Adiabatic Equation Derivation Troubleshooting

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The discussion centers on a user struggling to derive the adiabatic equation correctly, resulting in answers that do not match the solution manual. Despite understanding the book's method, the user is unable to identify the discrepancies in their own approach after extensive effort. They seek assistance in pinpointing the mistake or suggestions to align their method with the book's solution. The urgency of the situation is emphasized by the user's inability to rest until the issue is resolved. Overall, the thread highlights a common challenge in mastering complex derivations in thermodynamics.
MotoPayton
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I have been struggling to find my mistake for over 2 hours now and I still haven't exactly matched my answers with the books solution. I feel that my method should give the same answer the solution manual obtained however they are slightly off.

I understand the book method completely.

Can someone tell me why my method doesn't work or find a way to make it work. I won't be able to sleep until I know.

Thanks

Book Question:

Capture-2.jpg


Book Solution:

solution.jpg


My solution:

DSCN8328.jpg


Derivation of adiabatic equation to avoid confusion:

DSCN8329.jpg

 
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