An ice-making machine inside a refrigerator operates in a Carnot cycle. It takes

Question

An ice-making machine inside a refrigerator operates in a Carnot cycle. It takes heat from liquid water at 0.0C and rejects heat to a room at a temperature of 24.2 C. Suppose that liquid water with a mass of 75.3 kg at 0.0C is converted to ice at the same temperature.

Take the heat of fusion for water to be Lf = 3.34×105 J/kg .

Part A

How much heat |QH| is rejected to the room?

Express your answer in joules to four significant figures.

An ice-making machine inside a refrigerator operates in a Carnot cycle. It takes heat from liquid water at 0.0C and rejects heat to a room at a temperature of 24.2 C. Suppose that liquid water with a mass of 75.3 kg at 0.0C is converted to ice at the same temperature.

Take the heat of fusion for water to be Lf = 3.34×105 J/kg .

Part A

How much heat |QH| is rejected to the room?

Express your answer in joules to four significant figures.

Explanation / Answer

TOTAL HEAT TO BE EXTRACTED FROM INSIDE THE REFRIGERATOR = HEAT EXTRACTE FROM THE WATER

TO FREEZE

Q2 = M L--------(1)

HERE M = 75.3Kg

and L = 3.34x10^5J/Kg

substituting the above values in eqn (1) we have

Q2 = (75.3)(3.34x10^-5)

     = 25.15x10^6J-------(2)

LET Q1 BE THE HEAT REJECTED THEN

Q1 / Q2 = T1 / T2-----(3)

           =273 + 24.2 / 273+ 0

          = 297.2 / 273 = 1.0886

FROM EQN (3) WE HAVE

Q1 = 1.0886xQ2

      =(1.0886)(25.15x10^6)

      = 27.3x10^6J-------(4)

MECHANICAL WORK DONE ON THE WORKING SUBSTANCE IS

W = Q1 - Q2-----(5)

SUBSTITUTING EQN (2) AND EQN(4) IN EQN(5) WE HAVE

W = [ 27.3 - 25.15]x10^6

W = 2.15x10^6J

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