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.

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.