A hollow metallic sphere of radius 20cm surrounds a concentric metallic sphere of radius 5cm. The space between the two sphere is filled with a nonmetallic material. The inner and outer sphere are maintained at `50^(@)C` and `10^(@)C` respectively and it is found that 100J of heat passes from the inner sphere to the outer sphere per second. Find the thermal conductivity of the material between the sphere.

Answer

A, C

Explanation

`a=r_1=5cm 0.05 m,`
`b=r_2=20cm =10^(2)C.`
Now considering a small strip of thickness `dr` at a distance 'r'
`A=4 pi (r_2)`
`H=(-4 pi (r-_2)ld theta)/(dr)`
`-ve because as 'r' increases 'Q' decreases `
`int_(a)^(b)(dr)/(r^(2)= (-4 pi K)/(H) int_(a)^(b) d theta`
on integration H=(dQ)/(dt)=K(4 pi ab(theta_1-theta_2))/(b-a)`
`Putting the values we get `
`(Kxx4xx3.14xx5xx20xx40xx10^(-3))/(15xx10^(-2))=100`
`K=(15)/(4xx3.14xx4xx10^(-1))`
`=2.985=3W//m-^(@)C.`