Planet Earth/2a. Energy and the Laws of Thermodynamics

1i. Time: The Invention of Seconds using Earth’s Motion

Planet Earth
2a. Energy and the Laws of Thermodynamics

Measuring Energy

On Bloom Street in Manchester, England, is a tiny pub called The Goose. Based on online reviews it is not a very good pub with dirty bathrooms and a rude bartender, and over the years its name has changed with each owner. It is located in the heart of the Gay Village district of Manchester, but if you travel back in time two hundred years ago, you could purchase a Joule Beer at the pub. Joule Beer was crafted by a master brewer from Manchester named Benjamin Joule, who made a strong English port, a beer that had made him famous and rich in the bustling English city. When his son James Joule was born with a spinal deformity, he lavished him with an education fit for the higher classes. More a scientist than a brewer, his son James Joule became obsessed with temperature. He would always carry a thermometer wherever he went, and measure differences in temperature. Taking diligent notes of all his observations, particularly when helping his father brew beer. Determining the precise temperature for activities such as brewing was an important skill his father taught him, but James took it to the extreme. Thermometers were not necessary a new technology for the day, Daniel Fahrenheit and Anders Celsius had devised thermometers nearly a century before, which still bear their respective unit of measurement in degrees (Fahrenheit and Celsius). No, James Joule was singularly obsessed with temperature because it simply fascinated him. What fascinated him the most, was how you could change temperature of substances, such as a pail of water, using all sorts of ways. One could place it over a burning fire, one could run an electric current through it, or one could stir it at a fast rate, and each of these activities would raise the temperature of the water. Measuring the change in temperature was a way to compare mathematically the various methods employed to heat the water. James Joule had developed a unique way to measure vis viva.

Vis viva is Latin for living force, and in the century before James Joule was born, the term was used to describe the force or effect that two objects had when they are colliding with each other. Isaac Newton determined vis viva as the sum of an object’s mass multiplied by its velocity. The faster the object traveled and the more mass the object had, the more vis viva the object would carry with it. Gottfried Leibniz, on the other hand, argued that velocity was much more important, and that faster objects would have an exponential increase in vis viva. While the two men debated, it was a woman, who discovered the solution.

Émilie du Châtelet, the Cannonball and the Bullet

Her name was Émilie du Châtelet, and she is perhaps one of the most famous scientists of her generation. Émilie was born into lesser nobility, married a rich husband, and dedicated herself to science. She studied with some of the great mathematicians of the time, invented financial derivatives, took the famous poet Voltaire as a lover, and wrote several textbooks on physics. In her writings she described an experiment where lead balls of different mass are dropped into a thick layer of clay from different distances. The depth of the ball into the clay was exponentially greater for balls dropped higher, than they were by increasing their mass. This demonstrated that that it is velocity that is more important rather than mass, but this is difficult to measure.

Imagine a cannon ball and a bullet. The cannon ball measures 10 kilograms and the bullet 0.1 kilogram (smaller in mass). If each are fired at the same velocity, the cannon ball would clearly cause more damage because it has more mass. However, if the bullet traveled 10 or 100 times faster, would it cause an equal amount of damage? The clay experiments showed that the bullet needed to only travel 10 times faster to cause an equal amount damage. Although this was difficult to quantify, as measuring vis viva was challenging.

Origin of the Word Energy

In 1807, the linguist and physicist Thomas Young, who would later go on to decipher Egyptian hieroglyphs using the Rosetta Stone, coined the scientific term Energy, from the ancient Greek word, ἐνέργεια. Hence it was said that Energy = Mass x Velocity². This was the first time the word Energy was used in a modern sense. Today, we would call this Kinetic Energy, energy caused by the motion or movement of something. The equation is actually:

{E_{\text{kin}}={{\frac {1}{2}}mv^{2}}}

Where E_kin is the Kinetic Energy, m is the mass of the object and v its velocity. Note that there is a constant factor ½ in the equation. This slight modification was proposed later by Gaspard-Gustave Coriolis, for which the Coriolis Effect is named after, about the same time that James Joule was having his obsession with thermometers.

