 We're now going to work the last part of the example problem and that was the part that asked us to calculate the maximum volume that the system would expand to if it was operating at constant pressure so this is a demonstration of adiabatic flame temperature with constant pressure combustion and if we have constant pressure combustion fixed mass pdv will exist and so if we write out the form of the first law for the fixed mass system we have that form there and what we do we take our boundary work and we basically make a substitution for there and for there as we saw earlier when we looked at the forms of the first law for adiabatic flame temperature when we do that that simplifies this equation to the following and we said that that was the same form as for the steady flow first law adiabatic flame temperature so just like before when we were looking at the problem with constant volume combustion what we'll be doing is we'll be using the table and values that we came up with right after we did the stoichiometric balance and we'll be getting the values again the biggest challenge here is we do not know the temperature of the products and so we have to leave that as an unknown but I'll go through the same process and sub in the values to this equation just like we did for the previous segment when we looked at constant volume combustion so that's the equation that we get for the first law and you'll notice again we do not know the temperature of the products and consequently we have to leave the enthalpy values on a per kilomole basis for CO2, H2O and N2 as being unknown and then we have to do trial and error subbing values in and seeing how close we get to this value on the right hand side of the equation so we'll proceed and do the trial and error approach so that's what we get for the first law with the temperature either being 2350 or 2300 and if we look back at our previous equation this is what we're trying to match on the right hand side so let me put that in the middle the value there was 754555.16 so look at that I really picked those values well didn't I because we can see this is right in the middle of those two numbers so we know that the final temperature we have is somewhere between 2350 and 2300 the way that we will determine that is we will perform an interpolation and that's what we then get for the adiabatic flame temperature if we're dealing with a constant pressure system now when we compare back to the value that we have for constant volume there we had 2816.46 Kelvin that was constant volume so you can see that when we have constant pressure and we have expansion we do not get to the same high temperature that we did with constant volume but the question asks us to calculate the maximum volume if we're dealing with constant pressure so this is the number that we have for constant pressure what we'll do we'll proceed just like we did last time and we will use the ideal gas law in order to determine the volume so we have two forms of the ideal gas equation what we can then do is we can isolate for the volume of the products and what we find is that if we have constant pressure allowing our piston cylinder device to expand we get up to 6.65 so we're going from 0.8 liters all the way up to 6.65 liters if we allow it to freely expand so those are two demonstrations of adiabatic flame temperature for fixed mass either a constant volume or a constant pressure process and you can see it's a little bit complex because you do not know the temperature of your products and consequently what you need to do is guess values and then once you've guessed them you compare them to how things turn out and you do interpolation in order to get the final adiabatic flame temperature so that concludes this lecture and it also concludes the coverage of combustion and so I would like to thank you for your time and attention bye bye