1.

The figure shows a system of two concentric spheres of radii

Answer»

`(r_(1)r_(2))/((r_(2)-r_(1)))`
`(r_(2)-r_(1))`
`(r_(2)-r_(1))(r_(1)r_(2))`
`1n((r_(2))/(r_(1)))`

SOLUTION :Consider a concentric spherical shell of radius R and thickness DR as shown in the FIGURE.`(r_(1)ltrltr_(2))`
The radial rate of flow of heat through this shell in steady state will be
`H=(dQ)/(dt)=-KA(dT)/(dr)=-K(4pir^(2))(dT)/(dr)`
`rArrint_(r_(1))^(r_(2))(dr)/(r^(2))=-(4piK)/(H)int_(T_(1))^(T_(2))dT`
This on integration and simplification gives,
`H=(dQ)/(dt)=(4piKr_(1)r_(2)(T_(1)-T_(2)))/(r_(2)-r_(1))`


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