A metallic rod of cross-sectional area $9.0\,\,cm^2$ and length $0.54 \,\,m$, 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 $1 \,\,gm$ for every $33 \,\,sec$. The thermal conductivity of the rod is ....... $ Wm^{-1} K^{-1}$
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Rate of heat transfer $=\frac{K \times A \times \Delta T}{l}$ $A=9 \times 10^{-4} m^{2}$
$\Delta T=100 K$
$L=0.54 m$
Rate = latent heat of fusion Itimes mass melted per sec $=333.5 \times(1 / 33) J / g$
putting values $\Longrightarrow \frac{K \times 9 \times 10^{-4} \times 100}{0.54}=333.5 \times(1 / 33)$
$K=60.63 W /(m K)$
rounding off, $K=60 \mathrm{W} /(\mathrm{mK})$
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