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$$ μ$$s) for the temperature of the sphere to drop to $$100$$ K is

Question

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$$ μ$$s) for the temperature of the sphere to drop to $$100$$ K is

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$$43$$$$π$$$$r3$$×ρ$$CdTdt=$$σ$$4$$$$π$$$$r2T4$$⇒$$r3$$×ρ$$CdTdt=$$σ$$T4$$⇒rρ$$C3$$σ$$T4dT=dt$$⇒rρ$$C3$$σ∫$$100200$$ $$dTT4=$$∫$$0t$$ dt⇒rρ$$C3$$σ∫$$100200$$ $$dTT4=$$∫$$0t$$ dt⇒rρ$$C9$$σ×$$1061$$−$$18=t$$∴$$t=7r$$ρ$$C72$$σ×$$106$$

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 $μ$ s) for the temperature of the sphere to drop to 100 K is

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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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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 $μ$ s) for the temperature of the sphere to drop to 100 K is