A deep rectangular pond of surface area A, containing water (dens… - Vidyadip

MCQ

A deep rectangular pond of surface area $A,$ containing water (denstity $=\rho,$ specific heat capactly $=s$ ), is located In a region where the outside air temperature is at a steady value of $-26^{\circ} {C}$. The thickness of the frozen ice layer In this pond, at a certaln 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
$26 \mathrm{K} / \mathrm{\rho r}(\mathrm{L}-4 \mathrm{s})$
B
$26 \mathrm{K} /\left(\rho \mathrm{x}^{2}-\mathrm{L}\right)$
✓
$26 K /(\rho x L)$
D
$26 \mathrm{K} / \mathrm{\rho r}(\mathrm{L}+4 \mathrm{s})$

✓

Answer

Correct option: C.

$26 K /(\rho x L)$

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

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

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