A small sphere (emissivity`=0.9, radius =r_(1)`) is located at the centre of a spherical asbestos shell (thickness`=5.0` cm , outer radius `=r_(2)`) The thickness of the shell is small compared to the inner and outer radii of the shell. The temperature of the small sphere is 800 K while the temperature of the inner surface of the shell is 600 K The temperature of small sphere is maintained constant. Assuming that `r_(2)/r_(1)=10.0` and ignoring any air inside the shell, find the temperature (in k) of the outer surface of the shell Take : `K_(asbestor)=0.085 W//m^(@)` C `sigma = 17/3 xx10^(-8) W//m^(2)k^(4)`

Answer

`0516`

Explanation

`(dQ)/(dt)=sigmaxx0.8xx4pir_(1)^(2)[800^(4)-600^(4)]`
`=kxx(4pir_(2)r_(2))/(r_(2)-r_(2))xx(600-T)`
`r_(2)r_(2) approx r_(2)^(2)`
`600-T=(17/3xx10^(-8)xx(0.9)/10xx1/100xx10^(8)xx100xx28xx10^(3)xx5/100)/(0.085) Rightarrow T=516 K`