 In this class what we're going to do we're going to take a look at a concept or a topic called the adiabatic flame temperature and what this is it is the maximum temperature that you would be able to get in a combustion process so it enables an engineer to calculate the max temperature that they may encounter for selecting materials or any other thing like that but it's called adiabatic flame temperature and just like it sounds adiabatic means that there's no heat transfer so we have combustion without heat transfer that's the hottest that it will be able to get and so that's the idea behind the adiabatic flame temperature there's no heat loss so this is a theoretical temperature and it is the maximum possible flame temperature so it's a useful number for engineers to use and determine the maximum temperature that they may have in a combustion process so what we're going to do we're going to take a look at adiabatic flame temperature for a number of different processes either steady flow or fixed mass and we'll begin with steady flow and in order to do that what I'll do is I'll write out the uh first law so that's the form of the first law now we're talking adiabatic flame temperature adiabatic means there's no heat transfer so that's gone and if we're dealing with steady flow uh steady flow typically does not have any kind of work involved and consequently the first law can be recast into just the balance of the enthalpy of the products and the reactants so that is the equation that we would use uh if we had a problem involving steady flow and we're trying to find the adiabatic flame temperature now for fixed mass systems what we'll do is we'll begin by looking at constant pressure so this would be a process whereby you have constant pressure combustion such as the brayton cycle was one that we looked at that had that but we're going to begin by looking at our boundary work although for the brayton that was a steady flow so it wouldn't apply with this so we have that for the boundary work and now what I'll do is I'll write out the first law so we have that now what we can see if we look at this equation here we have the pv term there and we have the pv term here and it's per uh it's our specific volume per kilomole multiplied by the number of moles so that we can make a substitution and it is equal to the pressure multiplied by the volume of the reactants minus the volume of the products which we said was the boundary work so that enables us to get rid of the boundary work and with that we can rewrite the equation and so we get that equation if we're dealing with fixed mass constant pressure and if you compare that to the equation above you'll see that these two equations are actually the same so for steady flow or fixed mass constant pressure we get the same result for the equation so the place where you be able to apply this equation especially one for steady flow would be gas turbine such as the Brayton cycle we said that was the constant pressure combustion process or a furnace and that would enable you to get the adiabatic flame temperature now the last thing that we'll look at for fixed mass is that of constant volume so writing out our boundary work for fixed mass we have pdv but if we say it's constant volume dv is not changing so boundary work is zero writing out the first law now we get that for the first law the first thing that we can do here adiabatic so there's no heat transfer that disappears boundary work we just said was zero with this so that disappears as well now we have this pv turbine here which isn't the easiest to deal with and we like to have another way to deal with that because it's hard to measure a specific volume on a per kilomole basis it's easy to measure pressure but not specific volume per kilomole so what we're going to do we're going to use the ideal gas equation in order to kind of clean up that formulation and if we look at the ideal gas equation on a per mole basis we have this we divide through by the number of moles and what we get is specific volume per kilomole is equal to rut and rut is something we can easily measure temperature and so we can plug it into that equation and clean it up a little bit so let's do that so that is the equation that we end up with for the adiabatic flame temperature when we're dealing with fixed mass constant volume applications of this equation one place that you could use it is heat addition in the ideal auto power cycle we're there we had a constant volume heat addition process so that gives you an example of how to calculate the adiabatic flame temperature be at a steady flow fixed mass constant pressure or a fixed mass constant volume what we'll do in the next couple of segments is we're going to work an example problem enabling us to apply the idea of adiabatic flame temperature to a specific problem