A lake surface is exposed to an atmosphere where the temperature is

Question

A lake surface is exposed to an atmosphere where the temperature is < 0 ∘ C . If the thickness of the ice layer formed on the surface grows from 2 cm to 4 cm in 1 hour. The atmospheric temperature, T a ​ will be (Thermal conductivity of ice K = 4 × 1 0 − 3 cal / cm − s − ∘ C ; density of ice = 0.9 gm / cc . Latent heat of fusion of ice = 80 cal/gm. Neglect the change of density during the state change. Assume that the water below the ice has 0 ∘ temperature every where)

TestHub · Accepted Answer

x k A ​ ( 0 − T ) d t P L − k T ​ ∫ d t 0.9 × 80 − T × 4 × 1 0 − 3 ​ × 60 × 60 − T − T T ​ = ( P A d H ) L = ∫ 2 4 ​ x d x = 6 = 4 × 60 × 60 6 × 80 × 1 0 3 × 0.9 ​ = 3 90 ​ = − 3 0 ∘ C ​

Physics - Heat & Thermo Question with Solution | TestHub

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