How Does a Turbojet Engine Work for a Mechanical Engineering Student?

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A mechanical engineering student at the University of South Florida is seeking assistance with a turbojet engine problem, expressing confusion due to a lack of thermodynamics knowledge. The project is not graded but is intended as a challenge from their advisor. After some initial struggle, the student indicates they have made progress and are close to a solution. They plan to share their final answer after consulting with their advisor. The discussion highlights the importance of seeking help and collaboration in engineering education.
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I'm brand new to this forum, although I've been browsing the threads for a while now. I'm currently majoring in mechanical engineering at the University of South Florida. I'm in my third semester, and I have been assigned this problem and I am struggling very much with it. (I haven't taken thermo yet, which is probably a decent amount of the confusion.)

It's not for a grade, it's just a side project my advisor assigned to me. I wanted to challenge myself, and it seems I have.

If anyone would be willing to help me at all, it would be greatly appreciated!

-Madj Ouhib
 

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Nevermind, pretty sure I figured it out!
 
Nevermind, I'm 'ballpark' with the answer. Not sure where I'm messing up.
 
Post your solution and we can help you locate your error.
 
Sorry, this is my last post in the thread. I was typing up an abstract and stuff for this problem. I went and saw my adviser, finally got the correct answer. Here is the final solution.
 

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