Malfunction of a Refrigerator Light Switch The interior lighting of refrigerators is provided by incandescent lamps whose switches are actuated by the opening of the refrigerator door. Consider a refrigerator whose 40-W lightbulb remains on continuously as a result of a malfunction of the switch

Question

Malfunction of a Refrigerator Light Switch The interior lighting of refrigerators is provided by incandescent lamps whose switches are actuated by the opening of the refrigerator door. Consider a refrigerator whose 40-W lightbulb remains on continuously as a result of a malfunction of the switch (Fig. 6–58). If the refrigerator has a coefficient of performance of 1.3 and the cost of electricity is 8 cents per kWh, determine the increase in the energy consumption of the refrigerator and its cost per year if the switch is not fixed.

Accepted Answer

The lightbulb of a refrigerator malfunctions and remains on. The increases in the electricity consumption and cost are to be determined.
Assumptions The life of the lightbulb is more than 1 year.
Analysis The lightbulb consumes 40 W of power when it is on, and thus adds 40 W to the heat load of the refrigerator. Noting that the COP of the refrigerator is 1.3, the power consumed by the refrigerator to remove the heat generated by the lightbulb is

[latex] \dot{W}_{ ext {refrig }}=\frac{\dot{Q}_{ ext {refrig }}}{ COP _{ R }}=\frac{40 W }{1.3}=30.8 W [/latex]

Therefore, the total additional power consumed by the refrigerator is

[latex] \dot{W}_{ ext {total,additional }}=\dot{W}_{ ext {light }}+\dot{W}_{ ext {refrig }}=40+30.8=70.8 W [/latex]

The total number of hours in a year is

[latex] ext { Annual hours }=(365 ext { days } / yr )(24 h / ext { day })=8760 h / yr [/latex]

Assuming the refrigerator is opened 20 times a day for an average of 30 s, the light would normally be on for

[latex]\begin{aligned} ext { Normal operating hours } &=(20 ext { times/day })(30 s / ext { time })(1 h / 3600 s )(365 ext { days } / yr ) \&=61 h / yr\end{aligned}[/latex]

Then the additional hours the light remains on as a result of the malfunction becomes

Additional operating hours = Annual hours - Normal operating hours

= 8760 - 61 = 8699 h/yr

Therefore, the additional electric power consumption and its cost per year are

[latex]\begin{aligned} ext { Additional power consumption } &=\dot{W}_{ ext {total,additional }} imes ext { (Additional operating hours) } \&=(0.0708 kW )(8699 h / yr )= 6 1 6 ~ k W h / y r\end{aligned}[/latex]

and

[latex]\begin{aligned} ext { Additional power cost } &= ext { (Additional power consumption) }( ext { Unit cost }) \&=(616 kWh / yr )(\$ 0.08 / kWh )=\$ 49.3 / yr\end{aligned}[/latex]

Discussion Note that not repairing the switch will cost the homeowner about $50 a year. This is alarming when we consider that at $0.08/kWh, a typical refrigerator consumes about $70 worth of electricity a year.

Question 6.8: Malfunction of a Refrigerator Light Switch The interior ligh...

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