You are part of an engineering firm on contract by the U.S. Department of Energy

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 develop a program to help consumers measure the efficiency of their home appliances. Your job is to measure the efficiency of stove-top burners. The consumer will place a pan of room temperature water on their stove (with 1 gallon of water), record the initial room temperature in units of degrees Fahrenheit turn on the burner, and wait for it to boil. When the water begins to boil, they will record the time in units of minutes it takes for the water to boil. Finally, they will look up the power for the burner provided by the manufacturer. Using all of this information provided by the user, determine the efficiency of their burner. Assume the specific heat of water is 4.18 joules per gram degree Celsius. (Round your answers to three significant digits.) Click the icon to view conversion formulas for temperature scales. Click the icon to view the conversion table.

Explanation / Answer

we know that

C = ( 5/9) ( F-32)

given

F = 69

so

C = ( 5/9( ( 69-32)

C = 20.555

now

we know that

boling point of water is 100 C

so

energy used to increase temp of water = m x s x dT

given

mass = 1 gallon = 3785.42 g

now

energy used = 3785.42 x 4.184 x ( 100-20.555)

energy used= 1.258 x 10^6 J

now

we know that

energy = power x time

so

energy available = 1100 x 23 x 60

energy available = 1.518 x 10^6

now

efficiency = ( used / available ) x 1000

= ( 1.258 x 10^6 / 1.518 x 10^6) x 100

= 82.87

so

the energy efficiency is 82.87

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