A metallic cube having length of side ‘a’ is heated to certain temperature and then allowed to cool in air. Its initial rate of cooling is R. Another cube made of same material , having length of each side $$2a$$, is heated to same temperature and then allowed to cool in the same environment. Then its initial rate of cooling will be

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Infinity Learn · Accepted Answer

m.s.$$dTdt=$$σ.e.$$A(T4-T04)$$⇒$$-($$ρ$$a3)s$$.$$dTdt=$$σ.$$e(6a2)(T4-T04)$$∴Initial rate of cooling $$R=-dTdt=6e$$σρ$$sa(T4-T04)$$∝$$1a$$∴R'$$R=a2a$$⇒R'$$=R2$$

Radiation

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m.s.dTdt=σ.e.A(T4-T04)⇒-(ρa3)s.dTdt=σ.e(6a2)(T4-T04)∴Initial rate of cooling R=-dTdt=6eσρsa(T4-T04)∝1a∴R'R=a2a⇒R'=R2

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