Temperature shows in cross section a wall consisting of four layers with thermal conductivities `K_(1)=0.06W//mK,K_(3)=0.04W//mK` and `K_(4)=0.10W//mK` the layer thickness are `L_(1)=1.5cm,L_(3)=2.8cm` and `L_(4)=3.5` cm. The temperature of interfaces is as shown in figure energy transfer through the wall is in steady state.
Q. Thickness of hollow sphere is

Options

A. 0.6 mm
B. 0.52 mm
C. 0.7 mm
D. none of these

Explanation

For spherical surface at steady state
`P_("heater")+50W=120W`
`impliesP_("Heater")=70W`
At steady state `P_("Heater")=((100-t_(out))kA)/(l)=70=k'(t_(out)-20)` ….(i)
From te given observation
`50=k'(40-20)`
from equation (ii) `k'=(5)/(2)`
From equation (i)
`t_(out)=48^(@)`
`l=0.52mm`