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3 July, 21:48

A homeowner is considering these heating systems for heating his house: Electric resistance heating with $0.12/kWh and 1 kWh = 3600 kJ, gas heating with $1.34/therm and 1 therm = 105,500 kJ, and oil heating with $2.3/gal and 1 gal of oil = 138,500 kJ. Assuming efficiencies of 100 percent for the electric furnace and 87 percent for the gas and oil furnaces, determine the heating system with the lowest energy cost.

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  1. 3 July, 22:13
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    Oil Heating System has the lowest energy cost of $ 1.9 x 10^-5 / KJ

    Explanation:

    Let us consider each system one by one, and analyze its cost per unit KJ:

    Electric Resistance System:

    Cost = ($ 0.12/KWh) (1 KWh / 3600 KJ)

    Cost = $3.33 x 10^-5 / KJ

    This will be the final cost of system. Because efficiency of the system is 100%

    Gas Heating System:

    Cost = ($ 1.34/therm) (1 therm / 10550 KJ)

    Cost = $1.27 x 10^-4 / KJ

    The final cost of system will be given after dividing this cost by efficiency of the system:

    Cost = ($1.27 x 10^-4 / KJ) / 0.87

    Cost = $ 1.46 x 10^-4 / KJ

    Oil Heating System:

    Cost = ($ 2.3/gal) (1 gal / 138500 KJ)

    Cost = $1.66 x 10^-5 / KJ

    The final cost of system will be given after dividing this cost by efficiency of the system:

    Cost = ($1.66 x 10^-5 / KJ) / 0.87

    Cost = $ 1.9 x 10^-5 / KJ

    By analyzing the unit costs of each system, we find that the lowest cost is of Oil Heating System.
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