00:01
So we have kind of a little system here, but we have, i guess, i sketched it down here a little bit.
00:10
We have air coming in into a compressor with some work coming in.
00:16
So the, let's see here, then we have it coming into a mixing chamber.
00:23
Well, i guess i forgot to, well, let's just say half of it is, actually just add another little box here.
00:37
And we can, well, let's do this.
00:43
All right.
00:44
So it comes into a mixing chamber.
00:46
It mixes with some fuel, which we have here, one to one more basis of ethene and propane.
00:54
And then it comes into a combustion, and we're assuming an adiabatic combustion in here.
00:58
It then goes into a turbine.
01:00
The products go into a turbine, and we get some work out, and then they wind up leaving.
01:06
So we're told different things at different states here.
01:09
So let's see the fuel is added here at 25 c and 1 megapascal.
01:16
So we need to get the air up to 1 megapascal from atmospheric.
01:20
So it starts at atmospheric here and it comes up to 1 megapascal there.
01:28
And then it's mixed and the turbine, the exit we're told here is at 800k, an exit pressure of atmospheric.
01:39
And we want to find the mixture temperature before combustion, so right in there, and the, and also the work.
01:56
So again, we need to figure out the network that is coming out of this out of the turbine is what we want.
02:04
So let me look at something here.
02:07
All right.
02:08
Okay, too far, 12.
02:14
Just reading the problem statement again.
02:16
It says it also works here and find the mixture, okay.
02:19
So we gotta do out quite, there's quite a bit.
02:23
It sounds like a simple problem, but it was kind of a bit of work to get ourselves to the answer.
02:29
Oh, and we were told that there's 100 % theoretical error.
02:34
So we have, this is our reaction equation with the, extra air so we have some extra air coming out and and one thing we got to notice in this problem is that we have um two kilomoles of fuel um so this this whole is based on two kilomoles of fuel um and so we have 14 49 or 45 .7 kilo moles of air um per kilo for two kilo most of fuel um now we could have just divided everything by by two here and that would have made it maybe a little easier but that's not how i did it i just assumed that we had out two on a two kilo more fuel basis so to figure out the what was it we wanted to figure out the the we needed to figure out the temperature before the combustion well we need to figure out the temperature the temperature of the air coming in here because again we could so we're just going to look at a control volume of the compressor here so just around here and we know that the air we know that the pressure ratio of the air so we could basically i mean we could use the ideal gas laws just to to figure this out but again i just used the charts since we've been doing that so we have this pressure ratio here, which is basically 10.
04:21
And so we can figure out with the reduced pressure of the incoming air.
04:27
We can look that up, as we know, the critical pressure.
04:32
And we can then get the reduced pressure at the exit here.
04:37
And that's 13 .6.
04:39
So, you know, kind of, well, pretty high, high reduced pressure, just because, again, we know that, you know, we have a pretty high pressure 1 megapascal right here.
04:53
So then we can go to the charts again and look up, before we have a reduced pressure, look up the reduced temperature, and then convert it back to the real temperature, and we get the temperature of the air coming out of the compressor here is 571 kelvin.
05:13
So it's pretty hot.
05:18
And then we know then the, we can figure out the work that we needed to put into the compressor because in the end we're going to figure out, we want to figure out what this work is.
05:29
But if we just take a control volume of the whole thing, we need to figure out what this one is.
05:34
So that's just, again, we're assuming adiabatic compression.
05:37
So we have the change in entropy here.
05:40
And so this is the work going into the compressor.
05:43
And then this is, uh, let's see here.
05:49
We have the let's see here we can look we can again use just a constant heat capacity to get these these values for the enthalpy and so the change again we i looked it up well we could also use just you know we can use a variety of methods and but anyway i got it in terms of um kilo kilograms of fuel or kilograms of air.
06:20
So just basically the same old compressor analysis that we've done many times past.
06:27
So we wind up with about 8 megajoules of work per kilomole of air.
06:36
So we got to remember that we have, that's how much work per kilomole of air we have, not per kilomol of fuel.
06:44
So now we need to look at, we've asked to figure out what the temperature is here.
06:50
So we can do a control volume around our mixing chamber here.
06:56
And again, assuming constant heat capacities for everything, the two fuel molecules come in and exit at the same temperature.
07:05
So that means we can collect these two things, the two terms for the fuel molecules we can combine.
07:11
So we have the heat capacity for the fuel, for one of the fuels, say ethene and one for the other propane.
07:18
And then the temperature change from them coming in here.
07:22
Here to them leaving...