\(2.2\) ग्राम नाइट्रस ऑक्साइड गैस \(\left( N _2 O \right)\) को \(1\,atm\) के स्थिर दाब पर \(310\,K\) से \(270\,K\) तब ठंडा किया जाता है जिससे गैस का संपीड़न \(217.1\,mL\) से \(167.75\,mL\) हो जाता है। इस प्रक्रम की आन्तरिक ऊर्जा में परिवर्तन \((\Delta U )\), ' \(x\) ' \(J\) है ' \(x\) ' का मान \(..........\) है। [निकटतम पूर्णांक] (दिया है परमाणु भार \(N =14\,g\,mol ^{-1}\) and of \(O =16\,g\,mol ^{-1}\). Molar heat capacity of \(N _2 O\) is \(100\,JK ^{-1}\,mol ^{-1}\) )

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.