What really is Energy?

James Joule demonstrated with his experiments that this Energy could be measured by the heat (change in temperature in a pail of water) that the activity produced. Initially his experiment involved electricity. In 1843 he demonstrated at a scientific meeting of the British Association for the Advancement of Science, that water with an electrical current passing through it would heat up, resulting in a gain in temperature. He wondered if he could demonstrate that kinetic energy (from the motion of objects) would also heat up the water. If true, he could calculate a precise unit of measurement of Energy, using temperature changes observed in water. At the same time, there was great many skeptics of his ideas, as many scientists of the day believed that there was a substance, a self-repellent fluid or gas called caloric which moved from cold bodies to warm bodies, an idea supported by the knowledge that oxygen was required for fire. James Joule thought this idea was silly. He countered with his own idea that what caused the water to raise its temperature was that the water was “excited” by the electricity, the fire, or the motion. These activities caused the water to vibrate. If he could devise an experiment to show that the motion of an object would change the temperature of the water, he could directly compare energy from a burning fire, electricity, and the classic kinetic energy of moving objects.

The Discovery of a Unit of Energy, the Joule

In 1845 he conducted his most famous experiment, a weight was tied to a string, which pulled a paddle wheel, stirring water in an insulated bucket. A precise thermometer measured the slight change in temperature in the water as the weight was dropped. He demonstrated that all energy, whether it was kinetic energy, electric energy, or chemical energy (such as fire), was all equivalent. Furthermore, James Joule summarized his discovery in stating that when energy is expended, an exact equivalent of heat is obtained. Today, Energy is measured in Joules (J), in honor of his discovery.

{\text{J}}={\frac {{\text{kg}}{\cdot }{\text{m}}^{2}}{{\text{s}}^{2}}}

{\text{J}}={\text{N}}{\cdot }{\text{m}}

{\text{J}}={\text{Pa}}{\cdot }{\text{m}}^{3}

{\text{J}}={\text{W}}{\cdot }{\text{s}}

Such that J is Joules, kg is kilograms, m is meters, N is Newtons (a measure of force), Pa is Pascal (a unit of pressure), and W is Watts (a unit of electricity), and s is seconds.

The common modern usage of electrical energy is measured in kilowatt-hours which is the unit that you will find on your electric company bill. A kilowatt-hour is equivalent to 3.6 megajoules (1,000 Watts x 3,600 seconds = 3.6 million Joules).

The Skeptic

In 1847, James Joule presented his research at the annual British Association of Science in the city of Oxford, which was attended by the most brilliant scientists of the day, Michael Faraday, Gabriel Stokes, and a young scientist by the name of William Thomson. While he won over Michael Faraday and Gabriel Stokes, he struggled to win over the young scientist named Thomson, who was fascinated, but skeptical of the idea. James Joule returned home from the scientific meetings absorbed with how to win over the skeptical William Thomson. At home, his summer was filled with busy plans of his wedding to his lovely fiancé, a girl named Amelia Grimes. They planned a romantic wedding and honeymoon to the French Alps, and while looking over the lovely brochures of places to visit in the French Alps, he stumbled upon a very romantic waterfall dropping down through the mountains called the Cascade de Sallanches. He convinced Amelia that they should visit the romantic waterfall, and wrote to William Thomson, to see if he could meet him and his new wife in the French Alps, he had something he wanted to show him.

In 1847 the romantic couple, and the skeptical William Thomson arrived at the waterfall to conduct an experiment. You could see why James Joule found the waterfall intriguing. The water does not drop simply from a cliff, but tumbles off rocks and edges as it cascades down the mountain side, and all this energy as the water falls adds heat, such that as James Joule explained to the skeptical William Thomson, the temperature of the water at the bottom of the waterfall will be warmer than the water at the top of the waterfall. Taking his most trusted thermometer, he measured the temperature of the bottom pool of water, and hiked up to the top of the waterfall to measure the top pool of water. The spray of the water resulted in different values. Wet and trying not to fall in the water, James Joule was comically doing all he could to convince the skeptical William Thomson, but the values varied too much to tell for certain. Nevertheless, the two men became lasting friends, and a few years later, when Amelia died during child birth, and he lost his only infant daughter a few days later, James Joule retreated from society, but kept up his correspondence with William Thomson.

