Chapter 2

Eternal Delight Energy is eternal delight. William Blake

Sisyphus in Hell On his trip to Hades, Odysseus (Odyssey, XI) meets Sisyphus, King of Ephyra, who might be his illegitimate father. Like Odysseus himself, Sisyphus is a great sailor and an even greater liar; the father and his unrecognized son are both extremely cunning. Sisyphus’s greatest feat is capturing Thanatos, the messenger of death, when he comes for him, thus upsetting the world, as nobody dies during some time until Ares manages to fix the mess. When the great deceiver finally ends up in Hell, he is compelled to roll a huge bolder up a hill. As soon as he reaches the top, the boulder slips from his sweating hands and rolls back down to the valley. Sisyphus is forced to repeat the same drill throughout eternity. (Fig. 2.1) In order to roll up the boulder, Sisyphus has to apply (muscular) energy to counter the force of gravity that opposes his efforts. As a result of his work, when the rock has reached the peak of the hill it has gained a kind of energy we call potential energy, Ep. The rock is able, it has the potency (hence the term ‘‘potential’’) to carry out some work while rolling down, and this work is proportional to the mass of the rock (m), the height of the mountain (h) and a fixed value that stands for the action of gravity (g), that is, Ep = m 9 h 9 g. Sisyphus transforms his muscular energy into potential energy, which can in turn be transformed into electricity: if he had been condemned to push up a large water container instead of a rock, the water running down could have powered a turbine connected to an alternator to generate electricity. In the whole process there is a flowing quantity whose magnitude remains unchanged while its quality is transformed (muscular, potential, electrical energy). Energy can neither be created nor destroyed: it can only be transformed. This is the first and most famous law of thermodynamics, formulated by the great English physicist J.P. Joule (1818–1889) after years of time-consuming experiments, based on the observations by the German physician and physicist J.R. von Mayer (1814– 1878).

J. J. Gómez Cadenas, The Nuclear Environmentalist, DOI: 10.1007/978-88-470-2478-6_2, Ó Juan José Gómez Cadenas 2012

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Fig. 2.1 Sisyphus rolling the boulder uphill. As it rolls down, it is able to perform work. We express this by saying that the boulder gains potential energy

Power The concept of power is as familiar to us as the concept of energy, but we often mistake one for the other. The correct definition of power is the capacity to do work per unit of time. Let’s take the example of two Sisyphuses toiling up the mountain, each with his rock, both of equal weight. One of them, more able-bodied than the other, manages to push the rock up at a faster pace (that is, he performs more work per unit of time, in other words, he develops more power), so he overtakes his fellow sufferer. Both, as we know, receive an identical reward: when reaching the top, the rocks slip from their hands. Both rocks are capable of doing the same work, so both convicts have generated (and consumed) the same amount of energy. The brawnier Sisyphus has a greater power, but this just means that he is able to do the work faster than his feeble fellow. It is important to realize that in order to relate the power generated or consumed by a process to the amount of energy consumed we have to resort to time. A stupid little example: which car consumes more energy, a small 100 Hp car or an SUV with 500 Hp? The obvious answer: it depends on how long the engine is running. All of the power of a Mercedes Benz does not use up a single drop of oil unless we start a car (but of course is doesn’t take us anywhere).

Units for Measuring Energy and Power

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Units for Measuring Energy and Power Energy is measured in different units, of which the most common in everyday life is the kilocalorie, which stands for the amount of energy you get from food. Everybody knows, for example, that the amount of energy an adult person needs daily is between two thousand and three thousand calories, depending on sex, age, build and activity level (a moderate diet for weight loss would allow about 1500 calories per day, and there are rapid weight loss diets where you have to limit yourself to 1000 calories). Sounds familiar, doesn’t it? It’s wrong, too. A 3000 calorie diet wouldn’t keep a 20 g mouse alive. When we use the word ‘‘calorie’’ we mean ‘‘kilocalorie’’, that is, one thousand calories. Thus, the average amount of energy we need is around 2500 kilocalories, that is, 2500 9 1000 calories, this is 2,5 million calories, in short 2,5 Mcal. The calorie is a common unit but does not belong to the so called International System of Units or SI, which includes the meter as unit of length, the kilogram as unit of mass and the second as unit of time. In the SI, the unit of energy is called Joule (in honor of the physicist J.P. Joule) and is represented by the symbol J. A calorie amounts to 4.18 J, so our 2500 kilocalorie (2.5 Mcal) diet represents an energy of 10.5 million Joules, or 10.5 MJ. The Joule, the same as the calorie, is used to measure small quantities of energy, that’s why we employ prefixes to make the numbers more manageable. Instead of speaking of an average 2,500,000 calorie diet, we say 2,500 kilocalories or 2.5 Mega calories. The same happens with the Joule. The most common prefixes are given in the following table. Prefix Kilo Mega Giga Tera Peta Exa

Symbol k M G T P E

Value One One One One One One

thousand million billion trillion quadrillion quintillion

Decimal 3

10 (1,000) 106 (1,000,000) 109 1012 1015 1018

Example (Joule) kJ MJ GJ TJ PJ EJ

Some examples: a pea contains 5,000 J (5 kJ) of chemical energy. A mouse needs about 50,000 J (50 kJ) a day, an adult man approximately 10.4 kJ. The oil tank of a passenger car holds around 1.25 GJ. Figure 2.2 shows the energy yield for different fuels. We can see that one kilogram of hydrogen is equivalent to two and a half kilogram of petrol, three of natural gas, seven of wood and ten of straw or dung. Considering fossil fuels, oil is the most energetic: one kilogram provides as much energy as two kilogram of coke, three of wood or four of straw.

