 We're now going to tackle the first part of the question and that is they want us to do constant volume combustion and determine the maximum pressure. So constant volume combustion. And for that what we'll be doing is we'll be using the form of the first law for fixed mass system for constant volume. So if you recall when we looked at the different forms of the first law for the adiabatic flame temperature we said that for constant volume the boundary work was zero and with that when we write out our formulation for the first law we had that they're dealing with adiabatic so heat is gone there's no boundary work and so with that we were able to rewrite the first law like so and so we have that equation for the first law. Now what we're going to do is we want to be able to determine the temperature of the product stream coming out of this and one of the challenges that we have here well what we'll do I'll begin by writing out the table. We'll do a table very much like we did earlier when we applied the first law to a reacting system. However the challenge that we're going to have is we don't know the temperature of the product so that will remain an unknown and that's what makes these questions a lot of fun for professors and a lot of stress for students. I think professors probably dream about giving these types of questions on final exams because there's so many iterations required as we will soon see. Okay so what we'll do we'll write out the different substances that we have so we have this equation or the table here now notice we do not have enthalpy for our products or the product temperature and the reason is because we do not know that temperature that's what we're trying to solve here that's the adiabatic flame temperature and that means that we have a big unknown here for each of these different substances and so that will be the way that we will formulate our first law so let's proceed to do that and what I'll do is I'll write in the values that we know and for the ones that we don't we will leave them as an unknown and I will show the value for the unknown as you'll see in the next equation that I'll put together. So that's the equation that we get by subbing in the values from the table into the first law for constant volume combustion and adiabatic flame temperature now what I'll do is I'll rewrite that and we end up with the following equation. So this is the equation that we get and what you'll notice is we have the enthalpy values for carbon dioxide, water vapor and nitrogen these are all of the things on the product side as well as the temperature of the product and it's equated to some number. Now we don't know the adiabatic flame temperature which is the temperature of the product and if we knew it we could then go into the tables and get the value of the enthalpy here the enthalpy there and the enthalpy there but we don't know that. Only way to solve this equation is by trial and error and what we need to do is we need to guess a couple of temperatures and with those temperatures we can then interpolate between the answers and help us converge on the final adiabatic flame temperatures. So I'm going to guess two temperatures and then we will go ahead and read the values from the table and see what we get and then we'll do an interpolation and so I'll show you that in the next section here. So there we get our results and if I go back a page you can see the right hand side was 734 387 with my two guesses I get one let me put that value it was 734 387 so 734 387.56 is what it should be and so you can see I was lucky with my guesses and that's partially because I do know what the answer is and that helps in solving this but by placing the guesses that I did and looking up the values we see that on this side we are above and on this side we are below so that means that our final temperature is going to be somewhere between 2850 and 2800 how do we determine that well the way that I'll do that is by doing an interpolation and that will get us close enough to the final adiabatic flame temperature so with that we get this for being the temperature of the products that is our adiabatic flame temperature when we have constant volume combustion with that now the question asked what is the maximum pressure if we have constant volume combustion so in order to answer that we need to take this temperature and use the ideal gas equation and that will enable us to get the pressure so let's proceed to do that so we have the ideal gas equation for our reactants and we have it also for the products I'm going to combine those enabling me then to isolate for the pressure of the products so when we do that we get this for being our final pressure 983 kPa or about 142.6 psi and this would simulate what we would have for the auto cycle if we were able to get the adiabatic flame temperature inside of the auto cycle if you recall the auto cycle looks something like this we started at state one we move up to a state two we then went into constant volume combustion taking us to state three and then that brought us down to state four and this was where we had our heat addition so with this calculation that would tell us it would provide us with an estimate of the maximum pressure that we may see in an auto cycle assuming that we have no heat transfer from the engine which we in reality do but that's assuming that we don't so that would be the max pressure that you could get for this particular case for example of the auto cycle so that provides us with a demonstration of how to do this for a max pressure of constant volume in the last segment what I'll do is I'll look what would the volume be if we were to restrict the pressure and have constant pressure so we'll proceed and do that in the next segment