Energy

Abstract

This chapter opens the book by connecting fundamental, and most likely familiar, concepts of forces, power and energy forms to the subject matter of nuclear energy. Energy forms addressed include potential, kinetic, mechanical, electrical, thermal, radiant, and electromagnetic energies. Basic laws recalled include conservation of energy and Newton’s law. Temperature is related to the average kinetic energy of atoms. The electronvolt (eV) is defined and tables of the Systeme Internationale (SI) units and prefixes are provided for reference. Einstein's theory of special relativity is introduced while establishing the equivalence of mass and energy via E = mc2.

Keywords

Energy

power

theory of special relativity

rest mass

relativistic mass

electronvolt

SI units

speed of light

electromagnetic spectrum

Chapter Outline

1.1 Forces and Energy

1.2 Units of Measure

1.3 Thermal Energy

1.4 Radiant Energy

1.5 The Equivalence of Matter and Energy

1.6 Energy and the World

1.7 Summary

1.8 Exercises

1.9 Computer Exercise

References

Further Reading

Our material world is composed of many substances distinguished by their chemical, mechanical, and electrical properties. They are found in nature in various physical states—the familiar solid, liquid, and gas, along with the ionic plasma. However, the apparent diversity of kinds and forms of material is reduced by the knowledge that there are only a little more than 100 distinct chemical elements and that the chemical and physical features of substances depend merely on the strength of force bonds between atoms.

In turn, the distinctions between the elements of nature arise from the number and arrangement of basic particles: electrons, protons, and neutrons. At both the atomic and nuclear levels, the structure of elements is determined by internal forces and energy.

1.1 Forces and energy

A limited number of basic forces exist: gravitational, electrostatic, electromagnetic, and nuclear. Associated with each of these is the ability to do work. Thus, energy in different forms may be stored, released, transformed, transferred, and “used” in both natural processes and man-made devices. It is often convenient to view nature in terms of only two basic entities: particles and energy. Even this distinction can be removed, because we know that matter can be converted into energy and vice versa.

Let us review some principles of physics needed for the study of the release of nuclear energy and its conversion into thermal and electrical forms. We recall that if a constant force F is applied to an object to move it a distance s, the amount of work W done is the product W = Fs. As a simple example, we pick up a book from the floor and place it on a table. Our muscles provide the means to lift against the force of gravity on the book. We have done work on the object, which now possesses stored energy (potential energy), because it could do work if allowed to fall back to the original level. Now a force F acting on a mass m provides an acceleration a, given by Newton’s law F = ma. Starting from rest, the object gains a speed v, and at any instant has energy of motion (kinetic energy) in amount

  (1.1)

For objects falling under the force of gravity, we find that the potential energy is reduced as the kinetic energy increases, but the sum of the two energy types remains constant. This is an example of the principle of conservation of energy. Let us apply this principle to a practical situation and perform some illustrative calculations.

As we know, falling water provides one primary source for generating electrical energy. In a hydroelectric plant, river water is collected by a dam and allowed to fall through a considerable height h, known as the head. The potential energy of water is thus converted into kinetic energy. The water is directed to strike the blades of a hydraulic turbine, which turns an electric generator.

The potential energy of a mass m located at the top of a dam is EP = Fh, being the work done to place it there. The force is the weight F = mg, where g is the acceleration of gravity. Thus, the potential energy is

  (1.2)

Example 1.1

Find the velocity of water descending through a dam with a 50 m head. Ignoring friction, the potential energy in kinetic form would appear at the bottom, that is, EP = EK. Using gravitational acceleration at the Earth’s surface* g0 = 9.81 m/s2, the water speed would be

* The standard acceleration of gravity is 9.80665 m/s2. For discussion and simple illustrative purposes, such numbers are rounded off to a few significant digits. Only when accuracy is important will more figures or decimals be used. The principal source of physical constants, conversion factors, and nuclear properties is the CRC Handbook of Chemistry and Physics (Haynes et al., 2011).

Energy takes on various forms, classified according to the type of force that is acting. The water in the hydroelectric plant experiences the force of gravity, and thus gravitational energy is involved. It is transformed into mechanical energy of rotation in the turbine, which is then converted to electrical energy by the generator. At the terminals of the generator, there is an electrical potential difference, which provides the force to move charged particles (electrons) through the network of the electrical supply system. The electrical energy may then be converted into mechanical energy as in motors, into light energy as in light bulbs, into thermal energy as in electrically heated homes, or into chemical energy as in a storage battery.

The automobile also provides familiar examples of energy transformations. The burning of gasoline releases the chemical energy of the fuel in the form of heat, part of which is converted to energy of motion of mechanical parts, while the rest is transferred to the atmosphere and highway. The vehicle’s alternator provides electricity for control and lighting. In each of these examples, energy is changed from one form to another but is not destroyed. The conversion of heat to other forms of energy is governed by two laws, the first and second laws of thermodynamics. The first law states that energy is conserved; the second specifies inherent limits on the efficiency of the energy conversion.

Energy can be classified according to the primary source. We have already noted two sources of energy: falling water and the burning of the chemical fuel gasoline, which is derived from petroleum, one of the main fossil fuels. To these we can add solar energy; the energy from winds, tides, or the sea motion; and heat from within the Earth. Finally, we have energy from nuclear reactions (i.e., the “burning” of nuclear fuel).

1.2 Units of measure

For many purposes, we use the metric system of units, more precisely designated as SI or Système Internationale. In this system (see NIST in the chapter’s references), the base units are the kilogram (kg) for mass, the meter (m) for length, the second (s) for time, the mole (mol) for amount of substance, the ampere (A) for electric current, the kelvin (K) for thermodynamic temperature, and the candela (cd) for luminous intensity. Table 1.1 summarizes these SI base units and important derived quantities. In addition, the liter (L) and metric ton (tonne) are in common use (1 L = 10–3 m3; 1 tonne = 1000 kg). However, for understanding earlier literature, one requires knowledge of other systems. Table A.3 in Appendix A lists useful conversions from British units to SI units.

Table 1.1

SI Base and Derived Quantities and Units

The transition in the United States from British units to SI units has been much slower than expected. To ease understanding by the typical reader, a dual display of numbers and their units are frequently given in this book. Familiar and widely used units such as the centimeter, the barn, the curie, and the rem are maintained.

In dealing with forces and energy at the level of molecules, atoms, and nuclei, it is conventional to use another energy unit, the electronvolt (eV). Its origin is electrical in character, being the amount of kinetic energy that would be imparted to an electron (charge 1.602 × 10–19 coulombs) if it were accelerated through a potential difference of 1 volt. Because the work done on 1 coulomb would be 1 J, we see that...