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

Question

Infinity Learn · Accepted Answer

mc−$$dTdt=$$σ$$T4A$$    ∴ $$dt=$$−mcdTσ$$AT4Integrating$$, we $$gett=$$−mcσA∫$$200100$$ T−$$4dT$$ ∴ $$t=43$$$$π$$$$r3$$ρcσAT−$$3($$−$$3)200100$$           $$=4$$$$π$$$$r3$$ρ$$c9$$σ$$4$$$$π$$$$r21(100)3$$−$$1(200)3=r$$ρ$$c9$$σ$$1(100)3$$−$$1(200)3=7r$$ρ$$c72$$σ×$$10$$−$$6sec$$

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

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