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Q.

A solid coper sphere of density ρ,specific heat  'C' and radius  'r' is at temperature T1. It is suspended inside a chamber whose walls are at temperature T2. The time required for the temperature of sphere to drop to T2 is rρCXeσ(1T231T13). Find the value of  'X' (e=emissivity of the sphere) 

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answer is 9.

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Detailed Solution

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The loss of energy due to radiation P=eAσT4
Hence, mc=dTdt=eAσT4
m=43πr3ρ and A=4πr2
=dTdt=3eσρcrT4(or)=0tdtrρc3eσT1T2dTT4
On solving we, get
t=γρc9er(1T231T13)
X=9

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