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.

Explanation

Let `K_(1)` and `K_(2)` be the coefficients 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 the vessels are identicel , 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)`
or `K_(1) t_(1) = K_(2) t_(2)`
or `(K_(1))/(K_(2)) = (t_(2))/(t_(1)) = (25 "min")/(10 "min") = (5)/(2)`