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Chapter 14: Problem 9

Convert \(1.00 \mathrm{kJ}\) to kilowatt-hours \((\mathrm{kWh})\).

Short Answer

Expert verified
Question: Convert 1.00 kJ (kilojoule) to kilowatt-hours (kWh). Answer: 1.00 kJ is approximately equal to \(2.78 \times 10^{-4}\, \mathrm{kWh}\).

Step by step solution

01

Convert kJ to J

First, we need to convert the given energy value in kJ to J (joules). Since 1 kJ equals 1000 J, then we have: \(1.00\, \mathrm{kJ} = 1.00 * 1000\, \mathrm{J} = 1000\, \mathrm{J}\)
02

Convert J to kWh

Now that we have the energy value in J, we can use the conversion factor to convert it to kWh. As we know, 1 kWh = 3,600,000 J. To find the equivalent value in kWh, we can divide the value in joules by 3600000: \(1000\, \mathrm{J} \times \dfrac{1\, \mathrm{kWh}}{3,600,000\, \mathrm{J}}\) An easy way to do this step is to cancel out the units and perform the calculation: \(\dfrac{1000\, \mathrm{J}}{3,600,000\, \mathrm{J}} \times 1\, \mathrm{kWh} = \dfrac{1}{3600}\, \mathrm{kWh}\)
03

Simplify the Answer

Finally, we can simplify the expression and write the answer as: \(\dfrac{1}{3600}\, \mathrm{kWh} \approx 2.78 \times 10^{-4}\, \mathrm{kWh}\) So, 1.00 kJ is approximately equal to \(2.78 \times 10^{-4}\, \mathrm{kWh}\).

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