Thermodynamics

Chapter 6 | 315Solution The lightbulb of a refrigerator malfunctions and remains on. Theincreases 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 thusadds 40 W to the heat load of the refrigerator. Noting that the COP of therefrigerator is 1.3, the power consumed by the refrigerator to remove theheat generated by the lightbulb isTherefore, the total additional power consumed by the refrigerator isThe total number of hours in a year isAssuming the refrigerator is opened 20 times a day for an average of 30 s,the light would normally be on forThen the additional hours the light remains on as a result of the malfunctionbecomesTherefore, the additional electric power consumption and its cost per year areandW # refrig Q# refrigCOP R 40 W1.3 30.8 WW # total,additional W # light W # refrig 40 30.8 70.8 WAnnual hours 1365 days>yr2 124 h>day2 8760 h>yrNormal operating hours 120 times>day2130 s>time211 h>3600 s2 1365 days>yr2 61 h>yrAdditional operating hours Annual hours Normal operating hours 8760 61 8699 h>yrAdditional power consumption W # total,additional 1Additional operating hours2 10.0708 kW2 18699 h>yr2 616 kWh/yrAdditional power cost 1Additional power consumption2 1Unit cost2 1616 kWh>yr2 1$0.08>kWh2 $49.3/yrDiscussion Note that not repairing the switch will cost the homeownerabout $50 a year. This is alarming when we consider that at $0.08/kWh, atypical refrigerator consumes about $70 worth of electricity a year.SUMMARYThe second law of thermodynamics states that processesoccur in a certain direction, not in any direction. A processdoes not occur unless it satisfies both the first and the secondlaws of thermodynamics. Bodies that can absorb or rejectfinite amounts of heat isothermally are called thermal energyreservoirs or heat reservoirs.Work can be converted to heat directly, but heat can beconverted to work only by some devices called heat engines.The thermal efficiency of a heat engine is defined ash th W net,outQ H 1 Q LQ H