In winter, people play hockey on Alta Lake in Whistler. However,it is not considered safe to by the Canadian Red Cross play hockeyon ice until the ice is 20 cm thick. On a winter day with atemperature −10◦C, it is observed that the lake has a 1cm thicklayer of ice over the entire surface.
Constants which may be of use: The thermal conductivity of iceis 2.18W/m · K. Density of ice 916.7 kg/m3 and water1000 kg/m3. Latent heat of fusion 334x103J/kg.
A. If the air temperature remains at −10◦C, find therate in cm per hour at which ice is added to the layer initially.The thermal conductivity of ice is 2.18W/m · K. Note: Write cm perhour as cm/hr.
B. Find the rate in cm per hour at which ice is added to thelayer as a function of the thickness x.
C. Estimate the time it takes before you can safely playhockey.
