Two hollow spheres of same thickness are filled with ice. The ratio of their diameter is 1:2 and the ratio of thermal conductivities of the materials is 2:3. The ratio of times in which the ice gets melted in the two spheres is :
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D1/D2 = 1/2 = r1/r2= 1/2
k1/k2 = 2/3
let in container1 , Q1 heat is required and in container2 Q2
heat is required
Ratio of time taken to melt complete ice =
Q1 / heat_current1 / Q2 / heat current2
4/3 πr1 ^ 3 ×ρice ×L f / △Q×k2 A1 / 1 = A
4/3 πr2 ^3 ×ρ ice ×L f / △Q×k2 A2 / 1 = B
A/B =
= k1 A2 r^3 (r1) / k1 A 1 r^3 (r2) [ r1&r2 = radius 1 and radius 2]
= 3×4×1 / 2×1×8 = 3 / 4
final ratio will be = 3:4
thank you ❤️
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