There are two identical containers \(C_1\) and \(C_2\) containing to identical gases. Gas in \(C_1\) is reduced to half of its original volume adiabatically, while the gas in container \(C_2\) is also reduced to half of its initial volume isothermally. Find the ratio of final pressure in these containers. ( \(\gamma\) be the adiabatic constant).

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.