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Two vessels of different materials are i...

Two vessels of different materials are identical in size and wall-thickness. They are filled with equal quantities of ice at `0^(@)C`. If the ice melts completely in 10 and 25 minutes respectively, compare the coefficients of thermal conductivity of the materials of the vessels.

Text Solution

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Let `K_(1)` and `K_(2)` be the coefficient of thermal conductivity of the materials and `t_(1)` and `t_(2)` be the time in which ice melts in the two vessels . Since both vessels are identical , so `A` and x in both the cases is same.
Now , `Q= (K_(1)A(theta_(1)-theta_(2))t_(1))/(L) = (K_(2)A(theta_(1)-theta_(2))t_(2))/(L) implies (K_(1))/(K_(2)) = (t_(2))/(t_(1))` = `(25"min")/(10"min") = (5)/(2)`
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