The experience at Cascade de Sallanches had a major impact on William Thomson. Watching the tumbling waterfall, he envisioned the tiny particles of water becoming excited, vibrating with this energy, as they bounced down the slope. He envisioned heat as vibrational energy inside molecules, and with increased heat, the water would turn to steam, and float away as excited particles of gas, and if cooled would freeze into a solid, as the vibrational energy decreased. He imagined a theoretical limit to temperature, a point so cold, that you could go no colder, where no energy, no heat existed, an absolute zero temperature.

Absolute Zero, and the Kelvin Scale of Temperature

William Thomson returned to the University of Glasgow, a young brash professor, intrigued with this idea, of an absolute zero temperature. A temperature so cold, that all the vibrational energy of matter would be absent. What would happen if something was cooled to this temperature, with the help of James Joule, he calculated that this temperature would be −273.15° Celsius. Matter could not be cooled lower than this temperature. In the many years of his research and teaching, William Thomson invented many new contraptions, famously helped to lay the first transatlantic telegraph line, and was made a noble, taking on the name Lord Kelvin, after the river that ran through his home near the University of Glasgow. Today, scientist use his temperature of −273.15° Celsius, as equal to 0° Kelvin, a unit of measurement that describes the temperature above absolute zero. Kelvins are often used among scientists, over Celsius (which is defined with 0° Celsius as the freezing point of water), because it defines the freezing point of all matter. Furthermore, Lord Kelvin postulated that the universe was like a cup of tea, left undrunk, slowly cooling down toward this absolute coldest temperature.

Scientists have since cooled substances down to the very brink of this super low temperature (the current record is 1 x 10⁻¹⁰° Kelvin, with larger refrigerated spaces achieving temperatures as low as 0.006° Kelvin). At these low temperatures, scientists have observed some unusual activity, including the presence of Bose–Einstein condensate, superconductivity and superfluidity. However, scientists still detect a tiny amount of vibrational energy in atoms at this cold temperature, a vibrational energy that holds the atoms together called zero-point energy, which had been predicted previously. The background temperature of the universe is around 2.73° Kelvin, which is heated slightly above absolute zero, such that in the coldest portions of outer space the temperature is still a few degrees above absolute zero.

Using this scale, your own solar system ranges from a high of 735° Kelvin on the surface of Venus to a low of 33° Kelvin on the surface of Pluto. The Earth ranges from 185° to 331° Kelvin, but mostly hovers around the average temperature of 288° Kelvin. Earth’s Moon varies more widely, with its thin atmosphere between 100° to 400° Kelvin, making its surface both colder and hotter than the extreme temperatures measured on Earth.

Potential Energy

Winters in Edinburgh, Scotland, are cold and damp. Forests were of limited supply in the low lands of Scotland, such that many of the city’s occupants in the early 1800s turned to coal to heat their homes. Burned in their fireplace, the coal provided a method to heat homes, but it had to be shipped into the city from England or Germany. The demand for coal was growing, as the city grew in population. A group of investors suggested bringing in local coal from the south. They constructed a trackway for which horse drawn carts could be used to carry heavy loads of coal into the city. However near the city was a steep incline, too steep for horses to pull up the heavy loads of coal. In was along this passage of track, that two large steam engines were purchased to pull the carts up this incline. Each steam engine was fed a supply of coal to burn in its furnace, heating water in a boiler, which turned to steam. The steam could be opened into a cylinder which would slide back and forth transferring heat into mechanical energy. The cylinder would turn a pully, and pull the carts of coal up the incline into the city. As young boy, whose father managed the transport of coal into the city, William Rankine was fascinated with the power of these large steam engines. Soon the horses where replaced by the new technology of steam locomotives, which chugged along with the power of burning coal. Rides were offered to passengers, and soon the rail line meant to transport coal, became a popular way for people to travel. William Rankine studied Engineering, and became the top scientist in the emerging field of steam power, and the building and operation of steam locomotives. In 1850, he published the definitive book on the subject, but his greatest work was likely a publication in 1853 in which he described the transfer of energy.

