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C h a p t e r 1 Energy – the driving force of change Energy is the driving force for all changes: winds, rains, storms, thunders, forest fires, earthquakes, waves, plant growth, food decay, ocean tides, formation and melting of ice, combustion, and growing old to name just a few. Furthermore, nuclear changes such as radioactivity, nuclear fission, and nuclear fusion (reactions) are also driven by energy. Energy, unlike matter, has no weight, size, shape, color or appearance, and its recognition is difficult. There are still some aspects about energy we do not fully understand.

Energy is the heart of nuclear technology, because all nuclear phenomena are caused Energy plays an important part by energy. In fact, the amount of energy And it’s used in all this work; involved in nuclear technology is so large Energy, yest energy with power so great, that it scares us. We, the human race, have A kind that cannot shirk. the nuclear technology to destroy the civilization and perhaps the planet Earth, if If the farmer had not this energy, we are not careful. Thus, we discuss some He would be at a loss, aspect of energy as an introduction to But it’s sad to think, this energy nuclear technology. Belongs to a little brown horse.

In this chapter, we are exploring the A school verse by Richard Feynman following questions. a Nobel laureate for physics

 What is energy? What are the forms of energy? How does energy convert from one form to another?

 How can amounts of energy be measured or determined? How does energy cause changes? How does energy behave?

 Why does it rain or snow? How is energy related to rain or snow?

1 Mechanical Work and Heat as Forms of Energy

HREF="#temperature MACROBUTTON HtmlResAnchor Temperature scales were invented to compare hotness or coldness, and their invention enabled us to measure quantities of HREF="#heat MACROBUTTON HtmlResAnchor heat. During the same period when temperature scales were invented, Newtonian physics had defined HREF="#mechanical MACROBUTTON HtmlResAnchor mechanical work, but a long time elapsed before James P. Joule (1818-1889) recognized that heat and mechanical work were inter-convertible. Then inter-convertibility between mechanical work and heat led to the concept of HREF="#energy MACROBUTTON HtmlResAnchor energy, which was coined to represent all elusive driving forces of changes

Mechanical Work Mechanical work, is defined in Newtonian physics, using distance, mass and force. Distance and mass are basic quantities, measured by comparing with the standard meter and kilogram. The force, however, is an elusive concept that is defined in terms of mass and distance (more precisely acceleration). Mechanical work is discussed fully in Newtonian mechanics, and only a brief review is given here.

 What are mass and distance? How are masses and distances measured, Newtonian mechanics and in what (SI or other) units? Strictly speaking, Newtonian mechanics is valid  What is force? only in a coordinate system with its origin at the How a force can be delivered? center of the solar system. What units are used for force? How much force is 1 N? The 1st law defines mass m as a measure of inertia. The 2nd law gives the acceleration a imparted to a  What is mechanical work? body by a force F What are the units for mechanical work? a = F / m Both F and a are vectors, having magnitudes and The SI units for mass and distance are directions. (Newton = kg-m/s2) kilogram (kg) and meter (m) respectively. They are measured by comparing with the The 3rd law states that actions of two bodies upon standard meter stick and kg mass. Please note each other are equal, but opposite. the following quantities and units.

Force, F, is the ability to accelerate (or decelerate) a mass m according to the law of motion,

F = m a, where a is the acceleration. A force with the ability to accelerate a 1-kg mass by 1 m/s2 is 1 Newton (N), which is the SI unit for force. Its basic dimensions are kg-m/s2. A Newton is the gravitational pull on a 102-g mass.

2 Forces exist in various forms: gravitational, electromagnetic, strong interaction (between nucleons), and weak interaction are four basic types of forces matter exerts over matter, and force can be delivered by mechanical (springs), chemical (bonding) and physical (steam expansion) means. In chemistry, the inter-atomic forces within a molecule holding atoms together are chemical bonds. Weak intermolecular forces are generally called Van der Waal’s forces or London dispersion forces, but strong intermolecular forces include hydrogen bonding, ionic and dipole attractions.

Without the concept of force, there is no means of comparing masses and vice versa. Concepts of force and mass are mutually dependent. However, on Earth, we always associate mass with weight. A 70-kg person weighing 686 N on Earth weighs 289 N on the moon while there is no change in mass. In a weightless region, everybody is equal (in weight)!

Force that causes no change of state does no A more elegant definition of work mechanical work. Gravity does no work on any stationary object. A force (F) acting on an Mechanical work, W, is a scalar quantity object, causing it to move a distance (s) in the or state quantity that is defined by a direction of the force, does mechanical work mathematical dot product of the two (W), and vectors: force, F, and the distance, s.

W = F s (J = N m). W (J) = F · s.(N  m) A force of 9.8 N pulling an object (1 kg) up by a distance of 10 m performs 98 Jules of work. The This is useful if you have the background SI unit for work is Joule (J), which is a in vector geometry and understand the dot Newton-meter (or 1 kg-m2/s2). product of vectors.

Work is a state quantity; the same amount of work is required if the initial and final states are the same. The length of time or the methods used to raise the weight has nothing to do with the amount of work done. The unit used for work in the imperial system is foot-pound whereas erg (dyne-cm) is the unit used in the cgs (centimeter-gram-second) system.

Another definition of work is the distance times the component of the force in the direction of the distance. Both formulations give the same results.

What happens to the force components that are not in the direction of the displacement? If we push a strong wall with great strength but the wall does not budge (s = 0), no useful work is produced; the effort (not work) is completely wasted. When a force is used to pull an object up a height, it gains HREF="#potential MACROBUTTON HtmlResAnchor potential energy, and when it accelerates an object, it gains HREF="#kinetic MACROBUTTON HtmlResAnchor kinetic energy.

Skill developing problems: 1. How much work is done to 1.0 L of water when it is pulled from the top of a water fall down by a distance of 100 m? Gravitational pull is 9.8 m/s2 (Ans. 980 J)

3 2. A fish with 1-kg mass in water faces a total resistance of 1.0 N. It gains 10 m/s speed over a distance of 1 m of movement. What is the average force exerted by the fish in this movement? (F = 50 N) 3. A sled weighing 50 kg experiences a gravitational force of 490 N. When it is pulled across a frozen lake, the average force due to friction is 10 N. Calculate the amount of energy required to pull the sled across the lake for a distance of 10 km. (105 J).

Potential and Kinetic Energy When a force acts upon an object for a distance, the state of the object has changed. The change in location results in a change in potential energy, and the change in velocity results in a change in kinetic energy. Although the concept of energy has yet to be defined, these terms are used loosely because most of you are already familiar with them.

 What are potential and kinetic energy, and how they are evaluated?

Potential energy is the mechanical work stored in a particle or body or system due to location or height in a force field. In a gravitational force field, g, a mass m kg raised to a height ht, has a potential energy Ep

2 Ep = m g ht in Joules (J), (g = 9.8 m/s being gravitational acceleration).

For example, a person weighing 70 kg (154 lb) against a gravitational force of m g walking up a set of stairs for a total height of 10 m would acquire a potential energy of

2 2 Ep = 70 x 9.8 x 10 kg-m /s (or J) = 6860 J = 6.86 kJ

Kinetic energy is the mechanical work possessed by a particle or body by virtue of its motion. An object with mass m moving at a speed of v has the kinetic energy (Ek) of

1 2 Ek = ( /2) m v

For example, a 70 kg mass moving at 14 m/s has a kinetic energy of

1 2 2 Ek = ( /2) 70 kg x 14 (m/s) = 6860 J

It can be shown that an object falling a distance of 10 m in a field of 9.8 m/s2 shall gain a speed of 14 m/s. In this process, all potential energy is converted to kinetic energy (Ep = Ek)

Skill developing problems:

4 1. A cat jumps down a 5-m cliff with no hesitation, but a dog doing the same may suffer serious injury, why? 2. How can the kinetic energy be stored and recovered during the braking process of a moving automobile? 3. During a marathon race, should a runner keep the same speed, run faster, or run slower on an up hill stretch of the track? What about the down hill stretch of the road? 4. A dog and a cat weighing 10.0 and 0.5 kg respectively had a free fall (no air resistance) from a cliff of 10 m in height. (1) Calculate the kinetic energies when they are just about to hit the ground. (2) Calculate the ratio of kinetic energy of the dog to 2 that of the cat. (g = 9.8 m/s ) (Hint: K.E. = P.E. = mgh; Ans: Ek.(dog) = 990 J; ratio = 20).

Temperature Scales You have used the Fahrenheit (F), Celsius (C ), and N F C K Kelvin (K) temperature scales, and know how to convert from one to another, but you might not be able to explain the principle of temperature 212 100 373.15 measurement.

12 98 37 310  Why do we need temperature scales and how did these scales develop? 0 32 0 273.15 -40 -40 233.15  What is the principle used to measure temperature?

 How have temperature scales affected the Newton (N), Fahrenheit (F), Celsius ( C), and development of science and technology? Kelvin (K) temperature scales.  What is 0K in the Celsius and Fahrenheit scales? 1 Sensation for hot and cold is instinct for humans and other animals. However, sensation is subjective and circumstantial. For example, if you place one hand in cold and one hand in warm water for a while, and then put both hands in the same bucket of water, the two hands feel differently.

