How to Calculate Time for Temperature Drop in Heat Radiation Problem?

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To calculate the time for a spherical black body to cool from 1000 K to 100 K, the relevant formula involves heat capacity, density, and the Stefan-Boltzmann constant. The surrounding medium is at absolute zero, which simplifies the radiation cooling process. Newton's law of cooling is not applicable due to the significant temperature difference, necessitating the use of Stefan's law instead. The derived formula for the time required is (CdR/9σ)(T2^(-3) - T1^(-3)). This approach provides a more accurate estimation of the cooling time under these conditions.
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Homework Statement



A spherical black body having R=0.1m and initial temperature T1=10^3 K is cooled by radiation.The surrounding medium is at a temperature T=0K.What time will it take for the temperature of the sphere to drop to T2=100K?
Given heat capacity is C and density d
The answer is :

(CdR/9σ)(T2^(-3) - T1^(-3))

Homework Equations


The Attempt at a Solution



I think just application of Newton's law of cooling will suffice...Isn't it?
 
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No, u can't use Newton's law of cooling because the temp. difference is large.
U can use stefan's law.
 
OK,I missed...
Then how to proceed?
 

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