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 \(26 \mathrm{K} /\left(\rho \mathrm{x}^{2}-\mathrm{L}\right)\)
C \(26 K /(\rho x L)\)
D \(26 \mathrm{K} / \mathrm{\rho r}(\mathrm{L}+4 \mathrm{s})\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(26 K /(\rho x L)\)

Step-by-step Solution

Detailed explanation

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

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From NEET

Explore more questions on app