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 t_{1} and t_{2} respectively. The ratio of the thermal conductivities of A and B is

(a) t_{1} ∶ t_{2}

(b) t_{2} ∶ t_{1}

(c) t_{1}^{2} ∶ t_{2}^{2}

(d) t_{2}^{2} ∶ t_{1}^{2}

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} $