Peking man used fire about 500,000 years ago. Humans have recognized heat and fire at the dawn of civilization. The objective of fire at that time was to provide warmth and illumination, since cooking was not an art until much later. Despite the lack of thermometers, people in Egypt, Mesopotamia, India, and China used fire to produce metals, and to work copper, lead, tin and iron into tools. Fire played such an important role in early civilization that Plato (427-347 BC) thought it was one of four primal substances from which all other matter was derived.

During the 2nd century, the Greek physician Galen suggested a temperature scale based on boiling water and ice. Arab and Latin physicians developed a scale of 0-4 degrees for hot and cold depending on human senses. In 1688, the French physician Guillaume Amontons

5 proposed to measure hotness and coldness by the variation in pressure of a fixed amount of gas contained in a constant volume. He defined absolute zero when the pressure is zero, and used a tube of mercury to measure the pressure. In 1701, Sir Isaac Newton (1643-1727) suggested 0 degrees for ice and 12 degrees for the human body as a temperature scale. G.D. Fahrenheit (1686-1736) proposed a temperature scale in 1714. The scale used a salt-water- ice mixture as a reference for 0, and the human body as 96 degrees. This scale had many more divisions than the one proposed by Newton, and the freezing point and boiling point of water was calibrated to be 32 and 212 degrees respectively. This finer scale greatly improved the precision of temperature measurements. The centigrade (Celsius) scale was proposed by the Anders Celsius (1701-1744) ten years after Fahrenheit’s proposal.

Using a temperature scale, Jacques-A.C. Charles (1746-1823) and Joseph L. Gay- Lussac (1778-1850) studied the expansion of gases. They found that hydrogen and most 1 other gases expanded /273 of their volumes at 0oC per degree C increase. This is known as the Charles-Gay-Lussac law of gases. In general, when the pressure is held constant, the A thermocouple consists of two different metals, volume of a gas increases the same amount as which give rise to a voltage depending on the the temperature increases each degree. temperature of their junction. William Thomson (1824-1907, known as Lord Kelvin of Glasgow) came up with the absolute temperature scale (K after Kelvin) in 1848 in conjunction with the Charles-Gay-Lussac law. Absolute zero corresponds to -273oC, and at this temperature, no heat can be extracted from the system any more.

Usually, thermometers use gases or liquids that expand upon heating. However, extreme low or high temperature measurements require instruments other than ordinary thermometers. For example, temperatures between -183 and 630oC can be determined from the electric conductance of platinum. In 1821, Thomas J. Seebeck (1770-1831) discovered that when the junctions of two dissimilar metals were placed in different temperatures, the circuit generated an electric potential (voltage). Such devices, called thermal couples, have been developed for temperature measurements. Spectra of light emitted by hot objects have also been used to determine their temperatures. Temperature measurements are an important part of scientific research and technological development.

Skill developing problems: Two bodies each equal in 1. On the Newton’s temperature scale of 0 for ice and temperature to a third body are water mixture and 12 for the human body equal in temperature to each temperature, what is the boiling point of water? other. What is the reading corresponding to absolute Maxwell (19th century, now known zero? (-88.5 N) as the 0th law of thermodynamics) 2. What is 0 K in the Celsius and Fahrenheit temperature scales? (-459.7 F) 3. What is the temperature at the surface of the Sun? (a few million degrees Kelvin).

6 Heat Like work, heat is also an elusive quantity. Intuitively, we know that an object containing a lot of heat is hot, but the description is inadequate. After having invented and used temperature scales, humans wanted to better understand heat.

 What is heat and how does it flow? How did our interpretation of heat evolve? What is the relationship or difference between heat and temperature?

 How is heat stored in an object or a system? What is the meaning of heat capacity? How does heat differ from chemical energy?

In 1760, Joseph Black (1728-1799) recognized that "heat is evidently not passive; it is an expansive fluid, which dilates in consequence of the repulsion subsisting among its own particles”. He considered this caloric fluid to be indestructible and to be accumulated when matter was heated. Is heat a fluid like water? Comparing heat with a fluid was a good step in our effort to understand heat. Black differentiates heat from hotness. Like mass and volume that describe amounts, heat is a typical additive quantity. Thus, heat, volume, and mass are extensive properties. In contrast, temperature is not a quantity measured in amount; it is a measure of the type called intensive property, as are pressure, density, heat capacity, latent heat of melting, latent heat of evaporation, etc.

With the help of a temperature scale and his caloric (weightless fluid) theory, Black defined heat capacity as the amount of calorie required for raising or lowering the temperature of a body by 1o. Furthermore, he realized latent heat of melting of a solid such as ice. He demonstrated that a fixed amount of ice always requires the same quantity of heat to melt. Now, we know that a fixed quantity of liquid also requires a certain amount of heat to evaporate. Heat capacity, latent heat of melting and heat of evaporation are also intensive properties. The caloric theory was believed for more than 100 years, until the middle of the 19th century, when the concept that heat was a fluid-like quantity could not explain phenomena related to HREF="#mechanical MACROBUTTON HtmlResAnchor mechanical work, HREF="#radiation MACROBUTTON HtmlResAnchor radiation, and HREF="#chemical MACROBUTTON HtmlResAnchor chemical reactions.

As an extensive property, the amount of heat must be precisely described. An amount of heat required to raise the temperature of 1.00 g of water from 288.5 to 289.5 K is defined as 1.00 calorie. This strict definition hints that the heat capacity for water changes

7 with temperature, even between freezing point and boiling point. On average, the heat capacity for water is 1.00 cal g-1 K-1, whereas the heat capacity for ice is only 0.50 cal g-1 K- 1.

Skill developing problems: 1. The caloric fluid concept explains what aspect of heat, but cannot explain what properties of heat? 2. On average, 1 cal. is required to raise the temperature of 1 mL water by 1 K. How many calories are required to warm up a cup (250 mL) of water (for tea) from 288 K to 363 K? (18.8 kcal.) 3. The heat of fusion for ice is 80 cal per gram (or 6.02 kJ/mole) and the heat of vaporization for water is 540 cal per gram (or 40.67 kJ/mol). The heat capacities for water and ice are 1.00 and 0.50 cal g–1 K–1 respectively. How much heat in kcal and kJ is required to convert one mole (18 g) of ice from 263 to 373 K. (Ans. 13.1 kcal or 54.6 kJ).

Inter-conversion of heat and Thermometer mechanical work That mechanical work can be converted to heat was discovered unexpectedly.

 Why is heat not a fluid? mgh  What is energy? Why is the concept of energy useful? How is energy stored in a body of material? Joules experiment demonstrated the  When energy is transferred from one place generation of heat by mechanical means. to another, what phenomena do you observe?

Sir Benjamin Thompson (1753-1814) used horse-turned machines for boring brass into cannons in the military arsenal at Munich. He observed the brass getting hot in this process, and concluded that heat is hardly a substance or fluid, but is generated by HREF="#mechanical MACROBUTTON HtmlResAnchor mechanical work done to the system. He recognized that heat is furnished as long as parts in it persisted moving. He calculated the equivalence between the heat generated and the mechanical work done to the system, and James P. Joule (1818-1889) who studied under J. Dalton, refined the experiments by measuring the temperature rise in water churned by a paddle driven by a descending weight. These experiments showed that heat, and HREF="#mechanical MACROBUTTON HtmlResAnchor mechanical work, are inter-convertible.

In 1852, Joule and Thomson discovered that temperatures of gases decrease when they are expanded. During expansions, heat is converted to mechanical work.

8 Since heat and mechanical work are inter-convertible, they should be treated as a single entity. This entity was called effort, living force, and travail, before the term energy was accepted. This term was coined by Thomas Young (1773-1829) in 1807, from the Greek words energia; en meaning in, and ergon, work. Since then, the term energy is used to mean mechanical work (or simply work), heat, and other HREF="#forms MACROBUTTON HtmlResAnchor forms of energy.

Energy can be quantified, but its meaning is elusive. Quantities of energy are expressed in various units depending on their forms. The basic or SI units are derived from those of mass (kg), length (m), and time (s). Most of you are familiar with various forms of energy, but a review is given in the next section.

To speak of the heat or work in a body is improper, because heat and work are really energy being transferred. Energy stored in a body is neither heat nor work. Upon absorption of heat, molecules or atoms in materials move faster, converting from solid to liquid or from liquid to gas. In 1738, Daniel Bernoulli (1700-1782) proposed that the motion of gas molecules gave rise to pressure. Kinetic energies of gases are proportional to their temperature. Once absorbed, the nature of heat has changed. Rudolf J.E. Clausius (1822-1888), James Clerk Maxwell (1831-1879), W. Thomson, and Ludwig E. Boltzmann (1844-1906), studied the relationship between temperature and energy of molecular motion. Many elegant theories have been developed as a result.

Heat is HREF="#energy MACROBUTTON HtmlResAnchor energy being transferred via a medium from a source of higher temperature to a target of lower temperature. Temperature is a measure of relative potential of energy. Molecules and atoms in a body of material rotate, vibrate, or move, and hence possess energy. When residing in a body of material, you probably don’t call it heat until it flows.

