A metallic rod of cross-sectional area 9.0,,cm^2 and length 0.54 ,,m , with surface insulated to pre

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10-2.Transmission of Heat

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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}$

A

$330$

B

$60$

C

$600$

D

$33$

Solution

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, $K=60 \mathrm{W} /(\mathrm{mK})$

Standard 11

Physics

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