At steady state, a refrigerator whose coefficient of performance is 3 removes en

Question

At steady state, a refrigerator whose coefficient of performance is 3 removes energy by heat transfer from a freezer compartment at 0 degrees C at the rate of 6000 kJ/hr and discharges energy by heat transfer to the surroundings, which are at 20 degrees C. a) Determine the power input to the refrigerator and compare with the power input required by a reversible refrigeration cycle operating between reservoirs at these two temperatures. b) If electricity costs 8 cents per kW-hr, determine the actual and minimum theoretical operating costs, each in $/day.

Explanation / Answer

a) COP = Heat transfer from freezer/Power input

3 = 6000/P

P = 2000 kJ/hr = 2000/(60*60) kW = 0.55 kW

b) Ideal COP = T_low/(T_high - T_low) = (0+273)/(20-0) = 13.65

Pideal = 6000/13.65 = 439.6 kJ/hr = 439.6/(60*60) kW = 0.122 kW

b) Actual cost = 0.55 kW* 0.08 $/kW-hr = $ 0.044 per hour = 0.044*24 $/day = 1.056 $/day

Theoretical cost = 0.122 kW* 0.08 $/kW-hr = $ 0.00976 per hour = 0.00976*24 $/day = 0.234 $/day

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