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  4. The two opposite faces of a cubical piece of iron are at 100° C and 0° C in ice. If the area of surface is 4 cm2, then the mass of ice melted in 10 min will be (Thermal conductivity of iron = 0.2 CGS units)

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Q. The two opposite faces of a cubical piece of iron are at $ 100{}^\circ C $ and $ 0{}^\circ C $ in ice. If the area of surface is 4 $ c{{m}^{2}}, $ then the mass of ice melted in 10 min will be (Thermal conductivity of iron = 0.2 CGS units)

CMC MedicalCMC Medical 2012

Solution:

$ Q=mL=KA\frac{({{\theta }_{1}}-{{\theta }_{2}})}{l}t $ $ \Rightarrow $ $ m=\frac{1}{L}\times KA\frac{({{\theta }_{1}}-{{\theta }_{2}})}{l}\times t $ $ =\frac{1}{80}\times 0.2\times 4\times \frac{(100-0)}{\sqrt{4}}\times 10\times 60 $ $ (\because {{l}^{2}}=4\Rightarrow l=\sqrt{4}) $ $ =\frac{0.2\times 4\times 100\times 600}{80\times 2}=300\,g $