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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hamzaahmeds hamzaahmeds · Answer 1 · 2020-02-16T16:06:03+01:00

Answer:

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.