A refrigerator has a coefficient of performance of 3.00. Theice tray compartment

Question

A refrigerator has a coefficient of performance of 3.00. Theice tray compartment is at -26.0°C, and the roomtemperature is 17.0°C. Therefrigerator can convert 24.0 g of waterat 17.0°C to 24.0 g of ice at -26.0°C eachminute.
What input power is required?
A refrigerator has a coefficient of performance of 3.00. Theice tray compartment is at -26.0°C, and the roomtemperature is 17.0°C. Therefrigerator can convert 24.0 g of waterat 17.0°C to 24.0 g of ice at -26.0°C eachminute.
What input power is required?

Explanation / Answer

       Given that the mass ofwater is m = 24.0 kg        Initial temparatureis T1 = 17.00C          final temparature isT2 = -26.00C             coefficient ofperformance of 3.00 ---------------------------------------------------------------            The energy requiredto change water to ice is                  dQ = m*Sw*(T1- 0 ) + m*Lice + m*Sice*(00C-T2)                         =m*Sw*(T1- 0 ) + m*Lice + m*Sice*(00C-T2)         where Sw = 4186J/kg.K is the specific heat of water                  Lice = 334 J/K is the latent heat of fussion of ice                  Sice =2060 J/kg.K is the specific heat of ice      Then the work done is dW = dQ/coefficient of performance                                                =dQ / 3.00      Then the power is P = dW /dt                                     =dW / (60s)                                    = --------- watt                   

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