Explanation Given information: Temperature of water is 0 °C , thickness of layerof ice is 4.00 cm , temperature of air is constant at − 10 °C . The expression for the rate of heat transfer is given as, d Q d t = k A Δ T x (1) The expression for the incremental energy is given as, d Q = L f ρ A d x Here, ρ is the density. A is the area. L f is the latent heat of fusion. Substitute L f ρ A d x for d Q in the equation (1). L f ρ A d x d t = k A Δ T x L f ρ A k A Δ T x d x = d t (2) Integrate the above equation. L f ρ A k A Δ T ∫ x d x = ∫ d t t = L f ρ k Δ T [ x 2 2 ] 0

Principles of Physics: A Calculus-Based Text

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ISBN: 9781133104261

Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

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Chapter 17, Problem 82P

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The time interval for the ice thickness to increase to 8.00 cm .

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Chapter 17, Problem 81P

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Principles of Physics: A Calculus-Based Text

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The time interval for the ice thickness to increase to 8.00 cm .

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Chapter 17 Solutions