Solving the Otto Cycle Ideal MEP Query

[ChrisHarvey]

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

 

[ChrisHarvey]

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

 

[brewnog]

Good work Chris. You doing MechE at Loughborough perchance?

 

[ChrisHarvey]

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.

 

[ChrisHarvey]

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