The figure shows a system of two concentric spheres of radii r₁ and r₂ and kept at temperatures T₁ and T₂ respectively. The radial rate of flow of heat in a substance between the two concentric sphere is proportional to

$fraction numerator straight r subscript 2 minus straight r subscript 1 over denominator straight r subscript 1 straight r subscript 2 end fraction$
$ln space open parentheses straight r subscript 2 over straight r subscript 1 close parentheses$
$fraction numerator straight r subscript 1 straight r subscript 2 over denominator straight r subscript 2 minus straight r subscript 1 end fraction$
$In space left parenthesis straight r subscript 2 minus straight r subscript 1 right parenthesis$

Solution

fraction numerator straight r subscript 1 straight r subscript 2 over denominator straight r subscript 2 minus straight r subscript 1 end fraction

open parentheses dQ over dt close parentheses space equals space open parentheses straight T subscript 1 minus straight T subscript 2 close parentheses fraction numerator 4 πr subscript 1 straight r subscript 2 straight K over denominator left parenthesis straight r subscript 2 minus straight r subscript 1 right parenthesis end fraction

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