 So we're now going to take a look at equations that enable us to determine the exergy within a system. And we've looked at two types of systems in this course. We're looking at fixed mass or closed systems, and we're also looking at open systems. So let's begin with the fixed mass system. And writing out the first law, we see that we have our energy over on the right-hand side. And we were saying that there was energy or sorry, exergy associated with the different forms of energy. So the exergy is the exergy associated with these different forms. And the exergy for this type of fixed mass system we will use phi to represent. And it will be equal to the exergy of the internal energy plus exergy due to kinetic energy plus exergy due to potential energy. So we can sub in the values that we just derived previously. And it's the first one for internal energy that's a little more complex. And for kinetic energy and for potential energy, it is relatively simple. Basically a one-to-one relationship between the energy itself and the exergy because all of that energy theoretically can be converted into useful work. Now usually with a process or any kind of system we're interested in the change in exergy between two states. So let's take a look at that. And if we're looking at change in exergy of fixed mass, we will have delta phi. That would be phi 2 minus phi 1. And then we'll just evaluate the change of the exergy phi term that we have. And so that's what we end up with for the change in exergy of fixed mass. And we can also have on a per mass basis delta capital X would then be equal to the mass times our delta phi or the change in exergy. Looking now for an open system or control volume, we'll again begin by writing out the first law. And again, the terms on the right hand side represent energy. And so we've come up with expressions for the exergy associated with those different energy types. So let's write out the exergy. And for this we're going to give it the symbol psi. So we have exergy associated with the enthalpy plus exergy associated with kinetic energy plus exergy associated with potential. Plugging in the values. Now we're usually interested in a change in exergy. And for that we have delta psi. So just evaluating the change. So those are equations that we can use to evaluate the change in exergy for either a fixed mass system, a closed system, or for an open system with a control volume. Now you'll notice I haven't given you any expressions yet for the heat transfer on the left or the work. And so what we'll do now is we'll take a look at how we can account for the exergy associated with both heat transfer and work. And then we will have all the things we need in order to start doing exergy analysis.