ENERGY

You may have an intuitive feeling of what we mean by “energy.” I associate it with the well- known comic character Popeye introduced in Elzie Segar’s comic strip in 1929. His “energy” is manifested by the big muscles that he develops when he eats spinach. W hen I was a kid, most of my friends hated spinach, and even today we are still looking for alternative energy sources. Physics defines energy as the ability to do work. This is not much of a better a definition than Popeye’s muscles. How do we measure “ability”? “ Work” in this definition is mechanical work defined as the product of force times the distance in which the force is applied (mental work does not count). As simple as this definition is, it does convey the concept that you can convert energy into work. There are rules that determine how efficiently you can make this conversion (these will be discussed later in this chapter), just as Popeye is able to convert spinach to muscle strength. It is much easier to define and do calculations on specific sources of energy. In Table 5.1, I list the specific sources of energy that play an important role in the discussion of global warming and possible solutions to the issue.

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Table 5.1.

Energy forms

The fundamental law that governs energy use is the law of conservation of energ y, which states energ y is a conserved quantity— it cannot be created nor destroyed, but it can only be converted from one form to another. Specific attempts to violate this law can be traced as far back as the 13th century. Machines that violate this law are called perpetual motion machines. One possible statement that can be extracted from the law of conservation of energy is that a perpetual motion machine cannot be constructed. A common belief was that one should be able to invent a machine that creates energy, and any statement to the contrary represents a defeatist att itude perpetuated by the priesthood of professional scientists. Th is attitude is understandable because the law was never proved. It is one of the key “axioms” on which modern science is based. The science derived from this law is so overwhelmingly supported by observations that any attempt to shake this foundation must be both convincing and reproducible (remember Chapter 1— there is no “absolute” truth in the scientific method). The trust in the validity of this law is so strong that the US patent office has standing regulations to reject any application for a patent that implies a violation of the law.

Heat and work represent special forms of energy. They do not constitute forms of energy of a system but rather energy in “transit” to or from the system. Heat is usually associated with energy delivered to a system that will result in temperature change or some phase change such as evaporation, melting, and so forth. Mechanical work done by the system implies conversion of some of the internal energy of the system to mechanical force that operates over a

distance (or the inverse— adding to the internal energy by applying work on the system). Th e internal energy of the system is approximately the sum of the energies of all the molecules of the system.

Until the 19th century, heat and work were considered separate quantities and were given a separate set of units: Calories and Btus to measure heat and joules to measure work. It was Sir James Joule (1818– 1889) who studied how water can be heated by vigorous stirring with a paddle wheel. The paddle wheel adds energy to the water by doing work on the water. Joule found that the temperature rise is directly proportional to the amount of work done— thus establishing heat and work as interconvertible forms of energy.

Today we associate heat and work with a degree of order associated with the transfer of energy. Work represents a very orderly dispensation of energy, such as pushing a cylinder in a piston along a straight line. Heat, on the other hand, represents a very disorderly dispensation of energy, such as increasing the velocity of molecules to move in all possible directions. We will return shortly to this issue.

TEMPERATURE

We all have common experiences with temperature as an indicator of what is hot and what is cold. We also know how to use various kinds of thermometers to measure temperature. We also know that unfortunately the scale that we use to measure the temperature depends on where we are—Fahrenheit in the United States and primarily Celsius in the rest of the world. Because the main topic of this book is the global greenhouse effect that connects temperature with sunlight, we will have to go a bit deeper.

Temperature is a property that does not depend on the quantity of a material. If we go to the ocean and insert a thermometer to measure its temperature and then take a small container, fill it with water, remove it from contact with the ocean, and measure the water temperature in the container, we will get approximately the same reading. This is because temperature is an “intensive” property. Another familiar intensive property that we have already encountered (Chapter 2) and that does not depend on the quantity of material is density. Heat and energy on the other hand are “extensive” properties, as they do depend on the amount of material. The amount of energy stored in the molecules of the water in the container is much smaller than the amount of energy stored in the ocean.

Temperatures in Fahrenheit and Celsius are related through the equation

Tf = 1.8T c + 32. [5.2]

Box 5.1

ENERGY AND MASS

Until the beginning of the 20th century, when Albert Einstein published his papers on special relativity, mass and energy were viewed as separately conserved quantities. Einstein’s famous consequence of the theory,

E = mc2 , [5.1]

puts an end to this dichotomy and, in the process, had a pronounced effect on our use and understanding of energy. Some of this has a direct effect on the global energy picture— a main concern of this book. In this equation, m is mass and c is the speed of light in empty space (a vacuum), which is a universal constant with an approximate value of

c = 3 × 108 m/sec (300 million meters per second).

