एक आदर्श गैस, \(\overline{\mathrm{C}}_{\mathrm{V}}=\frac{5}{2} \mathrm{R}\), को \(1 \mathrm{~atm}\) के स्थिर दाब के विरुद्ध रुद्धोष्म रूप से तब तक प्रसारित किया जाता है जब तक कि इसका आयतन दोगुना न हो जाए। यदि प्रारंभिक तापमान और दाब क्रमशः \(298 \mathrm{~K}\) और \(5 \mathrm{~atm}\) है, तो अंतिम तापमान _______ \(\mathrm{K}\) (निकटतम पूर्णांक) है। [ \(\overline{\mathrm{C}}_{\mathrm{V}}\) स्थिर आयतन पर मोलर ऊष्मा धारिता है]

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.