A solid copper cube of edges 1 cm is suspended in an evacuated enclosure. Its temperature is found to fall from 100oC to 99oc in 100 s. Another solid copper cube of edges 2 cm, with similar surface nature, is suspended in a similar manner. The time required for this cube to cool from 100oC to 99oC will be approximately

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25 s

50 s

200 s

400 s

answer is C.

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Detailed Solution

dTdt=eAσmcT4−T04=e6a2σa3×ρcT4−T04⇒ For the same fall in temperature, time dt∝adt2dt1=a2a1=2cm1cm⇒dt2=2×dt1=2×100s=200s As A=6a2 and m=V×ρ=a3×ρ

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