A solid copper sphere (density ρ and specific heat capacity c) of radius r at an initial temperature 200 K is suspended inside a chamber whose walls are at almost 0 K. The time required (in μs) for the temperature of the sphere to drop to 100 K is

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727rρcσ

772rρcσ

277rρcσ

780rρcσ

answer is B.

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Detailed Solution

43πr3×ρCdTdt=σ4πr2T4⇒r3×ρCdTdt=σT4⇒rρC3σT4dT=dt⇒rρC3σ∫100200 dTT4=∫0t dt⇒rρC3σ∫100200 dTT4=∫0t dt⇒rρC9σ×1061−18=t∴t=7rρC72σ×106

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