Question

A refrigerator has a coefficient of performance of 2.25, runs on an input of 135 W of electrical power, and keeps its inside compartment at 5∘C. If you put a dozen 1.0-L plastic bottles of water at 31∘C into this refrigerator, how long will it take for them to be cooled down to 5∘C? (Ignore any heat that leaves the plastic.) A refrigerator has a coefficient of performance of 2.25, runs on an input of 135 W of electrical power, and keeps its inside compartment at 5∘C. Answer with a unit of minutes. Please answer legibly.

Answer #1

Coefficient of performance of the refrigerator = COP = 2.25

Input power of the refrigerator = P = 135 W

Volume of the plastic bottle = V = 1 L = 0.001 m^{3}

Number of plastic bottles = n = 12

Density of water = = 1000
kg/m^{3}

Mass of the water = M

M = nV

M = (12)(1000)(0.001)

M = 12 kg

Initial temperature of the water = T_{1} = 31
^{o}C

Final temperature of the water = T_{2} = 5
^{o}C

Specific heat of water = C = 4186 J/(kg.^{o}C)

Amount of heat to be extracted from the water = Q

Q = MC(T_{1} - T_{2})

Q = (12)(4186)(31 - 5)

Q = 1306032 J

Time taken to coll the water = T

Work to be supplied to the refrigerator to extract Q amount of heat = W

W = PT = 135T

T = 4299.69 sec

T = 71.66 minutes

Time taken to cool down the water to 5 ^{o}C by the
refrigerator = 71.66 minutes

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