Let us first estimate how much energy is associated with 1 kg of mass:

E (of 1 kg of mass) = (1 kg) × (3 × 108 m/sec)2 = 9 × 1016 J (8.5 × 1013 Btu).

This is a lot of energy. It is so much energy that converting the mass of a small, loaded, 4- ton pickup truck into energy would satisfy the energy needs of the world for a full year.

Fortunately, the conversion of mass to energy takes place under very special circumstances.The object has to move at speeds close to the speed of light or overcome very strong binding forces such as nuclear forces.The strongest practical manifestation of the release of this energy is through the use of nuclear energy, for either military use in the form of nuclear weapons (atomic and hydrogen bombs) or peaceful use in the form of nuclear reactors. I will discuss nuclear energy in later chapters when I discuss alternatives to fossil fuels. The only nuclear reaction that we can control to generate this energy in a nuclear reactor is a fission reaction. In fission we split a heavy nucleus such as U- 235 by bombarding it with neutrons (this reaction will be discussed in Chapter 11 when we discuss alternative energy sources to fossil fuels).The total mass of the products is slightly less than the mass of the starting nuclei. This difference in mass is converted to energy. If we split 1 kg of U- 235 into lighter elements such as barium and krypton, we lose about 0.3 g, which is converted to 1.7 × 1013 J, or about 17 billion Btu.

So 75°F ≈ 24°C. These scales are based on standard reference points. The Celsius scale is defined such that the freezing point of water is 0°C and the boiling point of water is 100°C at normal atmospheric conditions.

There is a third temperature scale rarely used in everyday activities. We have avoided using this until now, but at this point it must be introduced. This is the Kelvin scale, Tk. It is related to the Celsius scale through

Tk = T c + 273. [5.3]

Thus 25°C is equal to 298 K . This scale is important because in liquids and gases it is approximately proportional to the average energy of a single molecule. Zero on this scale is an absolute zero in which all the molecules stand absolutely still— nothing moves. This situation is forbidden in physics (for reasons derived from the famous uncertainty principle), so the absolute zero temperature is an unattainable target. We can get very close to it (to about millionth of a degree), but we can never achieve it.

ENTROPY

The law of conservation of energy is a fundamental, universal law (meaning that we believe it to apply throughout the universe) that puts limits on our ability to create “something from nothing” at least as far as energy is concerned. It tells us that we cannot drive a car or operate an electrical power station without feeding it with some sort of fuel. We cannot create a perpetual motion machine that will move constantly without supplying it with energy. Th is sort of limitation offends some of us, but for most of us it is not very surprising. It is one of the pillars of the work ethic that we were exposed to since early childhood and try to pass on to our children and grandchildren.

W hat about the following scenario? Imagine that we are cruising on a vast ocean. Th e ocean contains a very large number (around 1045) of molecules of water. Each molecule moves randomly in all directions and interacts with other water molecules. All this energy is the internal energy of the ocean. Can we create an engine that will use a very small fraction of this energy to propel the ship? We are not violating any conservation law—we are not even depleting any reservoir because the sun will continue to hit the water, and our energy withdrawal will hardly cause any temperature change in the ocean. In practical terms, for us as passengers on that ship, we would be able to cruise the oceans forever without using any fuel (indirectly we are using solar energy)— we would enjoy a perpetual motion machine without violating the energy conservation law. Well, not surprisingly, we cannot do that. If it is too good to be true it probably is, but why?

The reason is that there is another fundamental law, as basic as the energy conservation law (some even think more basic) that states that left on its own, a system tends to evolve in such a way as to increase disorder. To paraphrase it: left on its own, the universe tends to evolve to a state of maximum mess (just like my grandchildren do to a room full of toys). You will notice that the statements start with “left on its own,” which means that my grandchildren can still fix up their room— but they will have to put energy into the effort; if they are not willing to exert the energy, the room will get messier and messier. This law is known as the second law of thermodynamics; thermodynamics is the scientific discipline that deals in processes involving the flow of heat. The first law of thermodynamics deals with the application of the law of conservation of energy to thermal processes. This all sounds a bit philosophical— why do we need it here? How can we use it to show that we cannot have our dream cruise? We need it because, as I will show in Chapter 6 when I discuss the solar energy cycle, the only commodity we get from outer space in a constant supply is “order” for us to dissipate. This “order” is carried by the solar radiation. In a sense, the greenhouse effect is a perturbation on this “order in” and “disorder out” balance that we engage in with the sun. We should get serious about the concept and try to quantify it in a way that will allow us to do some calculations and predict or explain some important observations in a quantitative way.

