Question

A metallic rod of cross-sectional area $9.0c{m}^2$ and length $0.54m$, with the surface insulated to prevent heat loss, has one end immersed in boiling water and the other in ice-water mixture. The heat conducted through the rod melts the ice at the rate of $1gm$ for every $33sec$. The thermal conductivity of the rod is :

• A. $330W{m}^{-1}{K}^{-1}$
• B. $60W{m}^{-1}{K}^{-1}$
• C. $600W{m}^{-1}{K}^{-1}$
• D. $33W{m}^{-1}{K}^{-1}$

Answer 1

The correct option is B $60W{m}^{-1}{K}^{-1}$

Rate of heat transfer = $\frac{K\times A\times \Delta T}{l}$
$A=9\times 10$${}^{-4}$ $m^2$
$\Delta T=100K$
$L=0.54m$
Rate = latent heat of fusion \times mass melted per sec
= $333.5\times \left(1/33\right)J/g$

putting values
$⟹\frac{K\times 9\times {10}^{-4}\times 100}{0.54}=333.5\times \left(1/33\right)$

$K=60.63W/\left(mK\right)$

rounding off, $K=60W/\left(mK\right)$