Adiabatic tube HW Problem

MotoPayton

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:



Book Solution:



My solution:



Derivation of adiabatic equation to avoid confusion:


1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

MotoPayton

going to bump this once