Question

Same quantity of ice is filled in each of the two metal containers $P$ and $Q$ having the same size, shape and wall thickness but made of different materials. The containers are kept in identical surroundings. The ice in $P$ melts completely in time $t_1$ whereas in $Q$ takes a time $t_2$. The ratio of thermal conductivities of the materials of $P$ and $Q$ is:

• A. $t_2:t_1$
• B. $t_1:t_2$
• C. $t_1^2:t_2^2$
• D. $t_2^2:t_1^2$

Answer 1

Answer: (A)

$t_2:t_1$

The amount of heat conducted is used to melt the ice in both cases.

So, generally, we may express this fact mathematically as:

$KA\frac{dT}{dx}t=mL$,

where the symbols have their usual meanings.

Now, as par given condition: $A,dT,dx,m$ and $L$ are constants.

So, $K\propto \frac{1}{t}$

$⟹$ $\frac{K_P}{K_Q}=\frac{t_2}{t_1}$