Consider a 24 KW hooded electric open burner in an area where the unit costs of
ID: 2997152 • Letter: C
Question
Consider a 24 KW hooded electric open burner in an area where the unit costs of electricity
and natural gas are $0.10/KWh and 1.20/therm (1 therm=105500 KJ), respectively. The
efficiency of open burners can be taken to be 73 percentage for electric burners and 38
percentage for gas burners. Determine the rate of energy consumption and the unit cost of
utilized energy for both electric and gas burner?
Explanation / Answer
Here we are comparing two different heat sources with two different efficiencies and two different costs. To have a common basis of comparison we have to compute the actual energy input required to provide 3 kW of useful heat. For the electric burner, where the efficiency is 73%, we have to provide (24 kW)/(73%) = 17.52 kW of electrical energy. Since this energy costs $0.1/kW, the total cost to provide 24 kW of useful energy is ($0.1/kW?h)(17.52 kW) = $1.752/h.
For the gas burner, where the efficiency is 38%, we have to provide (24 kW)/(0.38%) = 9.12 kW of energy from the gas. The cost of natural gas, which is $1.2 per therm can be converted to a cost per kWh using the appropriate unit conversion factors: ($1.2/therm)(1 therm/105 Btu)(3412 Btu/kWh) = $0.04094/kWh. Thus the cost for the natural gas that has to supply 9.12 kW is ($0.04094W?h)(9.12 kW) = $0.3734/h. Thus the natural gas will be cheaper even though it has a lower efficiency.
The cost of each fuel per unit of useful energy produced in the burner can be found by dividing the fuel cost (in dollars per hour) by the 24 kW of useful energy from the burner. For electricity, the cost of the useful energy is ($1.752/h)/(24 kW) = $0.073/(useful kWh) For natural gas, the cost of the useful energy is ($0.3734/h)/(24 kW) = $0.0156/(useful kWh)
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