Heat, light, mechanical and electric work, and sound are actually forms of energy in transmission. Heat is energy transmitted by conduction and convection. Light (HREF="#radiation MACROBUTTON HtmlResAnchor electromagnetic radiation) is energy transmitted via no medium. Mechanical and electrical works require the transmission of objects or electric charges, whereas sound is the result of energy transmission by a mechanical process.

In terms of nuclear technology, we often deal with high-energy subatomic particles. Energy of these particles is stored as kinetic energy. Temperatures of a collection of particles are related to their average speed, and we shall discuss these aspects in various chapters later.

Skill developing problems: 1. What is energy? Give an example to show how heat can be converted to mechanical work. Identify at least 5 different phenomena caused by energy. 2. Describe the nature of heat and work as energy in transition. 3. How is energy of molecular motion related to temperature?

9 Other Forms of Energy

As mentioned in the last section, heat, and mechanical work are two forms of energy. Other forms are light, electric work, sound, chemical energy, and nuclear energy. Some of these forms are energy in transmission, and some are hard to recognize as energy. We review some fundamentals of these forms of energy in the following sections.

Electric Energy Most technologies, including nuclear technology, involve electric energy. For example, kinetic energies subatomic particles are often expressed + - in electron volts, eV. Having ability to evaluate + - + - electric energy is important. + - + -  How much energy is 1 eV, 1 MeV or 1 GeV? + - + - Electric energy, E, possessed by a charge q experiencing a voltage V, is the product of q and Electric field V.

E = V q (units: J = V C)

The SI units are Joule (J), volt (V), and coulomb ( C) for E, V and q respectively. An electric Gravitational field charge experiences the electric field as a mass does the gravitational field. Similarity between pushing a charged particle The HREF="#power MACROBUTTON against an electric field and pushing a weight against HtmlResAnchor power P of output or input in a a gravitational field. circuit is,

P = V q /t = V i in watt where t represents time, and i = q/t is the current. The SI units for i, is ampere (C s–1).

The voltage drop V in a circuit is the product of i (in A) and resistance R (in Ohms, ),

V = i R (Ohm’s law)

Thus, we can re-write the power as

P = R i2 (Joule’s law)

 Power is rate of energy transfer, or energy input or output per unit time. A section is devoted to it later.

10 For example, the power delivered by 12 volt battery constantly discharging 50 amperes per second is 50 C/s x 12 V = 600 J/s (or 600 watts).

In nuclear technology, a commonly used energy unit is the electron volt, eV. The smallest amount of charge detected is the amount of charge of electron. The charge of an electron is 1.60219x10-19 C. Because the electron is negatively charged, 1 eV is the amount of energy (1.60219x10-19 J) to lower the electron by 1 volt. When an electron is accelerated by a 1000-V, it gains 1000 eV or 1 keV, and when accelerated by 1,000,000 V, it gains 1,000,000 eV or 1 MeV. For high energy, 1 GeV = 109 eV.

Units keV and MeV are often used to describe energy of subatomic particles such as electrons, protons, and neutrons, as well as photons in the X-ray or gamma region. Modern accelerators such as the DESY (Deutsches Elektronen Synchrotron) in Hamburg, Germany and the accelerator at Cornell University have accelerated protons to energies of 6.5 and 12 GeV respectively.

Skill developing problems: 1. What are the advantages and disadvantages of building dams for Joule and Electric Energy electric power generation? In 1840, Joule (a 22-year old Manchester 2. How much energy is delivered by a brewer) learned that the amount of heat battery operating at 12.0 V in a discharge produced per unit time (power P) by the of 150 C, when you start the engine? flow of an electrical current was Express this amount of energy in J, cal, proportional to the resistance ( R) of the and eV. (W = 1800 J) conductor, and to the square of the current 3. What is the resistance for a heating (i) flowing (Joule’s law). element operating 0.1 watts when V = 1.5 V? (Ans. P = Vi = V 2 / R; R = 22.5 ) P = R i2 4. What is the current for a heating element Since i = q / t, and V = i R operating at 60 watts and 12 V (DC)? P = V i How many electrons pass through per E = P t second? (Current = 5 A, No. of electrons = 3.3 x 1019 e/s). Combined with the discovery that 5. A 12-V storage battery delivers 100 A mechanical work also generate heat, he had while starting an engine. Calculate the quantified electric energy in terms of heat power delivered by the battery. How many and work. electrons per second pass the terminal? How much energy does each electron deliver? (Power = 1200 watt; 6.24 x 1020 electron per second; each electron delivers 12 eV; 6.24 x 1020 x 12 eV = 1200 J energy) 6. Describe the conversion between various forms of energy when you start an engine with a battery. 7. A stove operating at 1000 watt takes 10 minutes to heat 1 L of water from 20 to 100o C. Calculate the energy (in J and cal) consumption and efficiency. (Ans. 143 kcal, 56%).

11 8. A microwave oven operating at 600 watt takes 2 minutes to warm up 200 mL of water from 20 to 90oC. Calculate the efficiency of the process. (Ans. 81%)

The Electromagnetic Radiation Spectrum Electromagnetic radiation is a form of energy transmitted in the form of waves due to an oscillation of electric and magnetic fields travelling away from a source. Visible light is an example of the electromagnetic The Electromagnetic Radiation radiation. Electromagnetic waves travel at Spectrum constant speed in vacuum, and they have Long wavelength radio > 600 m characteristic wavelengths or frequencies. Classified by frequencies, the Broadcast radio band 600 - 200 m electromagnetic radiation spectrum Short wavelength radio 200 m - 0.1 mm consists of radio waves, TV signals, microwaves, infrared, visible light, Infrared 0.1 - 0.0007 mm ultraviolet, X-rays, and gamma rays. VISIBLE 0.7 - 0.4 um  Does light consist of waves, particles Ultraviolet 0.4 um - 1 nm or both? X-rays 1 nm - 0.1 pm  What phenomena of light beams Gamma rays 0.1 nm demonstrate wave properties? What type of waves are light? How energy is transmitted by light?

 What is the speed of light? How can this speed or velocity be measured?

 Describe differences and similarities among radio waves, TV signals, microwave, infrared, visible light, ultraviolet, X-rays, and gamma rays?

In 1666, Newton decomposed white light into a rainbow spectrum of red, orange, yellow, green, blue and violet using a prism, and using a second prism he combined the rainbow spectrum into a white beam. His experiments separated light into components, but whether light beams consist of particles or waves was not yet resolved.

12 Most phenomena of light can be explained by considering light as particles, except the color patterns formed on soap bubbles or thin oil films called Newton rings. This puzzles was solved by Thomas Young (1773-1829) who assumed light as a wave, and explained the color patterns as due to interference, a property observed for only waves not particles. Since then, all phenomena (reflection, refraction, and diffraction) of light have been explained by the electromagnetic wave theory, by which light is A color pattern seen in an oil film the transfer of energy by wave actions without a medium.

The universal speed of light was first calculated from the time difference required for the orbit of Jupiter’s moons when the earth was moving towards or away from the Jupiter, by the Danish astronomer Olaf Roemer. Further refinements give the speed of light as 299,792,458 (or 3x108) m/s.

The radiation spectrum covers radio waves used in broadcast, microwaves used in communication, infrared radiation usually considered as heat, visible light of various colors, ultraviolet light, X-rays, and gamma rays. All have wide ranges of wavelengths, which decreases in the order given above. With the universal speed (c = 3x108 m/s) and wavelengths, , of waves in the radiation spectrum measured, their frequencies, , can be evaluated,

 = c/.

The product of frequency and wavelength equals to the speed or velocity of light,  = c.

The wave number is the number of waves per unit length (m or cm), and it is the 1 reciprocal of wavelength,  = /.

The energy, E, transmitted by electromagnetic radiation is proportional to its frequency , or its wave number  according to Max Planck* .

E = h , (Planck’s equation) = h c/  = h c  where h = 6.62619 x 10-34 J s is the Planck constant, and h c = 1.9865 x 10-25 J m.

* Max K.E.L. Planck (1858-1947) studied the distribution of radiation energy of black bodies over the entire range of wavelengths at various temperatures. A black body is a perfect absorber and radiator of electromagnetic radiation. John William Strutt (1842-1919, known as Lord Rayleigh) derived a law that agreed with the long wavelength range. Wilhelm Wien (1864-1928, 1911 physics Nobel prize) gave the displacement law for the short wavelength range. However, there was no satisfactory theory to deal with the entire spectrum. In order to give a formula explaining the entire spectrum for all temperatures, Planck postulated that light was emitted as small bundles of energy called quanta, whose energy E is proportional to the frequency of light 

13 The equation was an assumption made by Planck . He assumed that light is emitted as small bundles of energy E called quanta. Light beams consist of many photons, I Rayleigh’s which are elements of electromagnetic N Prediction radiation. The amount of energy to be T transmitted by radiation determines the E Experimental curve N and Planck’s prediction photon frequency. Using his assumption, S the specific heat of substances, Stoke’s law I of phosphorescence and fluorescence T Wien’s Law phenomena, and black body radiation are Y explained. Furthermore, the assumption was confirmed by Einstein’s famous Frequency photoelectric experiment. Prediction using classical electromagnetic-wave theory The wavelength of a typical red light is 640 and experimental equilibrium radiation density of -9 nm (1 nm = 10 m). Its frequency is perfect absorber.

