A Few Useful Energy Quantities

Quickly, decide which of the following values is the largest. Hint: All of them represent solar intensity.

Now decide which of the following values is the largest. They are also units of solar intensity.

Here, it is childs' play to decide which is the largest, because all the values have the same units.

For many decades, the official system of units in The United States has been the International System of Units, called SI (Systeme Internationale). Canada changed abruptly to this system about 20 years ago, and now only the old people remember what a foot is, or what a gallon is. In the US, the reluctance to use sensible units has been very strong!

 

Concept	SI unit
length	meter
mass	kilogram
time	second
current	ampere

 
• The basic unit of length in the SI system is the meter (m), about 10% longer than a yard.
• The basic unit of mass in the SI system is the kilogram (kg), which is about 10% bigger than two pounds.
• The basic unit of time in SI is the second (s).
• In SI, the basic electrical unit is the ampere (A). (The British system has no electrical units whatsoever.)

On the Internet, it is not easy to express superscripts without using pictures that take too much time to load.  Therefore, we use a caret to express the exponent.  For example, we use m^2 to represent square meters.
 

It is important to remember that energy is measured in joules, and power is measured in watts. One joule = 1 watt ´ 1 second. People usually associate the watt with electricity, but that is because the SI system has traditionally been used only for electricity in the US. The watt is a general unit for power --- energy divided by time --- regardless of whether electricity is involved.

The so-called power company sends you a bill for energy (not power), but it uses a non-SI unit for time. To get the energy, they multiply kilowatts by hours to get kWh.

The largest efficiency possible is 1.0, or 100%. ("One-hundred ten percent" is an ahtlete's expression used to sell deodorant.)

Steam engines, gasoline, engines, diesel engines, turbine engines and the lot all have the purpose of converting heat into mechanical energy. The efficiency of heat engines is notoriously low, but not because the engineering is poor. Inevitably, they must throw away heat, and their waste heat must be hotter than the environment (lest the heat not leave the engine.)

Converting electric energy to mechanical energy (using motors) or mechanical energy to electricity (using generators) is often very efficient --- perhaps 90-95%.

Converting sunlight to electricity is not easy, for various technical reasons. There will always be energy losses that become heat. The only photocells available for large-scale applications are about 10% efficient. Some recent photocells made out of exotic materials have efficiencies approaching 18-19%. They are very costly, and very small.

The Heat Content table shows the heat that is released when various fuels are burned. By "wood," I refer to most wood (ash, oak, pine ...). A log of oak releases more heat than one of pine simply because it is heavier, not because the wood is different. Similarly, a kilogram of petroleum --- whether it be gasoline, diesel fuel, or crude oil --- releases the same amount of heat. However, crude oil is somewhat denser, so a bucketful of crude oil will release more heat than a bucketful of gasoline.

Coal always contains mineral impurities. Very poor coal has about 50% impurities, so when you "burn" a kilogram of very poor coal, you are really burning about a half kilogram of "real" coal; the rest is merely weight that becomes ash.

Methane is the major component of natural gas.

There is no natural supply of hydrogen, but hydrogen could be a manufactured fuel, made by removing it from water. It takes a lot of energy to do so, of course, but at least the hydrogen can be transported.

Energy is often measured in calories, kilocalories, or BTU (when people talk about heat) or in ergs, foot-pounds, or kilowatt-hours (when people talk about mechanical energy), or in barrels of oil or tons of TNT (chemical energy).

Power is often measured in BTU per hour (heat), horsepower (mechanical).

Time is measured in many common units, minutes, hours, days, or years.

Imagine how many ways you can dream up to express solar intensity, which must be in units of energy divided by area divided by time, or power divided by area. Just pick a combination: kilowatt-hours per day per acre, for example. How about BTU per year per square mile? Unfortunately, people use all those weird units!

If you find the table bewildering, remember this: if you measure things in SI units to begin with, you don't have to use any conversion factors whatsoever!

How can anybody make any sense of it all? The rule to make sense of it is:
 

where the R is the radius of the propeller (1/2 of the diameter), and the v is the wind speed. The symbol means that the power is less than or equal to the value calculated on the right.

California has some huge windmills ---some 3200 of them --- covering mountain sides in their windy areas. (Tehachapi, Altamont Pass, San Gorgonio) All together, they produce about 300 MW, which is about 1/4 as much power as a moderately large nuclear power plant produces, and is less than 10% of the electricity the small state of Connecticut consumes.

Water behind a dam has energy by virtue of being at high elevation. One kilogram has 9.8 joules of energy for every meter of elevation it has. A hydroelectric power plant uses that energy to turn a turbine, thereby to generate electricity. The power available depends upon how high the dam is, and how much water flows. The power available from a hydroelectric plant operating at about 85% efficiency can be calculated from

The average year in Connecticut brings us about 1.1 meters of precipitation. The land area of Connecticut is 5000 square miles, which is 1.3 ´ 10^10 square meters. The total volume of water falling on Connecticut in one year is about 1.4 ´ 10^10 million cubic meters. This amounts to 450 cubic meters per second. If we could use all of the water falling on the state, and we had a 200-foot dam (61 meters) to hold the water, we could get about 230 MW out of it, which is less than 10% of the Connecticut demand for electrical power. The Mayors of New Haven, Bridgeport, and most other major Connecticut cities might object to having their cities under water. So might environmentalists.

You can continuously get about 1/2 cord per acre per year of hardwood from Connecticut's forests. Note: 1/2 cord represents a certain amount of energy: 15.5 billion joules. 1 year is a certain amount of time: 31.6 million seconds and 1 acre is a certain area: 43,560 sq. feet = 4047 sq. meters. The acre produces about 500 watts (not electric!); the average power density is about 0.12 watts per square meter.

For use in formulas, the mass should be in kg, it is best to think of a gram as a milli-kilogram. (Oh, for a better name for the mass unit!)