You are part of an engineering firm on contract by the U.S. Department of Energy
ID: 996617 • Letter: Y
Question
You are part of an engineering firm on contract by the U.S. Department of Energy’s
Energy Efficiency and Renewable Energy task force to measure the power efficiency of
home appliances. Your job is to measure the efficiency of stove-top burners. In order to
report the efficiency, you will place a pan containing one gallon of room temperature water
on their stove, record the initial room temperature, turn on the burner, and wait for it to
boil. When the water begins to boil, you will record the time it takes the water to boil and
look up the power for the burner provided by the manufacturer. The specific heat capacity
of water is 4.18 joules per gram degree Celsius. After measuring the following stove-top
burners, what is the efficiency of each burner?
Room Temp [°F] Time to Boil [min] Rated Burner Power [W]
(a) 72 21 1500
(b) 69 18 1350
Explanation / Answer
'The specific heat of water is 4.18 joules per gram degree celsius' means that 4.18 joules energy is needed to raise the temperature of one gram water by one degree celsius.
1 gallon = 3.785 lit. = 3785 ml. So, weight of 1 gallon water is 3785 g.
72 degree fahrenheit = 22.22 degree celsius
69 degree fahrenheit = 20.55 degree celsius
a) provided energy to boil 1 gallon water = (100 - 22.22) X 4.18 X 3785 Joules = 1230580.71 joules
energy provided by the burner theoritically = 1500 X 21 X 60 = 1890000 joules
so, the efficiency of the burner = 1230580.71/1890000 = 0.65
B) Similarly,
provided energy to boil 1 gallon water = (100 - 20.55) X 4.18 X 3785 Joules = 1257002.28 joules
energy provided by the burner theoritically = 1350 X 18 X 60 = 1458000 joules
the efficiency of the burner = 1257002.28/ 1458000 = 0.86
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