Two thin walled spheres of different materials, one with double the radius and one-fourth wall thickness of the other, are filled with ice. If the time taken for complete melting of ice in the sphere

Question

Two thin walled spheres of different materials, one with double the radius and one-fourth wall thickness of the other, are filled with ice. If the time taken for complete melting of ice in the sphere of larger radius is 25 minutes and that for smaller one is 16 minutes, the ratio of thermal conductivities of the materials of larger sphere to the smaller sphere is

TestHub · Accepted Answer

∫ d R = ∫ 4 π r 2 K d r ​ = 4 π K 1 ​ [ r 2 ​ r 1 ​ r 2 ​ − r 1 ​ ​ ] time mL ​ = ( r 2 t ​ ) 4 π K Δ θ ​ Given that m = ρ × 3 4 ​ π r 3 . time ρ L ​ = ( tr K ​ ) × constant time ∝ K tr ​ 16 25 ​ = tr K L ​ 4 t ​ 2 r K s ​ ​ = 2 K L ​ 1 K s ​ ​ Therefore, K s ​ K L ​ ​ = 25 8 ​ .

Physics - Heat & Thermo Question with Solution | TestHub

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