Question

A deep rectangular pond of surface are A, containing water (density = r, 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 :-

• A. $\frac {26K}{\rho r\left(L-4s\right)}$
• B. $\frac {6K}{\left(\rho x^{2}-L\right)}$
• C. $\frac {26K}{\left(\rho xL\right)}$
• D. $\frac {26K}{\rho r\left(L+4s\right)}$

Answer 1

Answer: (C)

$\frac {26K}{\left(\rho xL\right)}$

Answer 2

KA \frac{[0-(-26)]}{x} dt$$= A(dx) \rho L

$\Rightarrow \frac{dx}{dt} = \frac{26K}{\rho K x}$

So, the correct option is (C): $\frac {26K}{\left(\rho xL\right)}$.