 = c / 6.4 x 10-7 = 3 x 108 (m/s) / (6.4 x 10-7 m) = 4.69 x 1014 /s (or Hz)

Thus, the energy of the red light photon is

E = h , Kinetic energy of electron = 6.6256 x 10-34 J s x 4.69 x 1014 /s = 3.1 x 10-19 J (1 eV / 1.6 x 10-19 J) = 1.9 eV per photon

The energy of a typical green light photon with wavelength 500 nm has more energy Threshold than a red light photon, Frequency

E = h c/ = 1.9865 x 10-25 (J m)/ 5.0 x 10-7 (m) = 4.0 x 10-19 J (1 eV / 1.6 x 10-19 J) Kinetic energy of electrons liberated from metal surface as a function of frequency. = 2.5 eV per photon

The wavelengths of X-rays are shorter than those of visible light. A photon of typical X-ray with a wavelength 0.1 nm has 5000 times more energy than that of green light,

E = h c /  = 1.9865 x 10-25 (J m) / 1.0 x 10-10 m

 Planck received the Nobel Prize for physics (1918) after his assumption was confirmed using photo-electric effect experiments by Albert Einstein (1879-1955). Experiments showed that electrons could be liberated from a metal surface by light of certain frequency (threshold) or higher, indicating that the light was proportional to the frequency, as proposed by Planck. Einstein further showed that the kinetic energy of the liberated electron is proportional to the frequency of the photons used. For his experiment, Einstein received the Nobel prize in 1919.

14 = 2.0 x 10-15 J (1 eV / 1.6 x 10-19 J) = 12500 eV or 12.5 keV per photon

The total amount of energy transmitted in a light beam is the sum of all photon energies.

Light as a form of energy is best illustrated by LASER, acronym for Light Spontaneous decay Amplification by Stimulated Emission of Green Radiation. When a rod of chosen material photons Stimulated decay, absorbs light energy, the material is raised Red laser to a higher energy state. The ends of the rod are polished flat, parallel, and coated with mirrors to reflect light. Thus, the emitted Mirror Partial mirror light travels back and forth in the rod stimulating further emission. The partial Red laser mirror on one end of the rod allows some light to pass through, and the emission is Green pumping light called LASER, which is a strong monochromatic, parallel, and coherent light beam. The rod material can be a solid, An oversimplified energy level diagram (for chromium liquid, solution, or gas. You already know ion in ruby) and laser generation device. that energy of LASER beams have been used for surgery to vaporize unwanted material. LASERS are also employed in nuclear fusion technology.

Review Questions: 1. Visible red light has a wavelength of 700 Key Constants and Formulas nm (1 nanometer = 10-9 m). Calculate the -34 frequency, the photon energy, and the Planck’s constant, h = 6.6256 x 10 (J s) 8 wave number (/cm).(Ans. Frequency = Velocity of light, c = 2.997925 x 10 m/s -25 4.23 x 1014 Hz, E = 2.8 x 10-19 J = 1.8 eV, h c = 1.9865 x 10 J m wave number = 1.43 x 106 wave/m = Wave length, wave number  = 1/ 14300 wave/cm). Frequency:  = c/ EnergyE = h  = h c /  = h c  2. Calculate the frequency, the wavelength, and the wave number (/cm) of a photon with energy 0.5 MeV. (frequency=1.21e20 Hz; wavelength =2.48e-12 m; wave number= 4.0e11 per m) 3. Photons in which of the following types have the highest energy: infrared, ultraviolet, X-ray, or microwave? 4. An argon laser has a wavelength of 514.5 nm; calculate the energy of its photon. (E = 3.86e-19 J) 5. The threshold of most metals is between 2 eV (for cesium) and 5 eV (for platinum). Calculate wavelengths of photons corresponding to these threshold energies. (Please fully explain the photoelectric effect.)

15 Chemical Energy A substance possesses chemical energy by virtue of its composition, chemical bonding, and state. The absolute amount of chemical energy in a substance is not a measurable quantity, neither is the quantity useful. All chemical reactions are accompanied by a change of energy. An endoergic reaction absorbs energy in the procedure. For example the electrolysis of water into hydrogen and oxygen is an endoergic reaction. Electric energy is used in the Ice in water is a cool drink! process. An exoergic reaction releases energy, which may be in the form of heat or light or both (burning of a gas), or in the form of electric energy (reactions in a battery). Endoergic and exoergic reactions are often called endothermic and exothermic reactions respectively. The terms endoergic and exoergic emphasize the energy concept whereas endothermic and exothermic refers to heat.

The study of absorption, emission, transformation and conversion of heat is known as thermodynamics, which is studied by scientists and engineers. In thermochemistry, elements at standard temperature (273 K) and pressure (101.3 kPa) are referred to as a zero-level of energy for reference. Energy levels (or contents) of their compounds are compared to these standards.

 What are endoergic, exoergic, endothermic, or exothermic reactions?

 How is energy stored in material by virtue of state, chemical composition, and chemical bonding?

 More new terms such as energy (or enthalpy) of fusion, energy (enthalpy) of vaporization, energy (enthalpy) of reaction etc. are introduced. What are these quantities and what are their amounts for a particular material? Where can you find the information?

To illustrate the various chemical energy, let us concentrate on 36 g (2 moles H2O, or 2H2O in chemical formulation) of water at various stages. When placed in a colder environment, heat can be extracted from ice at 273 K. So, ice at 273 K is not the lowest energy point yet.

If the ice at 273 K is heated, temperature will not increase until all the ice melts. Under ideal conditions, experiments show that 12 kJ will be required to melt 36 g ice. In other words, at the same temperature, 36 g water contains 12 kJ more energy than ice at the same temperature. This amount of energy is called enthalpy of fusion.

16 When water is heated, energy content increases. Since the heat capacity of water is 4H + 2O 4.184 J/K g, 15 kJ (= 36*100 * 4.184 J) is required to bring 36 g water from 273 to 373 K. By absorbing heat, the energy content of water increases.

Enthalpy of vaporization is the energy 1469 kJ, bond energy required to convert a liquid to a gas at the same temperature. For 36 g of water, 81 kJ is required. Thus, energy content of the steam is higher than that of water at the same temperature. 2H + O Water vapor and a mixture of hydrogen and 2 2 oxygen are gases, but when the gases in the mixture react, the energy or enthalpy of 484 kJ, energy of reaction will be released as light and heat. reaction The mixture of hydrogen and oxygen gases consists of diatomic molecules. Bond 2H2O(g)373K energies (971 kJ for 4 g of H2, and 498 kJ for 81 kJ, energy of 32 g of O2) are required to dissociate the vaporization hydrogen and oxygen molecules. Of course, 2H2O(l)373K mono-atomic gases mixture releases more 15 kJ, heat energy than does diatomic gases mixture in 2H2O(l)273K their reactions to produce water. 12 kJ, energy of fusion 2H2O(s)273K There are other types of energies in chemical process, but these are beyond the scope of this book. You are introduced to some interesting aspect of thermodynamics in this section, and you may find more thermodynamic properties (or data) for a substance in for example the CRC Handbook of Chemistry and Physics.

Despite huge amounts of chemical energy stored in various substances, energies released have not given measurable changes to mass of the systems or bodies of substance (see HREF="#mass MACROBUTTON HtmlResAnchor Mass and Energy for further details). For chemical and physical reactions, therefore, total mass changes before and after reactions are not measurable. Thus, mass and energy are treated separately, and they are said to be conserved individually or independent of each other.

The energy contents of food have been tabulated giving the unit calorie. However, the ‘calorie’ used by dieters in the past was really a ‘kilo-calorie’ as defined earlier.

1 food cal = 1 kcal = 4.184 kJ. (in old dietary literature, but new literature uses kJ.)

17 The major food energy is derived from Energy Content (kcal/g) of Major Food proteins, fats and starches (carbohydrates). Their heats of combustion and their Food Heat of Physiological physiological energy as food are slightly combustion energy different, because not all ingested food is Protein 5.4 4 absorbed and utilized. Most food is a cheese 4 combination of proteins, fats and starches plus beef 3 other nutrients such as water, vitamins and Fat 9.3 9 minerals. However, flavor, taste, and butter 8 sensation are more important than nutrition to Carbohydrates 4.1 4 most of us. potatoes 0.7 sugar 4 Review Questions: 1. What are endoergic and exoergic reactions or processes? Give some examples for each. 2. Define energy of reaction, energy of formation, energy of phase transition, and bond energy. 3. Use the bond energies H-H, 436; O=O, 498; H-O-H, 498*2 J/mol to show that the

energy of reaction for the reaction 2 H2 + O2 = 2 H2O is 622 kJ for each mole of O2 reacted. Discuss your results. 4. Experimental data indicate that burning 2.3 g of gasoline releases 110 kJ energy and the density of gasoline is 0.60 g/mL. Calculate the amount of energy released from burning 1.0 L (liter) of gasoline. (Ans: 28,696 kJ)

Energy and Mass Equivalence The kinetic energy gained by a particle increases its mass according to the special theory of relativity developed by Einstein in 1905. He derived an equation to calculate the Universal speed relativistic mass m of a particle from the rest 299,792,458 m/s mass mo by the equation:

m m = o v 1 - ( )2 c All electromagnetic radiation travel in empty space at the same universal speed.

