 Okay, so what we've been doing is we've been looking at ways of characterizing or coming up with expressions for the XRG due to different forms of energy. We also looked at the way to calculate XRG change for either a fixed mass or closed system as well as an open system. The last thing we want to do in today's lecture is we want to look at XRG associated due to heat, work, and mass crossing a boundary. So we'll begin by looking at heat. And for this, if you recall when we looked at the XRG due to internal energy, we took a heat source and we put it in a piston cylinder device and the heat flowed out of that and it went to the surroundings and we sent it through a reversible heat engine. Well, that's exactly what we're going to do whenever we have heat transfer. We're going to assume that whenever you have heat transfer, that that heat could theoretically flow through a reversible engine like the Carnot engine. And with that, we already have an expression for the thermal efficiency of a reversible engine so we can place that in here. T0 is the surrounding and T is the high temperature at which our heat source is flowing from. And we multiply it by Q. That is XRG associated with heat. Now for work, for work, we have two different types of XRG depending upon whether or not we have boundary work. Because if we have boundary work, we've got to be a little more careful because we could have work being performed on the surroundings. And so for work, we have work minus work surroundings, recalling that that is nothing more than the volume change of our boundary multiplied by the local dead state pressure, typically atmospheric 101.325. So that is if you have boundary work and if you have no boundary work, it's just work. Work can flow into work. So that's a pretty simple one. And finally mass. Mass is when you have any kind of fluid crossing the boundary, it is just the mass multiplied by psi which would be the XRG per unit mass and we looked at that a moment ago. So those are the ways to handle heat, work, and mass and be able to quantify the amount of the XRG associated with each of them. A couple of final notes to say about XRG. One is that XRG is always destroyed due to irreversibilities. And given that no matter what process we look at, in reality we will always have irreversibilities, XRG is always being destroyed. So consequently what we can write, we can write that the change in XRG, so XRG at state two minus XRG at state one is always going to be less than zero. Given that XRG is being destroyed, it is going down and consequently X2 will be less than X1. The other thing that we can say is that the XRG destruction is related to entropy generation. And given that entropy is always increasing, we can then write that XRG destroyed is always greater than zero. So those are two of the concepts. We bring in the entropy generation thing here. What we'll find when we're doing some of the problem solving, in certain cases you can go through and you can do the XRG analysis or what you can do is you can go and you can calculate the entropy generation, which we've seen earlier. And then you just multiply it by the temperature at the dead state. So if they're asking you to calculate XRG destroyed, you can either do it using entropy or you can use it using XRG analysis. And some of the problems it will look at, it's actually simpler to do the entropy generation. So with that, that concludes today's lecture. Thank you very much for your attention. Goodbye.