P3. After a particularly cold night, Alice leaves a tub of water outside. You may consider the ground and air to have temperatures of Te = -10°C and Th = 10°C respectively. How thick is the layer of ice that forms at the bottom of the tub of water, after the tub has been left outside for a long time? The tub of water initially has a layer of water of thickness ho = 10 cm. You may assume that the ground and air remain at a constant temperature throughout, and that the side lengths of the tub a, b > ho, i.e. the heat conduction is one- dimensional. Density of ice and water are Pice water have thermal conductivities of kjce = 2.22 W K-l m-1 and kw = 0.556 W K-1 m-1. 920 kg/m³ and pw = 1000 kg/m³. Ice and

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Chapter2: Steady Heat Conduction
Section: Chapter Questions
Problem 2.24P
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P3. After a particularly cold night, Alice leaves a tub of water outside. You may consider
the ground and air to have temperatures of Te = -10°C and Th = 10°C respectively. How
thick is the layer of ice that forms at the bottom of the tub of water, after the tub has been
left outside for a long time? The tub of water initially has a layer of water of thickness
ho
10 cm. You may assume that the ground and air remain at a constant temperature
throughout, and that the side lengths of the tub a, b » ho, i.e. the heat conduction is one-
dimensional. Density of ice and water are pice = 920 kg/m³ and pw = 1000 kg/m³. Ice and
water have thermal conductivities of kice = 2.22 W K-1 m'
-1 and kw
0.556 W K-1 m'
-1.
Transcribed Image Text:P3. After a particularly cold night, Alice leaves a tub of water outside. You may consider the ground and air to have temperatures of Te = -10°C and Th = 10°C respectively. How thick is the layer of ice that forms at the bottom of the tub of water, after the tub has been left outside for a long time? The tub of water initially has a layer of water of thickness ho 10 cm. You may assume that the ground and air remain at a constant temperature throughout, and that the side lengths of the tub a, b » ho, i.e. the heat conduction is one- dimensional. Density of ice and water are pice = 920 kg/m³ and pw = 1000 kg/m³. Ice and water have thermal conductivities of kice = 2.22 W K-1 m' -1 and kw 0.556 W K-1 m' -1.
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