James Joule had shown that motion could be transformed into heat, while the study of steam locomotives had demonstrated to William Rankine that heat could be transformed into motion. Rankine fully endorsed Joule’s idea of the conservation of energy, but he realized something unique was happening when energy was being transferred in a steam locomotive. First the water was heated using the fire from burning coal, this boiling water produced steam, but the engineer of the locomotive could capture this energy, holding it until the valve was open, and the steam locomotive begin to move. Rankine called this captured energy, Potential Energy.

A classic example of potential energy is when a ball is rolled up an incline. At the top of the incline the ball has gained potential energy. It could be held there forever, but at some point, the ball will release that energy and roll back down the incline, producing Kinetic Energy. In likewise fashion, a spring in a watch could be wound tight, storing potential energy, while the once the spring is sprung, the watch will exhibit kinetic energy, as the hands on its face move recording time. A battery powering a tablet computer is potential energy stored when charged, but once used for watching Netflix videos, its kinetic energy is released. The energy it took to store the potential energy is equal to the energy that was released as kinetic energy.

Rankine called kinetic energy, actual energy, since it did actual work. In his famous paper in 1853 he simply states,

“actual energy is a measurable, transferable, and transformable affection of a substance, the presence of which causes the substance to tend to change its state in one or more respects; by the occurrence of which changes, actual energy disappears, and is replaced by potential energy, which is measured by the amount of a change in the condition of a substance, and that of the tendency or force whereby that change is produced (or, what is the same thing, of the resistance overcome in producing it), taken jointly. If the change whereby potential energy has been developed be exactly reversed, then as the potential energy disappears, the actual energy which had previously disappeared is reproduced.”

To summarize William Rankine, the amount of energy that you put into a device is the same amount of energy that comes out of the device, even if there is a delay between the storage of the potential energy and the release of the kinetic energy.

Furthermore, Rankine went on to state that “The law of the conservation of energy is already known, viz: that the sum of the actual and potential energies in the universe is unchangeable.” It was a profound statement, but one also uttered by James Joule, that energy in the universe is finite, a set amount. Energy cannot be spontaneously created or spontaneously removed, it only moves from one state to another, alternating between potential and kinetic energy. The power to move the steam locomotives was due to the release of potential energy stored in buried coal, the coal was produced by ancient plants, which stored potential energy from the energy of the sun. Each step in the transfer of energy was a pathway back to an original source of the energy within the universe— energy just did not come from nothing. Such scientific laws or rules were verified by years of failed attempts to make perpetual motion machines. Machines that continued to work, without a source of energy are impossible.

Einstein’s Addendum

However, this scientific law or rule that energy cannot be spontaneously created was proven incorrect in 1905 by Albert Einstein, who first proposed that E=m⋅c². The total amount of energy (E) is equal to the total amount of mass (m), multiplied by the speed of light (c) squared. If you could change the amount of mass, it would produce a large amount of energy. This equation would go on to demonstrate a new source of energy—nuclear energy—in which mass is reduced or gained, and results in the spontaneous release of energy. This scientific rule or law called the Law of the Conservation of Energy, had to be modified to state that in an isolated system with constant mass, energy cannot be created or destroyed. The study of energy transfer became known as Thermodynamics, thermo- for study of heat, and dynamics- for study of motion.

