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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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