Two vessels A and B of different material are similar in shape and size. The same quantity of ice filled in them melts in time t_1 and t_2 respectively. The ratio of the thermal conductivities of A and B is

Q: Two vessels A and B of different material are similar in shape and size. The same quantity of ice filled in them melts in time t₁ and t₂ respectively. The ratio of the thermal conductivities of A and B is

(a) t₁ ∶ t₂

(b) t₂ ∶ t₁

(c) t₁² ∶ t₂²

(d) t₂² ∶ t₁²

Ans: (b)

Sol:
$\large \frac{\Delta Q}{\Delta t} = \frac{K A (T_1 -T_2)}{l}$

$\large \Delta Q = m L \; , \frac{\Delta Q}{\Delta t} = i $

$\large \frac{i_1}{i_2} = \frac{K_1}{K_2} = \frac{t_2}{t_1} $