Sizes of Power

We've looked before at approximate sizes of heat transfer coefficients and heat fluxes, and in this post we'll extend that to look at approximate comparative sizes of power—both generation and use.  This chart shows sizes from the power generated by the largest hydroelectric plant in the world to the power available from a tiny hearing aid battery.  Note that the scale is logarithmic: each line represents a factor of 10 increase over the preceding line.  The scale is shown in both Watts, which is a common unit of power for electricity, and in horsepower which is a common unit of power for engines.

The Three Gorges Power Plant in China is the largest power plant in the world, and can produce between 14,100 and 22,500 MW of electricity.  It is a hydroelectric plant which means that the electricity is produced by water turning turbines which are connected to generators.

Most typical utility-scale power plants, whether the heat source is nuclear decay heat, burning coal, or burning natural gas, are more in the range of 300-1200 MW.

Typical car engines vary between about 70 horsepower and 500 horsepower.  This is not to say that there aren't cars with even bigger (and smaller) engines than those, but that would be a typical range for cars that you might see on the street.

A riding lawn mower might be expected to have an engine in the 10-20 horsepower range, while a walk-behind push lawn mower more might be more like 3-5 hp.

In the U.S., many household circuits have fuses or breakers that trip at 15 amperes.  Certainly circuits can be wired for 20A or higher service, but 15A is typical.  With a line voltage of 120V, that means that you can't plug in devices that draw more than about 1800 W into a single circuit.  It is usually good practice to leave some margin of safety on tripping breakers or blowing fuses, so microwaves, toasters, and space heaters usually don't draw more than about 1200 W.

Average power consumption in U.S. households varies between about 700 W and 1700 W.  Note that this is an average power derived from dividing the yearly energy use by the total time (one year).  Of course, there are times during each day when the power use is much lower, and other times when it is much higher.

The human body can produce power as well.  Just imagine a person on a stationary bicycle attached to a generator.  People who measure such things report that elite athletes (think professional long-distance bicycle racers) can expend 500 W for hours at a time and short bursts in the neighborhood of 1500 W.  More average people would find it to be strenuous exercise to maintain an output of 200 W for an extended period.

In old incandescent light bulbs, the size was specified by the power that they drew which was proportional to the amount of light that you could expect.  While they are gradually being phased out and replaced by newer more efficient technologies which often specify light output directly, they still make a recognizable landmark in the power landscape.  Typical common light bulb sizes ranged from 40W to 250W, with the 100W light bulb being extremely common.

Batteries are a little difficult to characterize in terms of power because the rate at which energy is drawn off (the power) has a significant effect on the available battery capacity.  In general terms, however, a D-cell battery in normal intermittent service might draw between 38 mW and 750 mW with the former delivering about twice the total energy capacity of the latter.  A size 10 hearing aid battery is about 5.7 mm in diameter and 3.5 mm thick.  At a normal discharge rate, it could provide about 0.65 mW.

For those interested in power from the sun, the solar constant is about 1368 W/m^2 at the outer edge of the atmosphere.  By the time energy is absorbed by water vapor and other constituents of the atmosphere, the maximum amount that reaches the surface of the earth is in the general neighborhood of 1000 W/m^2.  Of course, that is at high noon, at sea level, on the equator.  The amount is considerably less when the sun is at an angle either because of latitude or time of day.  Solar energy to electricity conversion efficiencies vary widely, but whether photovoltaic or solar thermal, it would probably be unduly optimistic to assume an efficiency greater than about 15% for currently available, affordable systems.

It is also somewhat relevant to mention the mix of primary energy sources for electricity generation. In the U.S., coal and natural gas currently each account for about 33% of electricity generation. Nuclear accounts for another 20%, hydroelectric for about 6% and wind for about 5%.  All other sources including solar, geothermal, biomass, etc., add up to about 3%.