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In winter, people play hockey on Alta Lake in Whistler. However, it is not considered safe...

In winter, people play hockey on Alta Lake in Whistler. However, it is not considered safe by the Canadian Red Cross to play hockey on ice until the ice is 20 cm thick. On a winter day with a temperature −10◦C, it is observed that the lake has a 1cm thick layer of ice over the entire surface.
Constants which may be of use: The thermal conductivity of ice is 2.18W/m · K. Density of ice 916.7 kg/m3 and water 1000 kg/m3. Latent heat of fusion 334x103 J/kg.

a) If the air temperature remains at −10◦C, find the rate in cm per hour at which ice is added to the layer initially. The thermal conductivity of ice is 2.18W/m · K. Answer in cm/hour. The units are already written for you.

b) Find the rate in cm per hour at which ice is added to the layer as a function of the thickness X, where X is the number of centimeters.

c) Estimate the time it takes before you can safely play hockey

Answers: a) 2.56 cm/hr b) 2.56/X c) 3 days

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genius_generous answered 2 years ago
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