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 a steady value at the − 2 6 ∘ C .

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 a steady value at the − 2 6 ∘ 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 byNEET 2019 (Odisha)

TestHub · Accepted Answer

Key Idea If area of cross-section of a surface is not uniform or if the steady state condition is not reached, the heat flow equation can be applied to a thin layer of material perpendicular to direction of heat flow. The rate of heat flow by conduction for growth of ice is given by, d t d θ ​ = x K A ( θ 0 ​ − θ 0 ​ ) ] ​ where, d θ = ρ A d xL , θ 0 ​ = 0 and θ 1 ​ = − θ Given, θ 0 ​ = 0 ∘ C , θ 1 ​ = − 2 6 ∘ C The rate of increase of thickness can be calculated from Eq. dt d θ ​ ⇒ dt ρ AdxL ​ ⇒ dt dx ​ ​ = x KA ( θ 0 ​ − θ 1 ​ ) ​ = x KA ( θ 0 ​ − θ 1 ​ ) ​ = ρ AxL KA ( θ 0 ​ − θ 1 ​ ) ​ = ρ × L K [ 0 − ( − 26 )] ​ = ρ × L 26 K ​ ​

Physics - Heat & Thermo Question with Solution | TestHub

Options:

Doubts & Discussion