Q. Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in $20\ minutes$ and $40\ minutes$ respectively. The ratio of thermal conductivities of the materials is
A) 5 : 6
B) 6 : 5
C) 3 : 1
D) 2 : 1
Explanation
(d) $\frac{Q}{t} = \frac{KA(\theta_{1} - \theta_{2})}{l} \Rightarrow \frac{mL}{t} = \frac{KA(\theta_{1} - \theta_{2})}{l}$
$\Rightarrow K \propto \frac{1}{t}\ \ \ \ \lbrack\because$ remaining quantities are same]
$\Rightarrow \frac{K_{1}}{K_{2}} = \frac{t_{2}}{t_{1}} = \frac{40}{20} = \frac{2}{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.