A deep rectangular pond of surface area A , containing water (density = , specific heat capacity =s ), is located in a region where the outside air temperature is a steady value at the -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

Step-by-step solution

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 d t = .K A ( ₀- ₀ ) ] x where, d = A d x L, ₀=0 and ₁=- Given, ₀=0^ C , ₁=-26^ C The rate of increase of thickness can be calculated from Eq. aligned d dt & = KA ( ₀- ₁ ) x AdxL dt & = KA ( ₀- ₁ ) x dx dt & = KA ( ₀- ₁ ) AxL & = K [0