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Energy Conversions

Key Concepts

  • The SI unit for energy is the joule1.

  • The joule has been given the symbol J2

  • Most common conversion is between joules (J) and kilojoules (kJ):
    There are 1000 J in 1 kJ
    so 1000 J = 1 kJ
    initial unit conversion final unit
    joules (J) ÷ 1000 = kilojoules (kJ)
    kilojoules (kJ) x 1000 = joules (J)

  • The calorie3 is a non SI unit of measurement for energy4.

  • 1 calorie ≈ 4.18 joules5
          1 cal ≈ 4.18 J
    initial unit conversion final unit
    calories (cal) x 4.18 = joules (J)
    joules (J) ÷ 4.18 = calories (cal)

Units of Energy Conversions

SI Unit Conversions

factors 1012 109 106 103 102 101 10-1 10-2 10-3 10-6 10-9 10-12 10-15 10-18
prefix tera giga mega kilo hecto deca deci centi milli micro nano pico femto atto
symbol T G M k h da d c m µ n p f a

1 kilojoule (1 kJ) = 103 joules (1000 J) 1 joule (1 J) = 1 ÷ 103 kilojoules = 0.001 kJ
1 millijoule (1 mJ) = 10-3 joules (0.001 J) 1 joule (1 J) = 1 ÷ 10-3 millijoules = 1,000 mJ
1 microjoule (1µ J) = 10-6 joules 1 joule (1 J) = 1 ÷ 10-6 microjoules = 106µ J

The most likely conversions you will have to make will be between joules (J) and kilojoules (kJ)

  1. To convert kilojoules (kJ) to joules (J):

    multiply the number of kilojoules (kJ) by 1000 to give an energy value in units of joules (J)

    energy (J) = energy (kJ) x 1000

  2. To convert joules (J) to kilojoules (kJ):

    divide the number of joules (J) by 1000 to give an energy value in kilojoules (kJ)

    energy (kJ) = energy (J) ÷ 1000

Examples of Energy Conversions Using SI Units

  1. Convert 1 kilojoule to joules

    From the table above we see that kilo = 103 = 1,000
    1 kJ = 1,000 J

    1 kilojoule = 1,000 joules

  2. Convert 2.5 kJ to joules

    1 kJ = 1,000 J
    2.5 kJ = 2.5 x 1,000 J = 2,500 J

    2.5 kJ = 2,500 J

  3. Convert 5 millijoules to joules

    From the table above we see that milli = 10-3
    5 mJ = 5 x 10-3 J = 0.005 J

    5 millijoules = 0.005 joules

  4. Convert 250 J to kilojoules

    1,000 J = 1 kJ
    1 J = 1 ÷ 1,000 kJ = 0.001 kJ
    250 J = 250 x 0.001 kJ = 0.250 kJ

    250 J = 0.250 kJ

  5. Convert 25 µJ to kilojoules

    1 µJ = 10-6 J
    25 µJ = 25 x 10-6 J = 2.5 x 10-5 J
    1 J = 1 ÷ 1,000 kJ
    2.5 x 10-5 J = 2.5 x 10-5 ÷ 1,000 kJ = 2.5 x 10-8 kJ

    25 µJ = 2.5 x 10-8 kJ

Quick Question

Question 1.

Convert 0.343 kJ to J

    Check

Calories

A calorie is a larger measure of energy than a joule.


  • 1 calorie ≈ 4.18 joules
        1 kilocalorie ≈ 4.18 kilojoules
        1 kilocalorie ≈ 1000 x 4.18 = 4180 joules

  • 1 joule ≈ 1 ÷ 4.18 = 0.239 calories
        1 kilojoule ≈ 1 ÷ 4.18 = 0.239 kilocalories
        1 kilojoule ≈ 1000 x 0.239 = 239 calories

The most likley conversions you will need to make are between joules (J) and calories (cal)

  1. To convert energy in calories (cal) to energy in joules (J):
    multiply the energy in calories (cal) by 4.18 to give an energy value in joules (J)
    energy (J) = 4.18 x energy (cal)

  2. To convert energy in joules (J) to energy in calories (cal):
    divide the energy in joules (J) by 4.18 to give an energy value in calories (cal)
    energy (cal) = energy (J) ÷ 4.18

    Alternatively

    To convert energy in joules (J) to energy in calories (cal)
    multiply the energy in joules (J) by 0.239 ( since 1 ÷ 4.18 = 0.239) to give energy in calories (cal)
    energy (cal) = energy (J) x 0.239

Examples of Conversion Between Calories and Joules

  1. Convert 100 calories to joules
    • 1 calorie = 4.18 joules
    • 100 calories = 100 x 4.18 J = 418 joules

    100 cal = 418 J

  2. Convert 12.0 kilocalories to kilojoules
    • 1 kilocalorie = 4.18 kilojoules
    • 12.0 kilocalories = 12.0 x 4.18 kJ = 50.2 kilojoules

    12.0 kcal = 50.2 kJ

  3. Convert 150 kilocalories to joules
    • 1 kilocalorie = 4.18 kilojoules
    • 150 kilocalories = 150 x 4.18 kJ = 627 kilojoules
    • 1 kilojoule = 1000 joules
    • 627 kilojoules = 627 x 1000 = 627 000 joules

    150 kcal = 627,000 J

  4. Convert 10 joules to calories
    • 1 joule = 0.239 calories
    • 10 joules = 10 x 0.239 = 2.39 calories

    10 J = 2.39 cal

  5. Convert 1.2 kilojoules to kilocalories
    • 1 kilojoule = 0.239 kilocalories
    • 1.2 kilojoules = 1.2 x 0.239 = 0.287 kilocalories

    1.2 kJ = 0.287 kcal

  6. Convert 1500 joules to kilocalories
    • 1 joule = 0.239 calories
    • 1500 joules = 1500 x 0.239 = 359 calories
    • 1 kilocalorie = 1000 calories
    • 1 calorie = 1 ÷ 1000 = 0.001 kilocalories
    • 359 calories = 359 x 0.001 = 0.359 kilocalories

    1500 J = 0.359 kcal

Quick Question

Question 1.

Convert 12.5 J to cal

    Check


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1 The Ninth International Conference on Weights and Measures (1948) recommended the use of the joule (volt coulomb) as the unit of heat.
The joule is a derived SI unit for the measurement of energy.
The SI base unit for the measurement of energy is kg.m2 s-2
1 J = 1 kg.m2 s-2

2 The joule is named after the English physicist James Prescott Joule.

3 The calorie, from the Latin calor meaning heat, was first defined by Nicolas Clément in 1824 as a unit of heat.

4Other units for measuring energy are:

  • erg (1 J = 107 ergs)
  • British Thermal Units, BTU (1 J = 9.48 x 10-4 BTU)
  • electronvolts, eV (1 J = 6.24 x 1018 eV)
  • kilowatt hours, kWh (1 J = 2.78 x 10-7 kWh)

5 National Bureau of Standards defined a calorie as equal to exactly 4.1840 J
You will find this approximated to 1 cal = 4.18 J, even 1 cal = 4.2 J, when used in schools.
Note that this will effect the number of significant figures that you will be able to use in your calculations.

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