 The first air conditioning process that we will take a look at is that of heating and cooling, which is really one of the simplest that we will encounter, and so if you recall from our psychrometric chart that we drew a second ago in an earlier module, that was kind of the shape of it and we said heating and cooling were either going this way or we're going this way on the psychrometric chart because we're not changing in terms of specific humidity. We're not adding or removing humidity and this was our dry bulb temperature on the bottom there. So let's begin by looking at a duct in the generic schematic that we always use for HVAC and inlet conditions, temperature one, our specific humidity one, and relative humidity at one, and then we have some heating or cooling process, so a heat exchanger, and then we come out at state two and through this process some of these may or may not change depending upon the process that we're looking at and we will look at that in a second. So that's what our system schematic of the system might look like. Now let's do our mass balances. That's where we always begin whenever we work these problems. So we'll begin by looking at a mass balance of air. So the air mass balance is basically just mass of air at one equals mass of air at two pretty straightforward because we're not adding or removing air at any point. Next thing we can look at is water. So for the mass balance of water what we have is mass flow rate of water at one equals mass flow rate of water at two. We're not adding or removing moisture in this heat exchanger here because we're just doing simple heating or cooling and consequently we can make that comment. Now we can also re-express the mass flow rate of water in terms of our specific humidity and that's what we just saw in the earlier module. So let's do that. So there we've embedded the specific humidity and we've expressed it in terms of mass flow rate of air. And remember specific humidity, the units here are kilograms of water per kilogram of dry air. That's what we always non-dimensionalize things by when we're looking at HVAC. And so with that what we can look at first of all up here we said mass flow rate of air at one and two are the same. So we can take that into this equation here and when we make the substitution what we end up with is an equation that says omega one is equal to omega two. So our specific humidity in this process is not changing as we do our heating and cooling. So that's one piece of information that we'll take along. The next thing we want to do we'll look now at using the first law and applying it to this duct. So let's take a look at the first law. So that's our first law. Now if we take a look at our schematic again are we doing work anywhere in this system? Well we need to have a blower compressor or pump or something like that. We're not doing any work in this system. Consequently the work term is going to drop out. So what we can do is we can cancel work on both the left hand and the right hand side. And let's assume that this is going to be a heat addition process where we're doing heating, putting heating in. Consequently we can remove the heat out term. So what we can then do is rewrite the expression like this and then we have single inlet single exit. So we can write this for the enthalpy mass flow rate term and given that the mass flow rate and remember now whenever we have enthalpy here enthalpy is being expressed per kilogram of dry air and so with that what I can do is I can pull mass flow rate of air out here and then multiply h2 minus h1 which 2 would be the exit state. One is the inlet and to give you an example let's say we want to evaluate enthalpy at state 2. We have two options there. We either use the equations and remember that is kilojoules per kilogram of dry air and that is why I was able to use the mass flow rate of dry air there or what you do is you read your psychometric chart again provided that it is appropriate for the elevation that you are at or if you're using the one for example in any thermal textbook those will be at one atmosphere so if you're at sea level then you can use it. So that is how you handle simple heating or cooling it's really quite straightforward and this would be one of heat flowing into the system that we've looked at here.