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Abstract
Typically, the energy densities of solids or liquids such as coal and oil are measured in dimensions of energy per unit volume or energy per unit mass, whereas solar, wind, and hydroelectric sources are rated in dimensions of power per unit area. This article provides a unifying framework for comparing several prevalent energy sources on an energy-per-unit volume basis for the purpose of unifying conventional metrics. The energy density of oil is 35 to 45 gigajoules (10,000 kWh) per cubic meterFootnote∗. When measured using the methods presented, solar energy has a density of 1.5 microjoules per cubic meter, over twenty quadrillion times less than oil. Human energy density is approximately 1000 J/m3, while other inexhaustibles such as wind and tidal have energy densities of 0.5 to 50 J/m3. This article provides an educational engineering mathematics framework for calculating energy densities of prevalent energy sources. The goal is to provide a new perspective on how to compare energy sources on a more fundamental basis. Finally, the article provides a method of estimating the dollars-per-joule for natural resources versus human resources and concludes with commentary on how political decisions may be affected by energy densities and energy costs.
∗One gigajoule equals one billion joules, and there are 3,600,000 joules in a kWh. A cubic meter is about half the volume of a kitchen refrigerator.
ACKNOWLEDGMENTS
This work was funded in part by “A Green Alternative to Municipal Maintenance and Transportation,” Grant # C000021433″ through the Pennsylvania Department of Community and Economic Development with help from Pennsylvania State Representative James Roebuck. The author also thanks John Tetz, Richard Sadler, and David Gordon Wilson for valuable discussions on ethics and efficiency.
Notes
∗One gigajoule equals one billion joules, and there are 3,600,000 joules in a kWh. A cubic meter is about half the volume of a kitchen refrigerator.
1 kinetic energy (tidal low velocity) = ½ mv 2 = ½ × 1000 kg × (0.1 m/s)2 = 5 joules.
2 kinetic energy (tidal high velocity) = ½ mv 2 = ½ × 1000 kg × (1 m/s)2 = 500 joules.
3 The best endurance athletes can produce 400 to 600 watts for periods of minutes to hours.
4 Kinetic energy (human) = ½ mv2 = ½ × 50 kg × (2 m/s)2 = 100 joules.
5 This calculation is equivalent to determining the energy density of a slave or unskilled manual laborer.
6 In the expression mgh, the multiplication symbols have been omitted: mgh = m × g × h.
7 Twenty pounds is about ten kilograms, and a kilogram weighs about ten newtons. The bag thus weighs one hundred newtons. Lifting the bag into the car in one second requires 100 watts as seen in the following equation.
8 What is “energy return on energy invested?” Simply put, it means how many gallons of oil must be burned to extract one gallon of oil. If one gallon must be burned to extract one gallon, the EROEI ratio is 1:1, and there is obviously no point to burning a gallon of fuel, only to regain it. At the height of American and Saudi oil production this ratio may have been as great as 200:1. Only one barrel of oil was burned to extract 200 barrels.