 So what we're going to do now is we're going to take a look at the equations that we'll be using for solving air conditioning process problems. And we'll begin what I'd like you to do is recall the psychometric chart that we looked at earlier. Sometimes it's useful to look at the psychometric chart and then use it as a bit of a graphical tool enabling us to understand how a particular process might be working. So I'm just going to quickly sketch out what the psychometric chart kind of look like. And that was similar to what we had down here. We had temperature dry bulb and that was going from roughly zero degrees C up to about 50 degrees C. We had specific humidity on the vertical and symbol for that is omega. And up here this is where we said relative humidity was 100% so that would be fully saturated air. Now what we can do we can look at different processes that may occur and see where they would go on a psychometric chart. So to begin with let's say we have a process and I'll draw this here as being our initial point. And let's say we're heating the air. If we're heating the air we're increasing the temperature and we're not adding moisture or removing it's just simple heating. So that would be a process that we would describe with an arrow like this. On the flip side if we were cooling the air we're not removing moisture unless we get to the dew point but let's assume we're not. And so that might be a process that would describe cooling here. Now let's say we had a process whereby what we are doing is we are adding moisture or liquid to the air that's going to increase the specific humidity and it may or may not change the dry bulb temperature and so that might be a humidification process. It will certainly move in that direction. Now dehumidification where you remove moisture there your relative humidity is going to drop as will your specific humidity and so that would be a process going in this direction. And then you can have combinations of those. So to show examples of those combinations if you had a process that is doing this that might be cool and dehumidify and if you have a process that is going in this direction that might be heat and humidify. So when we look at different processes within air conditioning what we can do is we can look at this schematic of the psychometric chart and get kind of a gut feel for which way the process might be taking place in and use this as a bit of a guide. So with that what I want to do now is look at the schematic that we will use for these types of processes. So typically what we'll do is we'll draw out a duct because this is what any air conditioning duct would look like if you could go up above the ceiling tiles of the building you're in right now. You'll see metal ducts in and that is your air conditioning distribution system. And what we will show are multiple states. So beginning we have state one coming in and here we will have conditions let's say temperature one maybe we have relative humidity one maybe we know the specific humidity at one and then different processes that we may be running the air flow through so air is flowing through this duct and maybe we have a heating or a cooling coil for example and the way that we often show that is this curly thing and that's basically a heat exchanger and air to some sort of liquid heat exchanger and the liquid is either a heating fluid or a cooling fluid. So for this it could be Q dot in or in the case of heating or it could be Q dot out in the case of cooling and that will take us to a new state and we'll call that state two and that will then have again specific information for that state so T2 relative humidity to specific humidity to. And then let's say the next step that we want to have is humidification and so the way that we will illustrate that is we will put a bar which is basically a pipe with little nozzles on it and these are spray nozzles that they then generate either a mist of water or sometimes you will also inject steam depending upon the process by which you want to humidify. By injecting water you're going to get a little bit of an evaporative cooling effect and so you have to account for that as well. By injecting steam you can actually add humidification and heating at the same time and so in the winter in North America for example you'd want to have steam because then you don't have to preheat the air prior to that. And after that that will take us to state three where we are then exiting this conditioning section and our temperature will be T3 and then we would have relative humidity three specific volume three. So that is typically what one of our systems will look like and so that is the system schematic. What I now want to do is take a look at the conservation equations and those are the conservation equations of mass and energy that we will apply to these types of air conditioning processes. So to begin with so we are looking at conservation equations for both mass and energy. The mass conservation is going to be conservation of air mass, mass flow rate of air as well as water so we have those two things that we will be conserving mass with or you could combine them together usually treat them separate though as well as conservation of energy that is our first one which we have seen before. So let's begin by looking at conservation of mass and for that what we will do is we will look at the mass balance for air and here you just have quite simply mass flow rate of air in is equal to the mass flow rate of air exiting and so we use the subscript I and E I for inlet E for exit. So looking at our schematic that we just had on the screen here a second ago if we were to apply mass conservation of air to that schematic what we would have is mass flow rate air at 1 equals mass flow rate air at 2 equals mass flow rate air at 3 we are not adding or removing air at any point along the system that is what is conserved excuse me it is winter in Canada and I have a cold so that is why my voice is a little messed up. Mass balance of water let's take a look at that and I will do that on a new slide because it's a little more detailed and so if you're looking at the mass balance of water for that what we would have is mass water in equals summing of mass water exiting the system and for the above the one that we had from before our schematic let's go back and take a quick look at that. So this was our schematic and what we have we weren't seeing there is any humidification or dehumidification here so we didn't really make any comments on that however we certainly are adding water and oops sorry I should have added this onto the diagram what we have here is mass water in so that says that we're adding mass and that mass is water into the system so let's go back and take a look at our conservation of water or the mass balance for water so for that particular scenario what we would have is we would have the mass flow rate of water at one now it's air how can it be water flowing in the air well there is because remember it's an air vapor mixtures we have water vapor with the air and so that's the mass of water that is in the air stream coming in you always have a little bit of water vapor unless your relative humidity is zero which is very very rare so we have mass water coming in will equal mass water at state two remember that was just the heating or cooling so there was no addition or removal of water and then if we look at mass water of one plus the mass water in through the humidification process that will then be equal to mass water at state three so exiting our duct and the other thing that we can write is we can say that mass water at i so this is just any generic location can be expressed in terms of our specific volume or specific humidity sorry specific humidity omega multiplied by the mass flow rate of air so if you recall our specific humidity is expressed as being kilograms of water vapor per kilogram of dry air and so by multiplying these two so our specific humidity with the mass flow rate of air what we are then able to get is mass flow rate of water at that point in our air stream so those are two of our conservation equations that we can use the mass balance of water mass balance of air the last conservation equation is the first law of thermodynamics so let's take a look at that so writing out the first law and this is for a steady flow system and i've cast it for multiple input and output so that's our form of the first law which we will apply and you make your assumptions in terms of are you doing work or are you adding heat or removing it so we will be applying that at times and in this equation note that we have enthalpy so the place where we get enthalpy from you can either get it from the psychrometric chart provided that you have a psychrometric chart for whatever elevation you are at or what we do is we use the approximation equation that we talked about in an earlier lecture now your equation for the second part may be a little different especially for this enthalpy term here but nonetheless that is an approximation so either what you do for enthalpy you use your psychrometric chart or you use this equation here which then enables you to determine the enthalpy of your fluid stream so that is air conditioning processes in a generic manner next what we'll do is we'll take a look at a couple of the different processes that we talked about heating cooling humidification dehumidification