 Newtonian physics could not explain the phenomena related to the absorption of light by molecules or atoms, and shortcomings were found in motion of high energy particles. In an effort to find the elementary foundations of an adequate theory of matter, radiation, and electricity, and in the mean time stimulated by scientists H.A. Lorentz, M. Planck, A. Summerfeld, J. Stark and W. Wien, Einstein (1905) abandoned the concept of a universal or absolute space and time on which Newtonian kinematics was based. Einstein considered Newton’s laws of motion in relative coordinate systems or spaces, and further accepted the 1887 experimental result of A.A. Michelson and E.W. Morley that velocity of light is always the same, regardless of the motion state of the emitter. Incorporating these new concepts of space and time into the fundamental principles of conservation of energy and momentum, he unveiled a new field in 1905 called special theory

18 where v and c are the velocity of the particle and the velocity of light (3 x 108 m/s) respectively.

The consequence of his theory is far reaching, and all atomic and nuclear phenomena require some parts of his theory to be explained adequately.

 What is the significance of Einstein’s special theory of relativity?

 How can the increases in mass of a particle be measured? What is the mass increase for a particle moving at 1% of the velocity of light?

 Calculate the mass equivalence of 1 J and the energy equivalence of 1 g.

Einstein (1909) further showed that the relativistic mass, m, of a particle exceeds its rest mass mo (m = m - mo). The increase in kinetic energy E and increase in mass are related by a simple equation:

E = m c 2 which is often written as E = m c 2 by dropping the symbol of difference, . Mass can be converted to energy under the right conditions. This equation is the expression of the principle of the energy mass equivalence (der Ausdruck des Prinzipes der Äquivalenz von Masse und Energie), m being the mass equivalence of energy, and E being the energy equivalence of mass. For high-energy particles such as electrons and protons moving at the velocities close to that of light, the masses increase agree with results calculated by this equation.

No particle can be accelerated to a velocity equal to or greater than that of light, according to the relativistic mass equation, because its mass will be infinity when its velocity is the same as the speed of light (v = c) unless the rest mass, mo, is zero. As its kinetic energy increases, so does the mass of a particle. Note that the increase of a particle's mass is a continuous function, in contrast to energy states of a microscopic system being discrete according to Planck’s assumption.

Since energy and mass are equivalent, they must be considered together in the HREF="#conservation MACROBUTTON HtmlResAnchor law of conservation of energy. As mentioned earlier, only small amounts of energy is involved in chemical or physical changes, mass and energy are conserved independent of each other. The equation E = m c 2 permits the calculation of the total or absolute amount of energy for a mass m, but not all energy is available for doing work. The lowest mass of a particle is called ground state, but several excited states might be stable for an indefinite period.

For chemical reactions, the changes in mass due to release of energy are minute, undetectable. For example, when 2 g hydrogen reacts with 16 g oxygen to form 18 g water vapor, 242 kJ is released,

of relativity, which arrived at some startling results.

19 H2(g) + ½ O2(g) = H2O (g) + 242000 J

The mass equivalence of 241800 J is (= 241800/c2) 2.7 x 10-12 kg or about 3 nanograms, which was lost. Three nanograms are insignificant in 18 grams even on the most sensitive chemical balance.

In reactions involving nuclei, the amount of energy is relatively large. In nuclear reactions, the energy put into or released from a system is so large that the mass changes must be accounted for.

1 th Since mass and energy are equivalent, the mass is An amu is defined as /12 of the mass sometimes expressed in terms of energy. This is of a 12C atom, and 1 k mol 12C = 12 kg particularly true for the masses of nuclei or atoms. The atomic mass unit (amu) is equivalent to 931.478 MeV. 1 amu = (12 kg/k mol)/12 26 The energy equivalence of the rest mass of an electron is = (1 kg/k mol)/(6.022x10 k mol) 0.511006 MeV. As an exercise confirm these values by = 1.66x10-27 kg calculation.

Now, let us consider the fusion of deuterium, D, and tritium, T, in the formation of helium (He) with a neutron as the by-product. The reaction is given below, and the masses (in amu) for the particles are given below their symbols:

D + T = He + n + Energy Mass (amu): 2.01400 3.01605 4.00260 1.008665 0.01878

Since the sum, 5.03005, of masses of D and T is greater than the sum, 5.011265, of masses of He and n by 0.01878 amu, the energy released in this reaction is equivalent to 0.01878 amu or 17.5 Mev per He atom formed. When the unit amu is used, the weights given for the above equation are for each particle, not for a mole of particles as indicated in ordinary chemical reactions.

In units familiar to you, fusion of 2.01400 g deuterium and 3.01605 g tritium (total 5.03005 g) to give 4.00260 g helium and 1.008665 g neutrons (total 5.011265 g) has a loss of 0.01878 g. This amount will be measurable, and the energy giving off, E, can be calculated,

E = 0.01878 x 10-3 kg (3 x 108 m/s)2 = 1.69 x 1012 J/mol,

This is a large amount of energy! If this is the potential energy of a large automobile weighing 1000 kg at a height ht against a constant gravitational field g, the height ht is,

12 ht = 1.69 x 10 J / m g = {1.69 x 1012 (Newton m)}/ {1000 kg x 9.8 m s-2} = {1.69 x 1012 (Newton m)}/ {9.8 x 103 Newton} = 1.72 x 108 m = 1.72 x 105 km = 172000 km

20 This height is equivalent to a distance around the earth EIGHT times.

Review Questions: 1. What is the speed of an automobile Comparison of Energy Released weighing 1000 kg if it has a kinetic E = 2.7 x 10-9 g for energy of 8.45 x1011 J. (When about 2 g H2 + 16 g O2  18 g H2O; 2 g of D and 3 g of T fuse, the E = 0.01878 g for amount of energy released sends an 2.01400g D + 3.01605g T  4.00260g He + 1.008665g n automobile weighing 1000 kg to a speed of 41 km per second or 148000 km/hr) 2. Calculate the kinetic energy of an automobile weighing 2000 kg when it travels at 120 km/hr. Evaluate the mass equivalence of its kinetic energy. (1.1x106 J) 3. Calculate the mass equivalence (in kg) of 10000 kJ. (An undetectable amount of 1.1 x 10-10 kg.) 4. Calculate the energy equivalence of 1 amu (= 1.66053 x 10-27 kg), and express the energy in units of J and MeV. (see text box in the previous page) 5. Calculate the energy equivalence of the mass of an electron (= 9.109558 x 10-31 kg), and express the energy in units of J and MeV. (see Physical constant for the rest mass of electron)

 The circumference of the earth is about 20,037 km.

21 Energy Transfer and Conversion

Various energy forms given in the previous section inter-convert among each other, and HREF="#conversion MACROBUTTON HtmlResAnchor conversion factors, HREF="#power MACROBUTTON HtmlResAnchor rates of transfer, and the HREF="#conservation MACROBUTTON HtmlResAnchor principle of conservation of energy should be considered in these inter-conversions. Energy can be transmitted via a medium by mechanical means in the form of HREF="#sound MACROBUTTON HtmlResAnchor sound wave, which is an important mechanism of destruction by nuclear weapons.

Power  the Rate of Energy Transfer Power P is the amount of energy transferred per unit time, and energy E transferred in a period t is

E = P t. Power = m g v, v, pulling velocity The SI unit for P is watt named after James Watt* (1 watt = 1 J/s). mgh

Not only amounts, but also rates of energy transfer are important considerations. For example, walking 100 m is very different from dashing that distance under 10 s. The Performing the same amount of work at two different difference is power requirement. Sprinters rates. need very high power output for a short time.

 Why is a ten-speed bicycle easier to ride than a single-speed bicycle?

 A nuclear reactor is rated at 600 megawatt. How much energy is produced per day?

Kilowatt-hour is a commonly used energy unit, not power.

1 kilowatt-hour = 1000 J/s x 3600 s = 3.6 x 106 J (1 cal / 4.184 J) = 8.6 x 105 cal or 860 kcal.

This amount of energy enables the heating of 8.6 liters (2.3 US gallon) of water from 0o C to the boiling temperature if there is no wastage due to heating the air, the furnace etc.

* At age 29, James Watt (1736-1819) repaired the steam engine Newcomen which was used for pumping water out of English mines. He then improved the performance of steam engines. In order to compare the effectiveness, he compared his engines with the strength of an average horse. He defined a housepower (hp) as 550 foot-pounds per second (about the power of 1½ fine steeds at that time), and this became the standard for rating electric motors, automobile engines, diesel locomotives, and propeller-driven aircraft engines.