The physical property associated with this trend to “disorder” is called entropy. We connect it to thermal processes through a very simple equation:

Change in entropy = Q T k . [5.4]

Q in this equation is the amount of heat coming in to heat the system (when Q is positive) or going out to cool the system (when Q is negative). Tk is the absolute temperature (in Kelvin). The rationale behind this definition is that the absolute temperature, Tk, is associated with the

Q

average energy per molecule. So the ratio represents the average number of molecules that

T k

share the given amount of heat Q. Because all these molecules move in all possible directions, the disorder will increase with the number of possible, equally probable movements. Th is is analogous to a room with many drawers that have items randomly distributed, as compared to a single drawer stuffed with items. The disorder in the fi rst case is considered to be much higher than in the second case.

Let us restate the second law of thermodynamics in terms of entropy: Left on its own, a system will evolve in a way that will increase its entropy. So what happens with our wonderful cruise? The only thermal process involved is the extraction of heat from the ocean. We are decreasing the heat contents of the ocean (negative Q in equation 5.4) without any compensating increase in entropy because the heat energy is converted to work that represents a very low-entropy (high-order) process, hence the net result of the process is decrease in entropy— which is forbidden by the second law.

Let us apply the principle to another issue: we take a hot object and put it in contact with a cold object— what happens? Our everyday experience tells us that heat will move from the hot object to the cold object and that, as a result, the temperature of the hot object will decrease and that of the cold object will increase until the two objects equal the same temperature. From a perspective of energy conservation, heat can move either way without violating the law. Tk(H), the temperature of the hot object, is larger than Tk(C), the temperature of the cold

Q Q

object. So will be smaller (due to the bigger number in the denominator) than .

Tk (H ) Tk (C )

If we extract heat from the hot object (Q negative) and put it in the cold object (Q positive), the entropy of the hot object will decrease, but the entropy of the cold object will increase by larger amount, so the change in entropy is positive and in agreement with the second law.

As a final example, let us construct an abstract power station and try to see if the second law imposes any limit on our ability to generate power. This will be useful later when I discuss possible alternatives to current energy sources. The most common power stations generate electrical power by rotating a coil inside a magnet. Usually the rotation of the coil is performed by a steam turbine; hot steam at around 400°C enters the turbine to rotate the coil that generates the electricity. We get the steam by heating water with whatever energy source we choose— nuclear, coal, natural gas, and so forth. W hatever energy source we use, the energy of the hot steam is converted into the mechanical energy in the rotation of the coil that results in the production of electrical power. The internal combustion engine, which is mostly responsible for the propulsion of our cars, works on a similar principle: we inject a mixture of gasoline and air into a cylinder, the mixture gets compressed, and a spark ignites the mixture to a temperature higher than 1000°C. The fuel gets “ burned,” meaning that the hydrocarbons get oxidized by oxygen to produce carbon dioxide and water. The oxidation releases energy that heats the gas. The hot gas expands to push a piston that rotates the crankshaft that, in turn, rotates the wheels. We are converting the chemical energy in the fuel (by burning it) into heat energy and converting this heat into the mechanical energy of the car. In both cases an exhaust of cooler steam or exhaust gases exits the engine. The second law imposes an absolute limit on to the effi ciency of converting the heat energy. The limit depends on the operating temperature of the engine (approximately 400°C for the electric generator and 1000°C for the car engine). This limiting efficiency is called the Carnot effi ciency after the French physicist Sadi Carnot (1796– 1832). It states that

Maximum efficiency (as a percentage) = (1 – Tk (C ) ) × 100. [5.5]

Tk (H )

The temperatures here are in Kelvin— for the electric generator the hot source (hot steam) reaches the temperature of 400°C = 400 + 273 = 673 K . The cold sink is the exhaust gas that at ambient temperature will be 25°C = 25 + 273 = 298 K .

So the maximum efficiency of the generator will be

Maximum efficiency of the electric generator = (1 – 298 ) × 100 = 56%.

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We will see in future chapters that such limits on the efficiency of converting heat energy into work play a key role in discussing the intimate connections between the climatic change expected from the greenhouse effect and the foundational energy situation of our technological society.

