A deep rectangular pond of surface area A,containing water (density$$ $$=$$ ρ, specific heat $$capacity=s), is located in a region where the outside air temperature is at a steady value of –$$26$$°C. The thickness of the frozen ice layer in this pond, at a certain instant is x. Taking the thermal conductivity of ice as K, and its specific latent heat of fusion as L, the rate of increase of the thickness of ice layer, at this instant would be given by :

Question

A deep rectangular pond of surface area A,containing  water (density$$ $$=$$ ρ, specific heat $$capacity=s), is located in a region where the outside air temperature is at a  steady value of –$$26$$°C. The thickness of the frozen ice layer in this pond, at a certain instant is x. Taking the thermal conductivity of ice as K, and its specific latent heat of fusion  as L, the rate of increase of the thickness of ice layer, at this instant would be given by :

Infinity Learn · Accepted Answer

Let in a time interval dt, increase in thickness of ice layer be dx. It is assumed that density of ice $$=$$ density of water ρ dm $$=$$ (A$$ dx $$)ρdm x L $$=$$

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