7.2 Conservation of energy

Law of conservation of energy

Energy, as we have noted, is conserved, making it one of the most important physical quantities in nature. The law of conservation of energy    can be stated as follows:

Total energy is constant in any process. It may change in form or be transferred from one system to another, but the total remains the same.

We have explored some forms of energy and some ways it can be transferred from one system to another. This exploration led to the definition of two major types of energy—mechanical energy $\left(\text{KE}+\text{PE}\right)$ and energy transferred via work done by nonconservative forces $(W_{\text{nc}})$ . But energy takes many other forms, manifesting itself in many different ways, and we need to be able to deal with all of these before we can write an equation for the above general statement of the conservation of energy.

Other forms of energy than mechanical energy

At this point, we deal with all other forms of energy by lumping them into a single group called other energy ( $\text{OE}$ ). Then we can state the conservation of energy in equation form as

All types of energy and work can be included in this very general statement of conservation of energy. Kinetic energy is $\text{KE}$ , work done by a conservative force is represented by $\text{PE}$ , work done by nonconservative forces is $W_{\text{nc}}$ , and all other energies are included as $\text{OE}$ . This equation applies to all previous examples; in those situations $\text{OE}$ was constant, and so it subtracted out and was not directly considered.

When does $\text{OE}$ play a role? One example occurs when a person eats. Food is oxidized with the release of carbon dioxide, water, and energy. Some of this chemical energy is converted to kinetic energy when the person moves, to potential energy when the person changes altitude, and to thermal energy (another form of $\text{OE}$ ).

Some of the many forms of energy

What are some other forms of energy? You can probably name a number of forms of energy not yet discussed. Many of these will be covered in later chapters, but let us detail a few here. Electrical energy is a common form that is converted to many other forms and does work in a wide range of practical situations. Fuels, such as gasoline and food, carry chemical energy    that can be transferred to a system through oxidation. Chemical fuel can also produce electrical energy, such as in batteries. Batteries can in turn produce light, which is a very pure form of energy. Most energy sources on Earth are in fact stored energy from the energy we receive from the Sun. We sometimes refer to this as radiant energy    , or electromagnetic radiation, which includes visible light, infrared, and ultraviolet radiation. Nuclear energy comes from processes that convert measurable amounts of mass into energy. Nuclear energy is transformed into the energy of sunlight, into electrical energy in power plants, and into the energy of the heat transfer and blast in weapons. Atoms and molecules inside all objects are in random motion. This internal mechanical energy from the random motions is called thermal energy    , because it is related to the temperature of the object. These and all other forms of energy can be converted into one another and can do work.