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The thickness of ice in a lake 5 cm and the atmospheric temperature is $- 10^{0} C .$ Calculate the time required for the thickness of ice to grow to 7 cm. $(K_{i c e} = 4 \times 10^{- 3} c a l / c m s^{0} C)$ $ρ_{i c e} = 0.92 g / c m^{3}$ $L_{i c e} = 80 c a l / g$

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Detailed Solution

$Δ t = \frac{ρ L}{2 K T} (x_{2}^{2} - x_{1}^{2}) = \frac{92 \times 10^{- 2}}{2 \times 4 \times 10^{- 3}} \times \frac{80}{10} (7^{2} - 5^{2})$ $Δt = 22080 \sec = 6 .13 hr$

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