## Energy Storage, With a View Towards Energy Units

Energy storage devices come in many forms. Probably mankind's first use of an energy storage device was the ponding of water to drive water wheels. Even before that, the accumulation of fat in the body was an important energy storage mechanism for primitive mankind in temperate and cold climates. Today, technology gives us an array of modern energy storage choices such as batteries, fuel cells, fly wheels, compressed air, among others. See energy storage in Wikipedia, for instance, for a fuller list.

The most widely used and familiar storage device is the battery. Because it's energy is released as electricity, the battery has tended to be rated in amp-hours (amp is short for ampere) where amp measures the current that it supplies. The other important quantity of a battery, however, is the voltage. It is the amps times the voltage that measures the power of a battery; in fact, 1 amp-volt = 1 watt, the preferred unit of power. If one multiplies this by one second, then exactly 1 joule (J) of energy is delivered (1 joule = 1 watt-second).

Batteries are usually rated in amp-hours. This is not an energy unit. It merely says how long the battery is expected to deliver so many amps at the nominal voltage of the battery. The nominal voltage is important; for instance, a low-voltage lighting system at 12 volts is not nearly as bright as house lighting at 120 volts. The amp-hour rating is to be interpreted in terms of the voltage in order to really determine how much energy a battery can supply. In summary, because one hour has 3600 seconds:

1 amp-hour-volt = 3600 J

Could we then rate batteries in joules? Of course. But there is a small problem. Batteries cannot really discharge all their energy. As the current draw continues, the voltage begins to drop, thus slowing the delivery of the energy. At some voltage below the nominal voltage, the energy flows too slowly to power the attached bulb, or whatever, and the battery must be replaced. Modern batteries, such as lithium-ion types, are able to prolong the nominal voltage until nearly all the energy is discharged. Thus, only for these types of batteries is the total energy storage of the battery an acceptable measure of the actual energy that can be used. By adjusting for this phenomena, we could rate batteries in joules, realizing that this means "deliverable" joules.

It is interesting to estimate the energy capacity of a D-cell, commonly used in flashlights. A good D-cell is rated at roughly 6 amp-hours. Its nominal voltage is 1.5 volts. The product is 9 amp-hour-volts, which is 9*3600 J, or 32.4 kJ. Using the conversion chart, we find that this one battery holds the equivalent of 7.74 food Calories. Thus, a modest meal of 774 Calories would supply to our body the energy equivalent of 100 D cells. (Note that, if we measured all energy in joules, we would not have had to make these conversions to compare a battery and food intake!)