is much higher than the boiling point of nitrogen to so we would expect that nitrogen um even with the Van evolves model would be acting fairly much like an ideal gas. But let's see for the same conditions, we see that the pressure term raises the temperature and the volume term lowers the temperature and let's just see what happens um With this. So again, I won't bore you with the details, But the pressure gets raised 1.4, 8 Times 10 to the six pascal's and the volume gets lowered um to 1.96, 1 Times 10 to the -3 cubic meters. And that's still equal to 8.31 jules per Calvin times the temperature. And we can solve all that for the temperature, but we can see definitely the competing effects that are going on and that winds up giving us a temperature close uh huh. To what we expect from the ideal gas law, it's a little bit higher. So the pressure term does win out, meaning that the inter atomic forces are more important in the model at this set of conditions, then the fact that these are particles with extended sizes.