One end of a 0.35 m long metal bar is in system and the other is in contact with ice . If 10 ice melts per minute , what is the thermal conductivity of the metal ? Given cross - section of the bar $= 7 t i m e s 10^{- 4} m^{2}$ and latent heat of ice is $3.4 \times 10^{5} J / k g$ ,

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Solution

Given , l = 0. 35 m ;
$A = 7 \times 10^{- 4} m^{2}$ ,
$m = 10 g = 10 \times 10^{- 3} k g = 10^{- 2} k g;$
$L = 3.4 \times 10^{5} J / k g;$
$Δ Θ = 100 - 0 100^{0} C; t = 1 m i n = 60 s$
$∴ Q = m L = \frac{K A Δ Θ t}{l}$
$∴ K = \frac{m L l}{A Δ Θ t} = \frac{10^{- 2} \times 3.4 \times 10^{5} \times 35 \times 10^{- 2}}{7 \times 10^{- 4} \times 100 \times 60}$
$= \frac{3.4 \times 5}{6} \times 10^{2} = \frac{17.0}{6} \times 10^{2}$
$2.833 \times 10^{3} J / m s^{o} C$

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