00:01
So in this problem, we have, let's see, ethene and propane, you know, one -to -one mole ratio are both gases and burned with 120 % theoretical air.
00:12
The fuel is added at 77f and 150 psi.
00:17
And the air comes from the atmosphere at 77f and atmospheric pressure and then runs through a compressor to 150 psi.
00:28
And then it's mixed with the fuel.
00:29
And the turbine work is such that the exit temperature is 1 ,500 ranking.
00:35
The exit pressure is atmospheric.
00:37
And i want to find the mixture temperature before combustion and also the work, assuming an agribatic turbine.
00:48
Okay, so i sketch this down here a little bit.
00:52
So we have, let's see here, we have the air and it's getting compressed.
00:59
And then it gets mixed with the fuel, then it gets combusted, and then the product go through a turbine and we get work out.
01:07
So we're putting work in here to compress it, and we're getting work out here from the turbine, and we're obviously generating some energy from the combustion here, or i guess it would be here.
01:21
So let's see here.
01:26
We can look at our chemical combustion reaction here, and this is on basically a two -fussion.
01:33
Pound mole of fuel basis because we have two fuel molecules per per reaction.
01:44
So we have, let's see here, we have this amount of air per two power moles of fuel.
01:54
And because we want to figure out, we need, we're going to get some stuff on per pound mole of air.
02:04
So let's see here.
02:07
We can figure out the, um, we can figure out the, um, reduce pressure of the air.
02:16
Let's see here, of the air.
02:20
So that would be again using just an ideal gas law.
02:28
That is the reduced pressure is after the compressor, and it is 10 .9.
02:41
And that means we can go look up the temperature of the air.
02:46
In our charts.
02:49
And that winds up being 130 ranking.
02:55
So again, there's some work buried inside of here, but i assume you can do that now if you know this partial pressure or this reduced pressure, sorry.
03:05
So we can then look up the enthalpy of the air coming in and the air going out and then take the difference and that is the work going in.
03:19
And so that winds up being 120 bt per pound mass.
03:29
And now if we want to get it for pound mole of air, we can do that by multiplying by the molecular mass of the air and also using this no, just by multiplying by the molecular mass of air.
03:45
It gives us, well, this is pound mass of, yeah, air and so this would be this pound moles of air so we're going to need to convert things because we have an air basis here and then we have we're going to have a fuel basis here so that's why we need this kind of relationship here so now if we look at the mixing chamber we have flow rates the air coming in and fuel coming in the different types of fuel and then we have the same things coming out because we're just mixing here.
04:23
But there's no combustion taking place in the mixing chamber.
04:26
So at the exit of the mixing chamber, so if we write this all out and use ideal gas assumptions, again, we have the fuel molecules are coming in and leaving at the same temperature.
04:43
The air is coming in at a temperature we know after the compressor, and it's leaving at the same temperature as the fuel molecule...