એક બંધ પાત્રમાં \(200\, K\) તાપમાને \(0.1\) મોલ એક પરમાણ્વિક આદર્શ વાયુ ભરેલ છે. જો તેમાં \(0.05\) મોલ તે જ વાયુ જે \(400\, K\) તાપમાને છે તેને ઉમેરવામાં આવે તો પાત્રમાં રહેલ વાયુનું સંતુલન સમયે અંતિમ તાપમાન (\(K\) માં) લગભગ કેટલું હશે?

A \(269.5\)
B \(260.6\)
C \(250.5\)
D \(266.67\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(266.67\)

Step-by-step Solution

Detailed explanation

As work done on gas and heat supplied to the gas are zero, total internal energy of gases remain same \(u _{1}+ u _{2}= u _{1}^{\prime}+ u _{2}^{\prime}\) \((0.1) C _{ v }(200)+(0.05) C _{ v }(400)=(0.15) C _{ v } T\) \(T =\frac{800}{3} k =266.67 k\)

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.

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