Energy density, convenience, and cost are the biggest concerns when selecting a fuel for a particular application. Most other variables, such as pollution generation, long-term sustainability, and safety are, unfortunately, secondary at best in most cases.
Energy density can be measured by volume or by mass. In most cases, the volumetric measure of energy density is the more important because the space taken up by the fuel takes away from precious space that can be used for other things, like storage or living space.
For home heating and cooking, fuel is much cheaper than electricity. Natural gas is the usual choice, obviously not because of its energy density but because of its price and convenience. In many places, natural gas can be piped directly into a home or business so delivery and refueling are removed from the process entirely. Although its low energy density makes it an inconvenient choice for personal vehicles, some public transportation (particularly in California and Europe) runs on compressed natural gas† because it is cheap and burns relatively cleanly; although it may produce more greenhouse gasses and has roughly half the range of a more conventionally fueled vehicle.
In remote locations, natural gas is not available for piping into homes so more expensive propane or heating oil is used. In this case, mass is not important because the amount of fuel you can store is purely a matter of the volume of your storage tank. Heating oil has a higher energy density per volume, but propane is still a strong competitor because its pressurized nature makes it easy to get from bulk storage to where it is used. Propane is also a popular camping fuel because it is pressurized and also because weight is a concern, and it has the higher energy density by mass.
Of course, no discussion about fuel would be complete without talking about cars. On the surface, despite being a non-renewable resource, diesel fuel seems to be a no-brainer. It's cheaper than gasoline and has a higher energy density by both volume and mass. Unfortunately, diesel fuel doesn't work well in a cold engine, and people want to simply start up their cars immediately with no hassle. The few minutes saved every day by not pre-heating the engine is worth the extra cost of gasoline to most people. Ethanol burns cleaner and is renewable, being processed from plants, but is more expensive and breaks down plastics and rubber used in fuel systems, not to mention having much lower energy density. In some places, a gasoline/ethanol mix is available, but its practicality is debatable.
Space travel is a special case since the parasitic weight of fuel is extremely important, and the huge external hydrogen/oxygen fuel tank can be jettisoned to burn up on reentry into the atmosphere (although the solid fuel rockets on the space shuttle splashdown into the ocean with parachutes). Hydrogen has an enormous energy density by mass, but even when compressed its volumetric density is very low. Research into chemically storing hydrogen looks promising, however, to increase its volumetric density.
A quick glance at the energy density of batteries reveals that battery technology has a long way to go to catch up with fuels. It's no small wonder the electric car isn't very popular, and cordless electric lawn tools such as hedge trimmers, weed whackers, and lawn mowers aren't very practical for heavy use. Of interest is that lead-acid batteries are still popular despite their low energy density. Lead-acid batteries are cheaper by far than other kinds, and usually used in applications where weight is not important.
Note: energy densities vary somewhat by source and are approximate at best. For rough comparison only.
Material By Volume By Mass
Diesel Fuel 10,700 Wh/l 12,700 Wh/kg
Heating Oil 10,400 Wh/l 12,800 Wh/kg
Gasoline 9,700 Wh/l 12,200 Wh/kg
Butane 7,800 Wh/l 13,600 Wh/kg
LNG (-160°C) 7,216 Wh/l 12,100 Wh/kg
Propane 6,600 Wh/l 13,900 Wh/kg
Ethanol 6,100 Wh/l 7,850 Wh/kg
Methanol 4,600 Wh/l 6,400 Wh/kg
250 Bar NG 3,100 Wh/l 12,100 Wh/kg
Liquid H2 2,600 Wh/l 39,000 Wh/kg
150 Bar H2 405 Wh/l 39,000 Wh/kg
NiMH Battery 280 Wh/l 100 Wh/kg
Li-Ion Battery 200 Wh/l 150 Wh/kg
Lead-Acid Battery 40 Wh/l 25 Wh/kg
STP Propane 26 Wh/l 13,900 Wh/kg
STP NG 11 Wh/l 12,100 Wh/kg
STP H2 3 Wh/l 39,000 Wh/kg
Material By Volume By Mass
Liquid H2 2,600 Wh/l 39,000 Wh/kg
Propane 6,600 Wh/l 13,900 Wh/kg
Butane 7,800 Wh/l 13,600 Wh/kg
Heating Oil 10,400 Wh/l 12,800 Wh/kg
Diesel Fuel 10,700 Wh/l 12,700 Wh/kg
Gasoline 9,700 Wh/l 12,200 Wh/kg
LNG (-160°C) 7,216 Wh/l 12,100 Wh/kg
Ethanol 6,100 Wh/l 7,850 Wh/kg
Methanol 4,600 Wh/l 6,400 Wh/kg
Li-Ion Battery 200 Wh/l 150 Wh/kg
NiMH Battery 280 Wh/l 100 Wh/kg
Lead-Acid Battery 40 Wh/l 25 Wh/kg
(best volumetric type listed only)
Sources:
http://xtronics.com/reference/energy_density.htm
http://hypertextbook.com/
http://www.ior.com.au/ecflist.html
http://www.batteryuniversity.com
† Thanks, vuo, for pointing this out.
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