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NEET 2019 · Heat Conduction

Heat Conduction question from NEET 2019

Q46NEET 2019Difficult

Heat Conduction

A deep rectangular pond of surface area AA, containing water (density = ρ\rho), specific heat capacity = ss), is located in a region where the outside air temperature is at a steady value of −26∘C-26^\circ\text{C}. The thickness of the frozen ice layer in this pond, at a certain instant is xx.

Taking the thermal conductivity of ice as KK, and its specific latent heat of fusion as LL, the rate of increase of the thickness of ice layer, at this instant, would be given by

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Answer: (d)

  1. Water below the ice is at 0∘0^\circC, top of ice at −26∘-26^\circC; heat conducted through the ice layer: KA(26)x\dfrac{KA(26)}{x}
  2. This heat comes from freezing a layer dxdx: ρA dx L=26KAxdt\rho A\,dx\,L = \dfrac{26KA}{x}dt
  3. dxdt=26KρxL\dfrac{dx}{dt} = \dfrac{26K}{\rho x L}
  4. So the answer is (d).
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