Question

A snow maker at a resort pumps 240 kg of lake water per minute and sprays it into the air above a ski run. The water droplets freeze in the air and fall to the ground, forming a layer of snow. If all of the water pumped into the air turns to snow, and the snow cools to the ambient air temperature of -4.0°C, how much heat does the snow-making process release each minute? Assume the temperature of the lake water is 19.1°C, and use 2.00x10³ J/(kg·C°) for the specific heat capacity of snow.

Answer 1

Heat needed to cool water at 19.1 degrees to zero degrees
Q1 = mCw dT
Where m is the mass of water, Cw is the specific heat of water and dT is the change in temperature.
Q1 = 240 x 4186 x (19.1 - 0)
= 19188624 J

Heat needed for the phase change from 0^oC water to 0^oC ice
Q2 = mLf
Where Lf is the latent heat of fusion, Lf = 333.55 x 10³ J/kg
Q2 = 240 x 333.55 x 10³
= 80052000 J

Heat needed to cool ice at 0 ^oC to ice at - 4 ^oC
Q3 = mCi dT
= 240 x 2000 x 4
= 1920000 J

Total heat released, Q = Q1 + Q2 + Q3
= 19188624 + 80052000 + 1920000
= 101160624 J
= 1.01 x 10⁸ J