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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Infinity Learn · Accepted Answer

$$dTdt=eA$$σ$$mcT4$$−$$T04=e6a2$$σ$$a3$$×ρ$$cT4$$−$$T04$$⇒ 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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