 We're now going to take a look at the pressure, volume, temperature behavior of gas mixtures. And with this what we will be doing is introducing the concept of partial volume and partial pressure. So to begin with we're going to use a couple of laws that exist within the area of gases and the first one is Dalton's law. And what Dalton's law states mathematically is that the pressure of a mixture is going to be equal to the component pressures of each individual component in that mixture provided that each of the components is at the same volume and temperature. So graphically we could illustrate it in this manner. Imagine we have two containers that are identical in size and then we have a third container again identical in size. So what we can say here is the volume and temperature and we will assume that the volume and temperature of these containers are all the same. If in the first container we have gas A and in the second container we have gas B and the pressure in container A or with gas A is PA and the pressure here is PB. If we were to combine these two gases together and put them into the third container. So we're taking these two containers mixing the gases together but keeping them in the same volume and temperature. What we would find is the pressure of the combined gases is going to be PA plus PB. So that is Dalton's law illustrated and it's also written in terms of the summation above. A second law that we will be relying on here is Amagat's law and again I will write it out in terms of a summation saying that if we have the volume of a mixture it can be represented by the volumes of each of the individual components provided that each component is at a common pressure and temperature. So graphically we can illustrate that in the following manner. So imagine we have one container then we're going to have another container that is slightly bigger and then our third container is going to be of a volume that is equal to the sum of the first two volumes. So if we have gas A at pressure and temperature, gas B at the same pressure and temperature and then this is gas A plus B again at the same pressure and temperature we would have volume A, volume B. When we combine them together the volume of the final container will be VA plus VB and so that is a graphical illustration of Amagat's law which is also written in the summation in the top. So with this it comes or brings forward ideas with both Dalton's and Amagat's law. We can talk about component pressures and we can also talk about component volumes. So that would be the volume for individual component and the pressure. What we're now going to do is we're going to take a look and combine both Dalton's and Amagat's law along along with a law that we will often use for gas mixtures and that is the ideal gas equation and that written out in a mole basis can be expressed as PV equals nRT noise that we have n for moles. Sometimes they'll see mass there but just be aware that the gas constant R will change depending upon if you have moles or mass in that equation. And what we're now going to do is we're going to write an expression using the ideal gas equation for a component and we're also going to write an expression for the mixture and we're going to divide them by one another. So we'll begin with pressure. So if we have a component pressure at volume M and temperature M that's the mixture of volume and temperature and we're going to divide that by the pressure of the mixture. With the ideal gas equation we can rearrange the ideal gas equation up here and you can see that essentially all we need to do is take the volume onto the other side so we can re-express the pressure here in terms of the ideal gas equation. So we have the mixture volume and temperature and we have the number of moles of that component and we're going to divide by the number of moles of the mixture and the other things within the ideal gas equation remain the same and so with that we find that that is common, that's common, gas constant is common and so what we're left with is just the ratio of the moles in the component divided by the total moles in the mixture which we defined earlier as just being the mole fraction. Let me clean up that eye it's a little difficult to read so that is the mole fraction. Similarly if we do the exact same thing but now we look at the volumes in our mixture again what we get is the ratio of the volumes to the volume of the mixture is equal to the mole fraction so with that for our component pressure and component volume we can write out the following relationship. So our component volume divided by the mixture volume or component pressure divided by the mixture pressure is equal to the mole fraction and with this it brings up another term that we will use as we're evaluating properties of gas mixtures and that is the partial pressure which is what we call our component pressure it will be the mixture pressure multiplied by the mole fraction for that individual component and similarly for the partial volume it will be the mixture volume multiplied again by the mole fraction so those are two things partial pressure partial volume that we will use as we're evaluating some of the property data specifically I believe it will come up when we're looking at entropy. Now the partial volume is used where it was used for a very old method of determining what was in a gas mixture and it was with the device called the Orsat apparatus and what you could do is you would have the mixtures of a combustion process and you would absorb certain components out of your gas mixture and by measuring the change in volume you could then determine the mole fractions and from that determine the percent of the different components in exhaust gas but Orsat apparatus that would use partial volume and I just mentioned that as kind of a historical measurement technique but nonetheless what we'll do next that will conclude this lecture but the next lecture we will move into evaluating properties as well as working an example problem for gas mixtures and after we've done that then that will conclude looking at gas mixtures and then we'll be able to move into heating ventilation and air conditioning applications which is where we'll need to apply these concepts. Thank you.