એક \(12\; cm\) ત્રિજ્યા ધરાવતો ગોળાકાર કાળો પદાર્થ \(500\;K\) તાપમાને \(450\;W\) પવારનું ઉત્સર્જન કરે છે. જો તેની ત્રિજયા અડધી અને તાપમાન બમણું કરતાં ઉત્સર્જિત પાવર વોટમાં કેટલો થાય?

A \(450 \)
B \(1000 \)
C \(1800\)
D \(225\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(1800\)

Step-by-step Solution

Detailed explanation

According to \(Stefan-Boltzman\) law, rate of energy radiated by a black is given as \(E = \sigma A{T^4} = \sigma 4\pi {R^2}{T^4}\)

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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