22 The horsepower (hp) is a common unit for power, 1 hp = 745.700 watt = 178.107 cal/s; and 1 watt = 1.34102 x 10-3 hp. Note that a metric horsepower is slightly smaller than a hp, 1 hp = 1.0138 hp(metric). Conversion factors can also be derived from those used for energy.

Review Questions: 9. Assuming the average voltage to be 110 V, what is the current for an appliance rated for 1kilowatt? (Ideally, calculation of electric energy by alternate current (AC) should be carried out differently from that of direct current (DC), but you need not to worry about the complication for AC here. Current = 9.1 A) 1. Convert 1.0 kilowatt-hour to the following units: J, cal, and BTU. (1 BTU = 1055.06 J) 2. An electron is accelerated to give a kinetic energy of 931 MeV in 10-9 s. Calculate the power in this process. 3. A furnace is rated to give 13700 BTU per hour. Calculate the power in watt.(Ans: 4015 watt)

The Law of Conservation of Energy Energy, the medium for changes, and money, the medium for exchanges, are abstract and similar in many ways. Energy conserves, but money (or precisely value) does not. Energy exists in forms of potential, kinetic, mechanical, electrical, chemical, thermal, geothermal, electromagnetic radiation, and nuclear (mass equivalent). Energy converts among various forms without any loss or gain, states the law of conservation of energy. Your money exists in forms of real estates, jewelry, automobiles, audio and video systems, minerals, energy providing commodities, etc. Every time you buy, sell or exchange, you think you gain. So does the other guy. Money (or more precisely value) is not conserved.

 Is energy really conserved? How can you demonstrate that energy is conserved?

 A bouncing ball or a pendulum eventually stops, what happens to the energy?

 Is it possible to build a machine to perform useful work without consuming energy? (Such a device is called a perpetual machine; it creates energy).

Galilei Galileo (1564-1642) discovered that a body A ball hitting a surface both of perfect acquiring a velocity in its descent can rise exactly elasticity will bounce back as high as its as high as it fell, in his study of falling objects in a original height. uniform accelerating field. He discovered the law of conservation of energy in the conversion between HREF="#potential MACROBUTTON HtmlResAnchor potential and HREF="#kinetic MACROBUTTON HtmlResAnchor kineticenergies. Bouncing balls and pendulums illustrate this law. A ball falling from a height ho looses its potential energy at the same rate as it gains kinetic energy. At any height hi and a velocity of vi, the total energy is still m g ho,

23 1 2 m g ho = m g hi + ( /2) m vi

When the ball hits the surface, the height becomes zero and it attains the maximum velocity 1 2 vo, and m g ho = ( /2) m vo . This kinetic energy causes the ball to deform, converting to mechanical energy, which when returned is a force giving the ball an initial velocity - vo. Since the ball and surface are not perfectly elastic, there is always a loss in height on the return bounce. The difference in height is a measure of imperfect elasticity of the ball and surface.

Torricelli is well known for the discovery of the barometer. He also studied the flow of liquid. He observed that a liquid flowing out of the basal orifice of a vessel cannot, by virtue of its velocity at the efflux, ascend to a greater height than its level in the vessel. This statement is consistent with the law of conservation of energy.

Other historical observations consistent with the law of conservation of energy came from the usage and equilibria of pulleys, levers, and other simple machines.

Regarding the conversion between heat and work, the great contributor to the heat engine, N.L. Sadi Carnot (1796-1832) gave the following theorem: Whenever work is performed by means of heat, a certain quantity of heat passes from a warmer to a colder body. Carnot considered the quantity of heat invariable. Clausius took it a step further and considered the work performed comes from the heat lost.

Time and again, people misinterpreted their observations and claimed they found phenomena that appeared to have contradicted the law of conservation of energy. So far, no experimental result has violated this law.

The three laws of motion of Newtonian physics are consistent with the law of conservation of energy. The body with mass m is a system, and when no energy is given to it, its velocity does not change (law of inertia). Energy of m can be transferred by a force (law of acceleration). When two systems do work to each other, equal amount of work are done to each other (law of action and reaction).

Review Questions: 1. Kathy weighs 50 kg. Calculate the potential energy she gained by climbing to a platform 10 m above a swimming pool. If she has a free fall, how long would it take for her to reach the surface of the swimming pool? What is the speed on entry to water? Calculate the kinetic energy when she reaches water. (time = 9.8 s, v = 14 m/s). Let us assume that Kathy comes down very ‘slowly’ from the 10-m platform and wastes no energy for anything else except to raise her body temperature. Assume the heat capacity of her body as 0.8 kcal / kg-K (compared to 1.0 kcal / kg-K for water). Calculate the temperature increase of her body. (Temperature increase = 1.64 kcal / (70 x 0.8 kcal/K) = 0.029 K).

 Inspired by Galileo’s writings, Evangelista Torricelli (1608-1647) wrote a treatise on mechanics (De Motu, “Concerning Movement”), which impressed Galileo. As a result, he was invited to Florence, serving as secretary and assistant during the last three months of Galileo’s life.

24 2. The Niagara Falls have a height of 58 m (190 ft). If all the potential energy is converted into heating the water, its temperature increases. Calculate its temperature increase. (Ans: 0.14o C). 3. Why does sound propagate through a tube with much less attenuation than through open air? 4. Why does a beam of light transmit via an optical fiber to a long distance with little attenuation, but a light beam transmitted through a large body of transparent medium loses intensity? 5. Design an experiment or a demonstration to show one of the following: conservation of energy, conservation of matter, conservation of electric charge, conservation of momentum, or conservation of matter and energy regarding them to be equivalent.

Transmission of Energy by Sound Wave Humans produced the loudest sound by a nuclear explosion, which sent shock waves (loud sound) to a great distance.

 What is sound? How do sound waves transmit energy?

Sound waves transmit mechanical energy by means of pressure and volume change. When a fluid is disturbed at a point, energy expands in all directions, showing the disturbance at distant points by wave propagation. The average rate of energy transferred per unit time per unit area of the wave front is called the sound intensity I, (watt/m2). Cross-section of sound wave propagation. Dark and gray circles indicate fronts of certain pressure differences. As waves, sound is characterized by frequency, f (Hz), and intensity, I, (watt/m2). There is no limit in frequency of sound, but human ears detect those in the range of 20 to 20,000 Hz, 1 nearly 11 octaves. Our ears sense pressure variation of /10,000,000,000 atmosphere pressure 1 (atm), and become painful at a variation of /10,000 atm. In terms of pressure variation, the painful threshold is 106 times greater than that of hearing. The intensity, I, is proportional to the square of pressure fluctuation. Both hearing and painful thresholds depend on the frequency.

The sound intensity level (SIL) is measured in a decibel (dB) scale, which is based on the intensity I. At any frequency, the intensity Io just audible is referred to as SILo, and SIL is

SIL (dB) = SILo + 10 log (I/Io).

25 -12 2 At 1000 Hz, the threshold (I = 10 Watt/m ) of hearing is the reference (SILo = 0 dB). The intensity causing pain in ears is 1 Watt/m2, corresponding to an SIL of 120 dB,

-12 SIL = SILo + 10 log (1/10 ) = 120 dB

Comfortable hearing is between 50 and 70 dB, whereas 10 dB is a bel (after A. G. Bell, 1847-1922). A shock wave is due to a sharp difference in pressure from explosions, including nuclear explosion. Shock waves cause serious injuries to ears, and destroy buildings and structures.

Review Questions: 1. How do sound waves transmit mechanical Some Energy Units energy? J, erg 2. Describe the following terms: sound intensity eV, keV, MeV, GeV (bell), and sound intensity level (SIL) (dB). cal, kcal, BTU 3. Why does sound propagate through a tube -1 -1 with much less attenuation than through open cm (wave number) s (Hz) air? L atm 4. You stand at a point of 100 m from a blast amu (atomic mass unit) and experienced just a painful level (120 dB) of sound. What are the intensity levels for persons standing at 50 and 200 m from the source? (126 and 114 dB)

Conversion Factors of Energy A certain amount of energy in one form always converts to a definite amount in another form. One calorie is always equivalent to 4.184 Joules, a value determined by experiment.

 What units are used for energy? Where can you find energy conversion factors? Some Conversion Factors -13 The SI unit for energy is J (J = N m = kg m2 s-2 = C V), and 1 MeV = 1.602 x 10 J other units are given in the text box on this page. 1 eV/molecule = 23045 cal/mol -10 Conversion factors are given in another text box, and on 1 amu = 1.492416 x 10 J page v. = 931.4812 MeV 1 cal = 4.184 J The unit electron volt (eV) is the energy gained by 1 atm L = 101.3 J -19 accelerating an electron by 1 volt. An electron has a charge 1 eV = 1.602 x 10 J of 1.602 x 10-19 C, and 1 eV = 1.602 x 10-19 J. For high 1 J = 1 coulomb-volt 7 energy particles, units keV (1000 eV), MeV (1,000,000 1 joule = 10 ergs eV) and Gev (giga or 109 eV) are used. 1 BTU = 252 cal

26 Energy expressed in unit eV is the energy per particle or event. In bulk material, we deal with quantity in moles. A mole has an Avogardro number of particles. The conversion of units are illustrated below:

-19 J 23 particle 1 eV = (1.602x10 /particle) (6.022x10 /mol) J = 96485 /mol kJ = 965 /mol) (1 cal/4.184 J) kcal = 403 /mol

Review Questions: 1. A BTU is the heat required to heat 1 pound of air free water from 60 to 61 F. Convert 1 BTU to the equivalent of heat in kJ and kcal from this description. (1 BTU = 252 cal = 1054 J) 2. Ten mole of water has absorbed 4184 J (1000 cal) of energy. Calculate the average increase in kinetic energy of a molecule in eV.

