Question

The ice maker inside a refrigerator makes ice cubes at 0.0°C from water that is at 13.2°C when it first enters the ice maker. If this machine is rated at 224 W and has a 3.56 coefficient of performance, what is the maximum amount of ice it can produce in a 24 hourperiod without any interruption or stoppage? Assume that the ice maker works just like a refrigerator. The specific heat of water is 4184 J/(kg · °C), and the latent heat of fusion of ice is 33.4 ? 10⁴ J/kg.

________kg

Answer 1

Coefficient of performance of the ice make machine = COP = 3.56

Power supplied to the ice maker machine = W = 224 W

Heat removed from the ice maker machine = Q_c

Q_c = 797.44 W

Heat removed from the ice maker machine in 24 hours = E

Time period = T = 24 hours = 86400 sec

E = Q_cT

Mass of water = M

Initial temperature of water = T₁ = 13.2 ^oC

Final temperature of ice = T₂ = 0 ^oC

Specific heat of water = C = 4184 J/(kg.^oC)

Latent heat of fusion of ice = L = 33.4 x 10⁴ J/kg

E = M[C(T₁ - T₂) + L]

Q_cT = M[C(T₁ - T₂) + L]

(797.44)(86400) = M[(4184)(13.2 - 0) + 33.4x10⁴]

M = 177.01 kg

Maximum amount of ice that the ice maker machine can produce in 24 hours = 177.01 kg