Question

A lake is covered with ice that is 3.6 cm thick. The temperature of the ambient air is –15°C. Find the rate of thickening of ice. Assume the thermal conductivity of ice is 2.00 W/(m · K), the density of ice is 9.0 ✕ 102 kg/m3, and the latent heat of fusion is 3.33 ✕ 105 J/kg. µm/s?

Answer #1

So, let’s assume we have some thickness of ice, x(t). The next layer of ice, of thickness dx, will freeze once you’ve gotten the appropriate amount of energy sucked out of it, through the ice, into the cold air right above the ice.

Where dQ is the amount of energy you’re extracting, m is the mass of the next layer of ice, and L is the heat of fusion (335,000 J/kg) of water. The mass of that narrow slice is given by:

now,

or,

or, dx/dt = T /xL = [2.0x(0 - (-15 )) ]/(900x3.33 ✕ 10^5x0.036) = 2.78 x10^-6 m/s = 2.78 µm/s

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