In the cable television show Ice Road Truckers, people often have to drive large

Question

In the cable television show Ice Road Truckers, people often have to drive large trucks over frozen lakes. To prevent trucks from crashing through the ice, the ice needs to be at least 8.23 feet thick. Currently the ice is 7.04 feet thick, which is below the safe level. Today the temperature is well above freezing, but they are expecting a cold spell that could freeze the ice to safe levels are expectingta old sphelt hat colud theeze t he ice to saly tev esi well above freezing.but they As the owner of a trucking company, you want your trucks to use the ice road as soon as possible. If the average temperature during the cold spell is 12.87 and the water temperature is 32.0°F, how many hours will it take for the frozen lake to be safely passable? The latent heat of fusion of water is 3.33 x 105 J/kg and the thermal conductivity of ice is 2.180 W/m K. The density of water near freezing is 1000.0 kg/m3 and the density of ice is 917.00 kg/m3 Number hr

Explanation / Answer

T1 = 32F = 0 degrees

T2 = -10.63 degrees

dQ = K*A*dT*dt/y

but dQ = m*L = rho*dy*A*L

rho*dy*A*L = K*A*dT*dt/y

dt = (rho*L*/k*dT)*y*dy

integratin

t = (rho*L*/k*dT)*(y2^2 - y1^2)/2

time taken to grow from y1 = 7.04 (2.15 m)   to y2 = 8.23 feet (2.51m)

t = (1000*3.33*10^5/(2*2.18*10.63))*(2.51^2-2.15^2)

t = 12053492.4 s

t = 3348.2 hr

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