Thermodynamics The science of how heat behaves is called thermodynamics which was derived from the Greek words therme (heat) and dynamis (force). It was intensely studied in the 19th century motivated by the need to convert HREF="#heat MACROBUTTON HtmlResAnchor heat into HREF="#mechanical MACROBUTTON HtmlResAnchor mechanical work. The fundamental laws of thermodynamics are useful guidelines for solving many energy-related problems.

 What is heat and temperature? Why energy flow from one place to another? What are the four laws of thermodynamics?

 How can heat be converted into mechanical work? Demonstrate please.

 Can all the heat be converted into mechanical work? How much is lost if not all? What happened to the lost energy?

When the temperature of two bodies are the same, there is no net heat transferred between them when they are in contact. This is the 0th law of thermodynamics, and we have applied this law to measure the temperature of an object.

The 1st law of thermodynamics is the HREF="#conservation MACROBUTTON HtmlResAnchor law of conservation of energy. An early statement for the law was given by Clausius: When work is produced by a system using heat, a proportional quantity of heat is consumed; when work is done to a system, an equivalent amount of heat is produced.

To facilitate discussion, let us represent a system by A. The heat and work done to A empowers A to perform work according to its design. The work may be visible as it involves the expansion or contraction of the volume of A. The work done by A will not be

27 necessarily equal to the total energy input to A. Some energy is absorbed by A to raise its internal potential, Eip. Thus, Eip, of the system (A) is equal to the energy q input to the system subtract the work w done by the system:

Eip = q - w

The internal energy is due to the rise in temperature of A or phase transition for the substance in A. For example, the melting of ice at 273 K to water at the same temperature is a phase transition, so is the evaporation of water into vapor. Much work is done in the phase transition. The first law made it possible to account for all the energy transferred into and out of a system. Heat spent in raising the internal energy, unrecognized as energy in untrained eyes, was wastage in engineering processes. The 1st law of thermodynamics is another statement of the conservation of energy.

There are many implications due to the first law of thermodynamics, and thus it can be stated differently depending on your purpose. Common dreams are to build machines to perform work without putting energy into it. The 1st law suggests that perpetual motion machines are impossible.

The 2nd law of thermodynamics summarizes the experiences of converting heat into mechanical work: It is not possible to build a machine to convert all the heat into work. In other words, converting heat from one form into another cannot be made without waste, due to raising the temperature of the surroundings of the system. Most heat conversion processes are of low efficiency. Thus, the second law is not a limitation of the development of technology, rather it sets the condition for efficient machines. For example, hot exhaust gas carries energy with it in an internal combustion engine. The second law suggested that lowering the temperature of the exhaust extracts more energy of the burning fuel to do mechanical work.

There are many ways to state 1st and 2nd laws of thermodynamics, depending on the purpose. Those given here are intended to give a general description of how heat behalf.

A closed system is an isolated one such that no energy or mass is transferred into or out of. A closed system can be either at equilibrium, a state with no detectable change, or none- equilibrium, changes may still take place. For example, two liquids at the same temperature in a container will eventually mix. In this case, the driving force (energy) of change is called entropy, which is related to randomness for a collection of molecules or objects. Increasing of randomness and flowing of heat causes entropy to increase. For a perfect crystal at absolute zero (0 K), there is no available heat, and the entropy of any perfect crystal at 0 K is defined as zero. When a crystal or system absorbs heat, its entropy increases. When heat flows from one part to another part in a closed system, the entropy of the closed system increases. In a closed system, the 3rd law of thermodynamics states that the entropy tends to increase.

The laws of thermodynamics can be summarized in a sentence. Energy of a closed system strives for the lowest state, but its entropy strives for the highest state.

28 Review Questions: 1. What are the four laws of thermodynamics? 2. What is the implication of the 0th law of thermodynamics? 3. Design an experiment or demonstration to show that energy is conserved. 4. What is entropy?

Technology for Energy Conversion

The better the technology for utilization and At the end of the 17th century, energy production of energy we have, the better is our living resources from the Earth surface had standard. Thus, scientists, engineers, architects, exhausted, and deep coal and metal ore pits politicians, and almost everyone are concerned with suffered from floods by underground water. Steam engines in 1763 converted 2% of heat these issues: into useful work, but it filled the need at the time. Following the use of steam came the  How to make efficient use of energy? How to internal combustion engine, and the control the movement of energy? industrial revolution, which caused many social problems. Thus, directing energy  How to develop technology making the most movement is more than a technical problem, it involves social, economic and human efficient use of energy resources? factors.  What will be the energy demand in the near future? How to structure a community suitable for the available energy?

Machines are needed to recover residual heat; work is required to transfer heat from a cold place to a hot place (air conditioning). The laws of thermodynamics mentioned above must be considered in the utilization of heat. For the transfer of electric energy, laws of electricity and magnetism must be considered. Energy loss through transmission lines is often cited for the research on superconductor (or perfect conducting) materials.

For the transmission of radiation, the wavelength of radiation dictates the transmission medium. Infrared lens, microwave guide, fiber optics, ultraviolet filter, X-ray and gamma ray shielding are some of the gadgets related to the technology of radiation transmission.

Batteries, motors, photoelectric cells, internal-combustion engines, thermoelectric generators, electrochemical cells, fuel cells, etc. are machines for energy conversion. They convert energy from one form to another.

Part of nuclear technology is to build machines for the conversion of nuclear energy into heat and electric energy. The development of nuclear technology is closely related to the development of other technologies.

Review Questions: 1. What energy resources are available on the surface of the Earth? What is the origin for each of the resources? Give an energy cycle involving some of energy resources.

29 2. Why are incandescent light bulbs much less efficient in converting electric power to light than fluorescence bulbs? 3. Why a microwave oven takes shorter a period to warm up the same amount of water than the stove even if they operate at the same power?

30 Energy Resources and their Utilization

Solar, nuclear, and geothermal energies are the ultimate sources of our energy, with the solar energy being most important for the Earth. The Sun is a nuclear fusion reactor, and nuclear technology is being developed to imitate the energy producing process of the Sun.

Solar Energy The Sun provides nearly all energy on Earth. It provides wind power, hydropower, tides, waves, and plants, causing nearly all the global phenomena, floods, draught, tornadoes, hurricanes, plant growth, life, death and decay. Fossil fuel is energy from the sun long ago.

 How much solar energy reach the Earth surface, and in what form? What process provides the solar energy? What is the total energy output of the Sun?

 What phenomena are caused by solar energy? What energy resources on Earth do not come from the Sun?

Energy from the Sun is in the form of infrared (heat), visible, and ultraviolet radiation.

The Sun’s surface radiates 6.4 kJ cm–2 s–1, and the surface of the Sun is 6.1x1012 km2, (1 km2 = 1010 cm2).

On a cloudless summer day, the earth surface receives 80 kJ cm-2 day–1 (20 kcal cm-2 day–1). These values are important for any solar technology. The Earth receives 1.7x1014 kJ s–1 of energy from the Sun.

As to what provides the energy in the Sun, a detailed answer requires a lengthy discussion, and this will be discussed in the chapter on nuclear fusion. To make a small Sun on earth is one of the objectives of nuclear technology.

Review Questions: 1. What is the total power output of the Sun? Where does the energy go? What fraction of the energy from the Sun reaches the Earth? 2. The distance between the Sun and the Earth is 149,600,000 km. What is the time of flight for a photon from the Sun to the Earth? (8.3 m)

31 Geothermal and Nuclear Energies Cross Section of the Earth Geothermal energy is heat in the interior of the Earth, and nuclear energy is derived from materials present on Earth Earth accessible to man. crust

 What are the sources of energy? Lower Which is a major and which is a minor source of mantle energy?

Geothermal energy refers to the heat flow of the planet Inner core Earth. In this regards, thermal gradients, conductance of Outer Upper various material, thermal history, and heat distribution of core mantle Earth are information required for the development of technology to utilize this heat source. Aside from the heat in the hot interior of the earth, radioactive decay and other nuclear process may produce a small amount of heat in the interior of the planet Earth.

The heat flow from the interior to the surface of the Earth is small, only 0.063 J m–2. The temperature at depths less than 20 m oscillate annually, but it remains constant at greater depths. The earth crust is a poor thermal conductor. Little amounts of energy are derived from geothermal sources using machines such as heat pumps, in some limited areas where there are hot springs.

