Question

Consider a 2.4-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 = 105,500 kJ), respectively. The efficiency of open burners can be taken to be 73 percent for electric burners and 38 percent for gas burners. Determine the rate of energy consumption and the unit cost of utilized energy for both electric and gas burners.

Answer 1

Answer:

• electric: 2.4 kW; $0.1370 per kWh utilized
• gas: 4.61 kW; $0.1078 per kWh utilized

Explanation:

Electric burner

For a 2.4 kW electric burner, the rate of energy consumption is 2.4 kW.

If efficiency is 73%, the cost of utilized energy is ...

  ($0.10 /kWh) / 0.73 ≈ $0.1370 per kWh utilized

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Gas burner

If the utilized energy provided by the gas burner is the same as the utilized energy of the electric burner, then the rate of energy consumption will be ...

  2.4 kW(0.73)/(0.38) = 4.61 kW

In terms of kWh, the cost of gas is ...

  $1.20/(105,500 kJ)·(1 kJ/(kW·s))·(3600 s/h) = $0.04095 /kWh

If efficiency is 38%, the cost of utilized gas energy is ...

  ($0.04095 /kWh) / 0.38 ≈ $0.1078 per kWh utilized

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The cost of gas is about 21% less per utilized joule.

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Comment on rates

The "unit rate" will depend on the unit chosen. In order to avoid unnecessary units conversions, we have elected to stick with kWh as the unit of energy for both cases. You may be asked for different units. We trust you or Google can make the necessary conversions.