A perfectly insulating cylindrical glass is partially full of water. At the top of the water is a uniform layer of ice. The temperature of the water is 0 °C, and the temperature of the air above the ice is held fixed at – 19.00 °C. If the initial thickness of the ice layer is yi = 0.0950 m and the depth of the water below the ice is Yw = 0.0650 m, how long, in hours, will it take for the rest of the water to freeze? Assume that there is no transfer of heat through the sides or bottom of the glass and that the ice layer can slide freely up and down the glass. The latent heat of fusion of water is 3.33 x 10° J/kg, and the thermal conductivity of ice is 2.180 W/(m-°C). The density of water near freezing is 1000.0 kg/m³, and the density of ice is 917.00 kg/m³.

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A perfectly insulating cylindrical glass is partially full of
water. At the top of the water is a uniform layer of ice. The
temperature of the water is 0 °C, and the temperature of the
air above the ice is held fixed at – 19.00 °C.
If the initial thickness of the ice layer is yi = 0.0950 m and
the depth of the water below the ice is Yw = 0.0650 m, how
long, in hours, will it take for the rest of the water to freeze?
Assume that there is no transfer of heat through the sides or
bottom of the glass and that the ice layer can slide freely up
and down the glass.
The latent heat of fusion of water is 3.33 x 10° J/kg, and the
thermal conductivity of ice is 2.180 W/(m-°C). The density
of water near freezing is 1000.0 kg/m³, and the density of
ice is 917.00 kg/m³.
Transcribed Image Text:A perfectly insulating cylindrical glass is partially full of water. At the top of the water is a uniform layer of ice. The temperature of the water is 0 °C, and the temperature of the air above the ice is held fixed at – 19.00 °C. If the initial thickness of the ice layer is yi = 0.0950 m and the depth of the water below the ice is Yw = 0.0650 m, how long, in hours, will it take for the rest of the water to freeze? Assume that there is no transfer of heat through the sides or bottom of the glass and that the ice layer can slide freely up and down the glass. The latent heat of fusion of water is 3.33 x 10° J/kg, and the thermal conductivity of ice is 2.180 W/(m-°C). The density of water near freezing is 1000.0 kg/m³, and the density of ice is 917.00 kg/m³.
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