Solving the Otto Cycle Ideal MEP Query

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SUMMARY

The discussion centers on solving the ideal Mean Effective Pressure (MEP) of the Otto cycle, a key concept in thermodynamics. User Chris initially struggled with the algebraic manipulation required to derive the ideal MEP but successfully solved it after several hours of effort. The conversation also touches on the differences between relative efficiency and absolute efficiency in the context of Diesel engines, highlighting the importance of parameters such as compression ratio and cut-off ratio.

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  • Understanding of the Otto cycle and its thermodynamic principles
  • Familiarity with algebraic manipulation techniques
  • Knowledge of relative and absolute efficiency in thermodynamics
  • Basic concepts of compression ratio and cut-off ratio
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  • Research the derivation of the ideal MEP for the Otto cycle
  • Study the differences between relative efficiency and absolute efficiency in thermodynamics
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  • Explore advanced thermodynamic cycles beyond the Otto cycle
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Students and professionals in mechanical engineering, particularly those studying thermodynamics and engine efficiency, will benefit from this discussion.

ChrisHarvey
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Hi everyone. Sorry... I hope I don't bore you all - I fear this thread will be nowhere near as interesting as the most recent one on this forum on why aircraft fly! Anyway, I have a question relating to the Otto cycle - I'm revising my thermodynamics for an exam and on 1 of the past papers it asks me to, "Show that the ideal MEP of the Otto cycle is given by:"

(please follow link to see image)
http://wwwebworld.co.uk/photos/OttoMEP.gif

I have tried for many hours to get this (I'm not exaggerating) and to no avail. I'm on my easter break at the moment (from uni.) so I can't speak to my lecturer. Does anyone have a clue? I get the feeling I'm doing something stupid because it's not worth many marks and should therefore be easy.

Cheers,
Chris
 
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I have actually just managed to solve it, and as I thought, it wasn't particularly difficult - just tricky algebraic manipulation. If you don't see your way through to the end from the beginning you can easily end up working the wrong way with it.

If anyone's interested, I have my solution:

http://wwwebworld.co.uk/photos/OttoMEPSoln.gif

Cheers,
Chris
 
Last edited by a moderator:
Good work Chris. You doing MechE at Loughborough perchance?
 
I am at Loughborough, but I'm doing the aero eng course there, not the mech eng although I think I'm right in saying the 1st years for both courses are relatively similar.
 
Does anybody know what relative efficiency is please (in the context of Diesel engines if it makes any difference)? I've done this [different] question, where I'm given relative efficiency, and I've treated it as absolute efficiency just to see what would happen (getting the wrong answer) but didn't have to use half the data given, i.e. compression ratio (rv) and cut-off ratio (rc). Now I'm looking back thinking "how could I possibly use these ratios to give me absolute efficiency?" In short: what is relative efficiency and how is different to absolute efficiency?

Thanks again,
Chris
 

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