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 c

Question

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 35 sec . Find the thermal conductivity of the rod in SI unit. [Latent heat of fusion of ice = 80 cal / g & J = 4.2 J / cal ]

TestHub · Accepted Answer

Let the thermal conductivity of rod is 'k'

$\frac{KA}{L} (100 - 0) = \frac{Δ Q}{Δ t}$

$\frac{Δ Q}{Δ t}$ is the power which is melting ice

$∴ \frac{Δ Q}{Δ t} = \frac{1 \times 80 \times 4.2}{35} ∴ \frac{9 \times 1 0 ^{- 4}}{0.54} \times 100 K = \frac{80 \times 4.2}{35} ∴ K = 57.6 Wm^{- 1} K^{- 1}]$

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