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2 Eternal Delight 120

100

MJ/kg

80

60

40

20

0 Energy

Hydrogen

Petrol

Oil

114

45

42

Natural gas Anthracite Charcoal 35

30

29

Soft coal

Wood

Straw

22

15

12

Fig. 2.2 Calorific power of different fuels

A unit of energy that is used quite often is the ton of oil equivalent or toe. Its value is the amount of energy released by burning one ton of oil. If one kg provides 42 MJ (Fig. 2.2), from one ton you get thousand times as much, that is, 42 GJ. This unit allows us to compare several fossil fuels in terms of energy. For example, 1 ton of natural gas is equivalent to 0.83 toe, 1 ton of anthracite is equivalent to 0.7 toe and one ton of coke is equivalent to 0.52 toe. Unlike the (kilo)calorie, the most well known unit of power, the watt (W), does belong to the SI. Its name honors James Watt (the inventor of the first modern steam engine) and is defined as the work of one Joule per second (that is: 1 W = 1 J/s). When we say that a light bulb has a power of 100 W, we mean that in order to keep it lighting we need 100 J of electrical energy per second. So, if the bulb remains on for 5 h a day, the energy it consumes per day is 5 9 60 9 60 9 100 = 1,800,00 J or 1.8 MJ. Curiously enough, the basal metabolic rate of a stout adult male is about the same, around 100 W. To find out how much energy this metabolism consumes in a day we have to multiply by 24 h because the basic chemical processes that keep us alive are switched on all the time. So that’s 24 9 60 9 60 9 100 = 8,640,000 or 8,6 MJ. We mustn’t confuse the kilowatt (kW), a unit of power (work per unit of time), with the kilowatt hour (what we are charged for in the electricity bill). The kilowatt hour (kWh) is a unit of energy which results from multiplying the power of one kilowatt by the time of one hour and is equivalent to 3.6 MJ. We can see that it measures larger quantities of energy than the Joule and can be more convenient. The typical energy consumed by a European family that uses electricity for lighting and household appliances (but nor for heating and air conditioning) is around 250 kWh a month (about twice as much in the US). By adding heating, air

Units for Measuring Energy and Power

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conditioning and an electrical stove, this goes up to about 500–1,000 kWh a month. Finally, there is another common power unit not included in the SI: the horsepower (HP), which we still use to refer to the power of automobiles and which is literally a measure of the power of a draft horse. People used to compare the first steam engines with these horses. When we say that our car has 100 HP we are literally referring to a herd of one hundred horses pulling our vehicle, and to their capacity to perform the work per unit of time, though one century ago, few people would have been wealthy enough to afford the stables and the grain needed to feed such a bunch of animals. A horsepower of one is equivalent to 745 W.

Entropy and Dark Energy The so-called second law of thermodynamics was formulated by the German physicist Rudolph Clausius (1822–1888), who in an article published in 1865 coined the term entropy, defined as the disorder of an isolated system. The second law of thermodynamics can be expressed in a very condensed but a little cryptical form: The entropy of an isolated system increases continuously.

In plain language, this means: In an isolated system the amount of available energy to perform work becomes smaller and smaller over time. A straightforward example: before burning, a piece of coal holds ‘‘high quality’’ energy due to its very organized crystal structure. So its entropy is low. Once the coal has been burnt, the energy it contains does not disappear, but is transformed into heat, a very disorganized (high entropy) form of energy. The total energy of the system remains the same, but once the internal energy of the coal has turned into heat it cannot be used again to produce useful work. That’s the reason why a perpetuum mobile, or perpetual motion machine, will never work, however ingenious the design may seem. Every engine produces heat because of the friction of the parts and therefore energy is continuously dissipated, which leads to a standstill of the engine if there is no provision of fuel. In fact, heat occupies a peculiar place in the scale of energies. Any kind of energy can be turned into heat, but heat itself cannot be converted into any other kind of energy. On the other hand, our common experience tries to persuade us that the second law of thermodynamics does not hold. To begin with, living creatures seem to violate it at all stages, from the moment of conception and the development of individuals (where a disorganized bundle of cells organizes into something as extremely orderly as a human being), to the evolution of species, which seems to progress from the simple (unicellular animals and plants) to the complex (men and angels). And then, how come there are renewable energy sources, if the increase of entropy should do away with them? How is it possible that the wind keeps blowing? Shouldn’t the second law of thermodynamics deprive us of this useful energy? The answer to both questions is the same. Our planet is not an isolated

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system, but an open one, receiving a continuous flow of energy from the sun. This is the energy that plants profit from in order to create biomass through photosynthesis; the energy that generates the winds that move the wind turbine blades, the energy nature makes use of to move the unrelenting machine of evolution. However, the universe is by definition an isolated system, so the second law of thermodynamics predicts its famously tragic thermal death. As time passes, the immense energy released by the Big Bang is being transformed into nebulae, galaxies, stars and living beings. Unfortunately, it doesn’t end there. Eventually the stars will go out, galaxies will move apart from each other, and the universe will be thrown into disarray. And as the universe expands the particles it is made up of become cooler and cooler, until the moment of maximum disorder arrives, and with it the cold, the most absolute solitude. Until recently we physicists believed there was another possible Grand Finale, with the universe contracting again, pulled by gravity, inverting the second law of thermodynamics, turning on the stars, forming ever tighter and denser cumuli finally leading to the initial singularity that created us. The latest observations seem to suggest otherwise. There is something, a force we don’t understand and which rushes to push the universe into continuous expansion and thermal death. For want of another name, we call it Dark Energy, an expression that in fact might be appropriate, given the end it hurls us against. It has appeared rather recently (given the time scale of the Universe) and to understand its origin is possibly the greatest mystery physics faces in the 21st century. But that’s another story.

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