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Question dealing with adiabatic process

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chuackl

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A cylinder is closed at both ends and has insulating walls. It is divided into two compartments by a perfectly insulating partition that is perpendicular to the axis of the cylinder. Each compartment contains 1 mol of oxygen, which behave as an ideal gas withγ=7/5. Initially the two compartments have equal volumes, and their temperatures are 550K and 250K. The partition is then allowed to move slowly until the pressure on its two sides are equal. Find the final temperatures in two compartments.

Guys i have the solution to this question but it appear different from the answer. If you people have time kindly solve this question and see what answer you people obtain.
 

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