7.6 Conservation of Energy

Learning Objectives

By the end of this section, you will be able to:

• Explain the law of the conservation of energy.
• Describe some of the many forms of energy.
• Define efficiency of an energy conversion process as the fraction left as useful energy or work, rather than being transformed, for example, into thermal 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

$${\text{KE}}_{\text{i}}+{\text{PE}}_{\text{i}}+W_{\text{nc}}+{\text{OE}}_{\text{i}}={\text{KE}}_{\text{f}}+{\text{PE}}_{\text{f}}+{\text{OE}}_{\text{f}}\text{.}$$

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.

Table 7.2 gives the amount of energy stored, used, or released from various objects and in various phenomena. The range of energies and the variety of types and situations is impressive.

Transformation of Energy

The transformation of energy from one form into others is happening all the time. The chemical energy in food is converted into thermal energy through metabolism; light energy is converted into chemical energy through photosynthesis. In a larger example, the chemical energy contained in coal is converted into thermal energy as it burns to turn water into steam in a boiler. This thermal energy in the steam in turn is converted to mechanical energy as it spins a turbine, which is connected to a generator to produce electrical energy. (In all of these examples, not all of the initial energy is converted into the forms mentioned. This important point is discussed later in this section.)

Another example of energy conversion occurs in a solar cell. Sunlight impinging on a solar cell (see Figure 7.27) produces electricity, which in turn can be used to run an electric motor. Energy is converted from the primary source of solar energy into electrical energy and then into mechanical energy.

Efficiency

Even though energy is conserved in an energy conversion process, the output of useful energy or work will be less than the energy input. The efficiency $\text{Eff}$ of an energy conversion process is defined as

$$\text{Efficiency}(\text{Eff})=\frac{\text{useful energy or work output}}{\text{total energy input}}=\frac{W_{\text{out}}}{E_{\text{in}}}\text{.}$$

Table 7.3 lists some efficiencies of mechanical devices and human activities. In a coal-fired power plant, for example, about 40% of the chemical energy in the coal becomes useful electrical energy. The other 60% transforms into other (perhaps less useful) energy forms, such as thermal energy, which is then released to the environment through combustion gases and cooling towers.

Test Prep for AP Courses

Section Summary

• The law of conservation of energy states that the total energy is constant in any process. Energy may change in form or be transferred from one system to another, but the total remains the same.
• When all forms of energy are considered, conservation of energy is written in equation form as $${\text{KE}}_{\mathrm{i}}+{\text{PE}}_{\mathrm{i}}+W_{\text{nc}}+{\text{OE}}_{\mathrm{i}}={\text{KE}}_{\mathrm{f}}+{\text{PE}}_{\mathrm{f}}+{\text{OE}}_{\mathrm{f}}$$, where $\text{OE}$ is all other forms of energy besides mechanical energy.
• Commonly encountered forms of energy include electric energy, chemical energy, radiant energy, nuclear energy, and thermal energy.
• Energy is often utilized to do work, but it is not possible to convert all the energy of a system to work.
• The efficiency $\text{Eff}$ of a machine or human is defined to be $\text{Eff}=\frac{W_{\text{out}}}{E_{\text{in}}}$, where $W_{\text{out}}$ is useful work output and $E_{\text{in}}$ is the energy consumed.

Conceptual Questions

Consider the following scenario. A car for which friction is not negligible accelerates from rest down a hill, running out of gasoline after a short distance. The driver lets the car coast farther down the hill, then up and over a small crest. He then coasts down that hill into a gas station, where he brakes to a stop and fills the tank with gasoline. Identify the forms of energy the car has, and how they are changed and transferred in this series of events. (See Figure 7.28.)

Problems & Exercises