Another source of energy not coming from the Sun is nuclear power, which can be divided in two categories: fission or splitting of heavy elements such as uranium and plutonium, and fusion or combination of light elements such as hydrogen, tritium, and deuterium. The science of these processes is very simple, but the technology for their utilization and maintenance is very complicated. Many aspects should be studied. The major purpose of this book is to introduce the various aspects related to nuclear phenomena, and the minor purpose is to consider the impact of nuclear technology on various issues.

Radioactive decays also produce energy, but the amount of energy is small for any large- scale application as a source of energy.

Review Questions: 1. What are the major energy resources on the planet Earth? 2. What is a heat pump? How does a heat pump get an efficiency of 200%? Is the principle of conservation of energy violated in this case?

32 Energy Conservation The Energy Crisis Energy conservation means preservation of energy supplying On October 17th, 1973, the leaders of Arab nations met in the Capital of Kuwait to proclaim an oil boycott commodities or making the most efficient (Darmstadter, 1975). Between 1974 and 1978 the use of energy. The media coined this Organization of Petroleum Exporting Countries met phrase between 1974-1978, a period regularly and set the oil prices. This triggered the energy when the energy crisis hit every country. crisis during 1974 - 1978.

Since HREF="#conservation During the period of energy crisis, gasoline price was high, and many gas stations limit the purchase of gasoline to 10 MACROBUTTON HtmlResAnchor gallons each time. Many gas stations did not have enough energy is always conserved, the terms supply, and motorists often had difficulty buying gasoline. conserving energy and energy conservation are fallacious, non- Due to the high cost of transportation, prices of goods and scientific, and erroneous. However, these services went up, causing a high inflation rate. Inflation cut the purchase power of workers, and wage demand of labor terms had been used since the seventies went up. Thus, the energy crisis caused social problems. to mean making more efficient use of energy, extend the limit of energy utilization, and not to waste energy. Their usage is so common that we can no longer ignore it. The energy crisis prompted the concern over the environment in the 1980s and 1990s. The realization of a limit in chemical energy reserve on the planet Earth led to the recognition of the Earth being a limited ecological system.

 In your opinion, will energy demand of the world cause a crisis in the future?

 How can you extend the benefit of energy utilization as an individual, as a group, as a nation or in the global village?

 What will be used to supply energy for the world when oil and coal are depleted?

Having experienced the energy crisis made all oil-dependent nations, especially the U.S., nervous when Iraq invaded Kuwait. Oil or energy was certainly an important factor for the Persian Gulf War in 1991.

Review Questions: Lessons Learned from Energy Crisis 1. List ten tips for saving energy in your home. In the long run, the energy crisis was a good lesson for 2. List ten rules for a university to save energy. the world to learn that energy reserve is limited. The 3. Discuss the impact of doubling the price of public has been warned for some time, but no one listened until the crude oil price reached $40 a barrel. gasoline. The hardship during this period pushed the 4. How is urban design related to energy developments of technology for better utilization of consumption of a community? energy. Cars making more efficient use of energy were built, methods were developed to derive more fuel from lower grade crude oil, alternate fuels were tried, and other energy sources than oil were tapped.

33 The Impact of Eenergy in Level Society Demand Energy consumption is a measure of living standard. As the living standard improves world wide, energy consumption and demand increase. Cost  How do you manage your personal energy consumption to derive the most benefit? Arbitrary Coordinate  How does a society manage the energy supply, demands, and utilization? Typical curves depicting market forces of price and What forces are used to manage energy? demand. There are two forces to control energy demands: cost and regulations. Cost is related to price of energy and income, Cost is the market force that is less noticeable than government regulations. Regulations are often seen as heavy-handed. In Canada and the United States, the market force dominates, but occasionally the government steps in with regulations. Taxing policy, however, has a hand on each of the two forces.

Cost is determined by taxes, level of supply, differential pricing due to amount of consumption and purpose of end use etc. When the cost is high, the demand is low, and as cost is lowered, the demand goes up. Because the cost and demands vary as curves, the market force is more acceptable for the public. How the market forces work is a subject discussed in an introductory economic course.

Regulation by policy sometimes is brought about suddenly, and this force may not be popular. However, in the formulation of a policy, there are many factors to be considered. Energy demands is a function of population, population density, work force, number and type of industries, income level, social acceptance etc. Sound policies work, but unfit policies invite abuse and protests.

Regarding nuclear energy, its development is expensive at the initial stage with only a slim prospect of return on investment. Initially, only government allocates funds for the research and development. The cost of development may not be added to the pricing in the sale of nuclear power.

Review Questions: 1. What are the major forces for the management of energy related commodities and technologies in the public domain? 2. Discuss how costs affect your personal consumption of energy?

34 Exercises

1. Write an essay using one of the following as your title: Hotness and heat; Mechanical work and heat; Energy as driving force of change; Conservation of energy and energy conservation; Black out (power failure); The visible light; Electromagnetic radiation; Infrared; X-rays; Photoelectric effect; Methods of energy storage; Conversion of energy; Energy mass equivalence; Entropy; Sound and music; Fighting for energy (energy related wars); Conflicts over energy; Energy policy of a household; Guidelines of energy usage for an institution; The sun.

2. From a reliable source, find information about and then write a short story on any one of the following people. Make your story interesting to read. Plato (427-347 BC); Newton, I (1643-1727); Fahrenheit, G.D. (1686-1736); Celsius, A. (1701-1744); Charles, J.A. (2746-1823); Gay-Lussac, L. (1778-1850); Seebeck T.J. (1770-1831); Black J. (1728-1799); Thompson B. (1753-1814); Joule (J.P. (1818-1889); Young T. (1773-1829); Bernoulli D. (1700-1782); Clausius R.J.E. (1822-1906); Maxwell J.C. (1831-1879); Thomson W.; Boltzmann L.E. (1844-1906); Watt J. (1736-1819); Galileo (1564-1642); Torricelli E. (1608-1647); Carnot N.L.S. (1796-1832); Planck M.K.E.L. (1858-1947); Strutt J.W. (1842-1919); Wien W. (1864-1928); Einstein A. (1879-1955).

3. A 12 fl-oz serving (350 mL or 260 g) of beer contains 7% (by volume) alcohol is rated to give a food energy of 150 kcal. As an approximation, assume all the energy comes from the alcohol. Calculate the food energy value of 3.5 fl oz table wine containing 12% (by volume) of alcohol. Ignore the small amount of other chemicals present in wine and beer. Express this amount of energy in kJ, and kilo-watt-hour. Assume you use the energy to raise your potential energy by going vertically up a height. What is the height? If you have this amount as kinetic energy, what is the velocity?

4. Calculate the velocities of a neutrons which have a kinetic energy of 0.52 MeV and 0.025 MeV. (Ans: 1.0 x 107 m/s and 997 m/s respectively without using the theory of relativity, which should be used for the high-energy neutrons). What is the velocity of an electron if it has a kinetic energy of 0.52 and 0.025 MeV? Should you use the theory of relativity to calculate the kinetic energy of electron?

5. Energy content of 36 g liquid water at 273 K is 12 kJ more than 36 g ice at the same temperature. Calculate the mass equivalence of 12 kJ in g and in amu. Is this amount detectable with a balance that can be used to weigh 36 g? Do the same for 1200 kJ and 1x1012 kJ.

6. Do you expect the temperature of water to be different before and after it flow down a waterfall of say 500 m? What happens if all the potential energy is converted to the kinetic energy of the water molecules?

7. What are the three laws of Newtonian physics? What are the four laws of thermodynamics?

35 8. Which one do you favor as an instrument to manage energy resources, free market force or government regulations?

9. Give the energies of the photons in units eV and Hz for various regions of the Photon Energy in Various Region of the electromagnetic radiation spectrum. Electromagnetic Radiation Spectrum

Region, in eV in Hz

Radio (long) Radio Radio (short) Infrared VISIBLE Ultraviolet X-rays Gamma rays

36 Further reading and work cited

Brandwein, P.F., Stollberg, R, Burnett, R.W., (1968), Energy, its forms and changes, Harcourt, Brace & World, Inc.

Darmstadter, J. (1975), Conserving energy, John Hopkins University Press.

Einstein, A. (1905), On the electrodynamics of moving bodies (Zur Elektrodynamik bewegter Körper), original in Annalen der Physik 17, 891, reproduced in The collected papers of Alber Einstein, vol. 2, 276, Edited by Stachel, J, Prenceton University Press (1989).

Einstein, A. (1909), On the development of our views concerning the nature and constitution of radiation (Über die Entwickelung unserer Anschauungen über das Wesen und die Konstitution der Strahlung) reproduced in ibid, vol. 2, 564.

Maiman, T.H. (1960), Stimulated optical radiation in ruby, in Nature, 187, 493.

Weber, M.J. (1982), CRC Handbook of laser science and technology, vol I, Lasers and Masers, CRC Press.

Zukav, G. (1979), The dancing wu li masters, Bantam Books.

Web Sites on Energy

Energy outlook and policy: http://www.igc.apc.org/awea/wew/othersources/otheroutlook.html

Energy and economics: http://www.investaweather.com/energy/energyhmpg.htm

Energy and environment research center: http://www.eerc.und.nodak.edu/

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