Question

An ice-making machine inside a refrigerator operates in a Carnot cycle. It takes heat from liquid water at 0.0∘C and rejects heat to a room at a temperature of 24.5 ∘C. Suppose that liquid water with a mass of 84.4 kg at 0.0∘C 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. Answer in J

Answer 1

The heat absorbed by the carnot engine when the ice freezes

Q=mL_f =84.4*(3.34*10⁵) =-2.82*10⁷ J

Q_C = 2.82*10⁷J

For Carnot cycle

Q_C/Q_H = T_C/T_H

=>Q_H=Q_C*(T_H/T_C) =(2.82*10⁶)(273+24.5/273)

Q_H = 3.07*10⁷ J