LIGHT

Figure 5.1 shows a beautiful, common experience— when the conditions are right, and sunlight mixes with rain, we see a rainbow in the sky. We can also generate a rainbow on our own by taking a garden hose on a sunny day, putting our finger on the nozzle, and generating a fine spray— if we are lucky, then we will see a rainbow. We can achieve similar results by taking a source of white light and passing it through a glass prism. All this indicates that what seems to be “white” light is actually a superposition of colors. W hat are these colors?

Figure 5.2 shows a familiar image— we throw a pebble into a small pond and see wave creation at the point of impact. The wave moves in approximately concentric circles until it dissipates. The motion of the wave is one common mechanism through which the water in the pond propagates the energy provided by the pebble. Another common mechanism is through currents in which the motion of the water molecules carries the energy.

Waves are important to our discussion because light exists as a special kind of wave called an electromagnetic wave. Some of us think that in the water wave, water moves with the wave. However, in reality, the water molecules move only up and down, oscillating in height without changing their surface position while the energy of the wave propagates parallel to the surface, away from the disturbance. In an electromagnetic wave, electric and magnetic fields oscillate up and down perpendicular to the direction of energy propagation of the wave and perpendicular to each other.

The simplest form of wave is shown in Figure 5.3. W hat we also show in the figure is a schematic description of an electromagnetic wave consisting of two kinds of simple waves, one for the electric field and one for the magnetic field. Both waves are perpendicular to each other (one black and one gray in the figure) and the direction of propagation is perpendicular to both waves.

Direction of wave motion

Figure 5.3. Characteristics of a simple wave and a schematic drawing of an electromagnetic wave

Let us now concentrate on the simple wave in Figure 5.3. One can see the amplitude of the perturbation (the height of the water or the intensity of the electric or magnetic field) as a function propagation of the wave. We can show this amplitude either by freezing the perturbations in time the way that I have photographed the water wave in Figure 5.2— in that case, the simple wave will show the amplitude as a function of location— or by standing in one place and looking at changes in the amplitude as a function of time, passing through crests and troughs in a periodic way. Figure 5.3 shows the amplitude as a function of location. Th e distance between two crests (or two troughs) is the length of the wave, measured in units of distance such as meters. If we stand in one place and count the number of crests (or troughs) that pass in a second, then we get the frequency of the wave measured in units of cycles per second or Hertz.

Electromagnetic waves travel in empty space (a vacuum) at the speed of light— a universal constant that constitutes the highest speed that anything in the universe can achieve. Th e wavelength and the frequency of light are connected to each other through the following relationship:

c = wavelength × frequency, [5.6]

where c is the speed of light in vacuum that approximately equals 300 million m/sec (3 × 108 m/sec). The distribution of wavelengths or frequencies represents the spectrum of the radiation. Table 5.2 lists the electromagnetic spectrum.

W hat we can see from the table is that the spectrum spans more than 10 orders of magnitude in wavelengths (it is unbounded at the lower and higher ends) and correspondingly more than 10 orders of magnitude in frequency. Visible light is only a very small part of

Table 5.2.

Electromagnetic spectrum

this vast spectrum. The beautiful colors that we see in the rainbow are due to a separation of the parts of visible white light according to wavelength. Our eyes can distinguish between the different wavelengths and we associate colors with these wavelengths—the long- wavelength region of the visible part of the spectrum we associate with the color red and the short- wavelength region we associate with the color blue. The other colors are in between these two.

Many experimental obser vations with light can be explained in terms of the wave nature outlined here. The most convincing of these are interference and diffraction, phenomena characteristic of waves. Some experiments, however, cannot be explained by the wave nature of light. The most famous of these experiments is the photoelectric experiment in which light generates an electric current when metals are illuminated with light of short enough wavelength. To explain the photoelectric effect, Albert Einstein postulated that light consists of individual particles called photons and that each photon has energy given by

E = h × f, [5.7]

where f is the frequency of the radiation and h is a universal constant called Planck’s constant.

This equation is very interesting because the right-hand side contains frequency, which is a wave property, and the left - hand side contains the photon’s energy, which is a property of a particle. So what is light—waves or particles? The conventional answer now is that it is both— in some experiments it behaves like waves and in others like particles. This is a way of stating the principle of complementarity proposed by Niels Bohr (1885– 1962). Light is not unique in having this kind of duality; it extends to matter as well.

The relationship between the energy of photons and frequency tells us that high- frequency radiation will have photons with high energy, and low-frequency radiation will have photons with relatively low energy.

In the beginning of the book I stated that our objective is to understand climate change from first principles. Chapter 5 is a short summary of many of these principles. But all this sounds like science for the sake of science— unrelated to the many things that concern us in life. In the next chapter I will try to change that.