A refrigerator is to cool 2 kg of water (at atmospheric pressure) from 40°C to 5°C. The coefficient of performance of the refrigerator is 3.10. Determine the work needed to operate the refrigerator during this cooling process.
Given: Water; m = 2 kg; T1 = 40°C; T2 = 5°C; B= 3.10
Assume: The water behaves as an incompressible substance with constant specific heats: c = 4.18 kJ/kg-K. For the water as a system, W = ?KE = ?PE = 0
For the water, the First Law for a closed system reduces to Q = m (u2 – u1)
For an incompressible substance with constant specific heats: Q = m c (T2 – T1) = -292.6 kJ
This is heat out of the water, and into the cool reservoir, to be input into the refrigeration system: QC = 292.6 kJ
For a refrigerator, |W|=QC/? = 94.4 kJ
This is work into the system, so W = -94.4 kJ
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