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

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

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