Entropy and Noether’s Theorem

Using the law of the conservation of energy, engineers imagined a theoretical device that alternated energy between potential energy and kinetic energy with zero loss of energy due to heat. In physics this is referred to as Symmetry. Energy put into a system is the same amount of energy that is retrieved from a system. Yet, experiment after experiment failed to show this, there appeared to always be a tiny loss of energy when energy went between states. This tiny loss of energy is called Entropy. Entropy is a thermodynamic quantity representing the unavailability of a system's thermal energy for conversion into mechanical work, often interpreted as the degree of disorder or randomness in the system. In the world of William Rankine, entropy was the loss of energy through heat, which prevented any system from being purely symmetrical between states of energy exchange. Entropy is the loss of energy over time which increases disorder in a system. However, the law of the conservation of energy forbid the destruction of energy. Einstein’s discovery that changes in mass can unlock spontaneous energy suggested that there might exist changes that unlock the spontaneous destruction of energy.

In 1915, at the University of Göttingen two professors were struggling to reconcile the Law of the Conservation of Energy and Einstein’s new Theory of Relativity, when they invited one of the most brilliant mathematicians to help them out. Her name was Emmy Noether. Emmy was the daughter of a math professor at the nearby University of Erlangen, and had taken his place in teaching, although as a woman she was not paid for her lessons to the students. She was a popular, and somewhat eccentric teacher, who students either adored, or were baffled by. When shown the problem, she realized that Law of the Conservation of Energy, described a symmetrical relationship between potential energy and kinetic energy, and could be reconciled with special relativity through an advance algebra technique called symmetry-flipping two math equations when they result in an identical, but symmetrical relationship. It would be like looking at a mirror to describe what exists in a room reflected in the mirror. It was a brilliant understanding, and resulted in a profound insight into the conservation of energy, which directly led to the birth of today’s quantum physics.

The important implications of Noether’s Theorem for you to understand is that Entropy is directly related to a system’s velocity and time. Energy is lost in the system due to the system’s net velocity in the universe or likewise time that has passed during that conversion of energy. Here on Earth, the motion of the Earth, which is measured either in time or velocity is the reason for the loss of that tiny amount of energy during the conversion between potential and kinetic energy. This insight is fascinating when you consider systems of energy traveling at the speed of light. Approaching the speed of light, time slows down until it stops, at which point the transformation of potential and kinetic energy is purely symmetrical, such that there is no entropy. Such insight, suggests that light, itself a form of energy, does not observe any entropy (heat loss), as long as it is traveling at the speed of light. Of course, light can slow as it hits any resistance such as gas particles in the Earth’s atmosphere, or solid matter such as your face on a sunny day. At this point, heat is released. Light traveling at the speed of light through the near vacuum of outer space, can travel at incredible far distances from galaxies on the other side of the universe to your eye on a dark starry night. It is because of this deep insight into Emmy Noether’s mathematically equations, that we can explain entropy, in the notion of time and velocity, as observed here on planet Earth.

The Four Laws of Thermodynamics

You can summarize what you have learned about the nature of energy and energy exchange into four rules, or laws of thermodynamics.

Law 0: If two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other. This basically states that we can use thermometers to measure energy as heat, when they are brought in equilibrium within a system.
Law 1: Law of the Conservation of Energy, which states that in an isolated system with constant mass, energy cannot be created or destroyed.
Law 2: The Law of Entropy, for energy in an isolated system traveling less than the speed of light, when there is an energy transfer between potential and kinetic energy there will be a slight loss of the availability of energy applied to a subsequent transfer due to the system’s velocity or time difference. Hence systems will become more disordered and chaotic over time.
Law 3: The Law of Absolute Zero: As the temperature of a system approaches absolute zero (−273.15°C, 0° K), then the value of the entropy approaches a minimum.

Energy usage has become more critical in the modern age, as society has invented new devices that convert energy into work, whether it is in the form of heat (to change the temperature of your home), motion (to transport you to school in a car), or electricity (to display these words on a computer), as well as the storage of energy as potential energy for later usage (such as charging your cellphone to later text your friends this evening). The laws of thermodynamics define how energy is moved between states, and how energy systems become more disorder through time by entropy.

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