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A hollow metal cube with side 0.5m and wall thickness $5 \times 10^{- 3} m$ is filled with ice. It is immersed in water tank maintained at 100ºC. Calculate the amount of ice melted in 335 sec. (conductivity of metal $= 0.5 W m^{- 1} K^{- 1}$ ,Latent heat of fusion of ice $= 335 \times 10^{3} J k g^{- 1}$ )

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15g

15 kg

$\frac{1.5}{6} g$

$\frac{15}{6} k g$

answer is A.

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Detailed Solution

Heat transferred to the ice is

$\frac{dQ}{dt} = \frac{kA (θ_{1} - θ_{2})}{l} = \frac{{mL}_{ice}}{time}$

$\Rightarrow \frac{0.5 {Wm}^{- 1} K^{- 1} \times 6 \times 0.25 m^{2} \times (373 - 273) K}{5 \times 10^{- 3}} = \frac{m \times 335 \times 10^{3}}{335}$

$\Rightarrow m = 15 kg$

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