# The law of conservation of energy

The law of conservation of energy: The total amount of energy in the universe is constant, although energy can be transformed from one form to another. The basic unit of energy is the joule. A watt is one joule per second. Thus a 100 watt electric bulb uses 100 joules per second of electric energy. That energy must come from somewhere and must be paid for. One pays for electric energy in kilowatt-hours which is 1,000 watts being delivered per hour. Thus a kilowatt-hour is 3,600,000 joules, since "kilo" means a thousand, and there are 3,600 seconds in an hour. At 10 cents per kilowatt hour, a joule is really cheap. 10 joules would lift a one kilogram weight one meter.

Schemes for powering cars or houses that require violating the law of conservation of energy can't work. Here's an example.

Several times I have received in email the following idea for powering cars with hydrogen from water. Run the car on hydrogen obtained by splitting water by electrolysis using the car's generator to get the electricity.

Here's why it won't work. The amount of energy you get from burning hydrogen and running a generator produces at most the amount of energy required to replace the energy used to split the water. There would be none left over to power the car. Actually, you would get considerably less energy than is needed to get more hydrogen to replace that burned. Most likely it would be about 20 percent.

Splitting water to get hydrogen is not an original source of energy. Rather it is a way of tranforming energy into a form more usable for a certain purpose. For example, nuclear energy can be used to split water (H2O) into hydrogen and oxygen. The oxygen is released into the air, and the hydrogen is liquefied and used to run cars in the same way gasoline is used to run cars. [The process is quite inefficient compared to running the car directly with a small nuclear reactor. Unfortunately, a nuclear reactor in a car would kill the occupants. Ships can use nuclear reactors, because they can afford the tons of shielding required to keep the neutrons away from the crew.] Solar electricity can also be used to split water, but solar energy is expensive.

What are the sources of energy that have been used?

Human muscle
A hard working human can put out about 100 watts, enough for a light bulb. To light an average home at night would require quite a few slaves turning generators. The energy for human muscle power is chemical energy from food. This energy comes from the sun and is absorbed by the crops. If you pay 5 cents per kilowatt-hour (kwh), you are getting for your 5 cents what could be generated by a man working hard for 10 hours.
Horse power
Horses are a better source of energy than humans. A horse can put out about 8 times as much energy as a human and is easier to keep working.
Coal, oil and natural gas
Chemically coal is carbon (C) with impurities. Natural gas is CH4, i.e. carbon and hydrogen, oil and the gasoline made from oil are hydrocarbons, compound of hydrogen and carbon of various compositions. Octane is C8H18 for example. When burned, oxygen from the air turns the carbon into CO2, carbon dioxide, and the hydrogen into H2O, water, usually in the form of steam. Energy is released because the fuel + oxygen from the air has more energy than the products of burning the fuel. You can get the fuel back from the combustion products by reversing the chemical reaction of burning, but then you must supply the energy. All these fuels are the remains of plants that got energy from sunlight when they grew millions of years ago. The supplies of these fuels won't last more than a few hundred years, maybe quite a bit less. At present, burning these fuels is the largest source of energy for our civilization.
Water power
The sun evaporates water from the ocean, and some of it falls as rain or snow at high altitudes. Water at high altitude has potential energy compared to water at low altitude, and this energy can be obtained by damming the water and running it through electric generators. In the developed countries, most of the good sites for dams, lots of water at a high altitude, are already in use. A large expansion of water power isn't possible.
Direct solar power and wind
These work and have been politically favored in the advanced countries since the 1970s. However, they are still too expensive to compete with only moderate subsidies. The enthusiasts remain optimistic after all these years. My own opinion is that they will remain so expensive that if our civilization had to rely on them the standard of living would go down a lot. Some enthusiasts think they wouldn't mind that.
Nuclear energy
This generates about 20 percent of the world's electricity. Its expansion is temporarily held up by the influence of environmentalist ideology. See the Nuclear FAQ for details. Nuclear energy is humanity's best hope for the long term.

## Energy and power

These terms are often confused, because in ordinary language they are sometimes synonyms. However, the distinction is important for science and engineering and is simple to state. Power is the rate at which energy is generated or used. The basic unit of energy is the joule, and the basic unit of power is the watt. A watt is one joule per second. Thus a hundred watt light bulb is using 100 joules of energy per second, turning the electric energy into light and heat. A 1,000 megawatt power plant is generating a billion joules per second. It gets that energy from burning fuel or from splitting atoms of uranium and plutonium. To get 1,000 megawatts it actually uses 3,000 megawatts from the fuel. The leftover 2,000 megawatts is inevitably produced as leftover heat as shown by the second law of thermodynamics.

A variety of units are used for power and energy. Kilowatts and megawatts are a thousand watts and a million watts respectively. A horsepower is 746 watts by James Watts's optimistic definition, but few horses can put out that power for long. Energy is measured in kilowatt-hours. A kilowatt-hour is therefore 3,600,000 joules. Another unit of energy is the British thermal unit or BTU, sometimes used in engineering. It is the amount of energy needed to raise one pound of water one degree Farenheit.

This is a very sketchy exposition. An elementary physics book will do much better.

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Send comments to mccarthy@stanford.edu. I sometimes make changes suggested in them. - John McCarthy