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Homework Statement
Consider a refrigerator whose 40-W light bulb remains on continuously as a result of a malfunctioning of the switch inside the refrigerator. The refrigerator has a coefficient of performance (COP) of 1.3 and the cost of electricity is estimated to be 10 cents per kWh (kilowatt-hour). Assume that the refrigerator is normally opened 20 times a day for an average of 30 s.
1-Determine additional power consumed by the refrigerator.
2-Estimate the additional electric power costs per year due to such malfunctioning per year.
Homework Equations
Coefficient of Performance = QL / W = heat transfer to/from cold body to system divided by work cost
Power = W / unit time
The Attempt at a Solution
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I'd just like verification as to whether or not I did this correctly, because I don't trust this problem.
The problem asks me to find the additional power consumed by the fridge, so I take this to mean the additional power cost of the malfunctioning lightbulb (not sure why the messed up lightbulb would affect the actual refrigeration much). So the EXTRA power consumed is just "actual power consumed per year - the normal power consumed per year".
First I convert the lightbulb power to KW, 40 W = .04 KW.
With a normally functioning bulb, the total time per day it'd be active is
20 opens/day * 30 sec/open = 600 sec/day = 10 minute/day = .1666 hours / day = 60.83 hours / year
normal active time = 60.83 hour / year
With this malfunctioning bulb, it would be active at all times
actual active time = 24 hour / day * 365 day / year = 8760 hour / year
Extra active time = actual - normal = 8760 - 60.83 = 8699 hours
Extra power = extra time * wattage = .04 KW * 8699 hour = 347.96 KW-Hour
Extra cost = extra time * cost per KW-hour = 10 cent/KW-Hour * 347.96 KW-Hour = 3479.6 cent = 34.79 $ per year
So if I'm right, those are the answers to the asked questions. What I'm leery of is the coefficient of performance. Am I right in assuming that was info meant to misdirect or distract me, or did I butcher this problem? Any and all help is greatly appreciated, thanks.