S1C6: Concept and forms of energy

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a) Essence and role of energy

In the very first chapter of this series, we explored the atomic depths and discussed the various particles discovered so far by scientists such as the electron, the neutron, the proton as well as those labelled elementary like the quarks and various types of bosons, the mediators of some of the four fundamental interactions identified to date: electromagnetism, gravity, the weak interaction, and the strong interaction. Together, these particles combine to form atoms and, in turn, still on the back of the fundamental interactions, these can aggregate into larger compounds called molecules. This ever more elaborate construction doesn’t stop there and the molecules are still subject to interactions, mostly electromagnetism driven by the concentration, location and movement of electrons, and these drive the attraction and reactions between molecules and the various macromolecules they can combine into.

Some of those compounds may happen to have useful properties or functions and, thanks to the safe storage and timely utilisation of information, they can start acting in a coordinated manner to form complex organisms – all this unconsciously of course. On the back of Part A spanning Chapter 1 to 5, we now understand the role of information and the nature of the various building blocks, but there is still plenty we need to look into and make sense of. In particular, what is the principle that drives the assembly of atoms into a molecule, explain what chemical elements will react or not and how organisms are powered. All this falls under the topic of energy and this will be the subject matter of this Part B. In this Chapter 6, I will start by focusing on a description of the different classes and form of energy.

Before getting underway, it will prove useful to attempt a definition of energy, one that is not circular! Dictionaries generally define energy as the capacity to do what is called work in physics, such as the application of a force on an object to move it. This is however an application-centric description, as if we had invented energy to serve our own purpose. In a similar manner, the various forthcoming types and classes of energy we will be discussing in this Part B are really handy human abstractions, ways of thinking through, making sense of phenomena, and computing expected outcomes. So far, just like scientists, I have failed to express the true nature of energy into a sharp, well phrased notion. Nonetheless, what I can affirm is what energy isn’t and fuel, a substance we burn through and deplete, probably tops the list. We will go into this when exploring the concepts of energy conservation and transfers.

b) Kinetic and potential energies

Energy can be thought of in terms of two different classes: potential and kinetic. To make sense of those, the concepts of system, position and motion need to be introduced and defined. In physics, a system is a set of objects with a physical relationship between them. Everything outside of the system is called the environment and an isolated system has little or no interaction with its environment. Think of the solar system, it is the collection of the sun, its orbiting planets, the satellites of those planets and other smaller objects like asteroids and comets. Ignoring the gravitational pull of other systems in the galaxies (and of other galaxies to a lesser degree), the system can be studied in isolation. Likewise, a basketball bouncing on the floor can be thought of as a system that includes the ball, the floor made of a specific material, and perhaps even the atmosphere in between them.

A position is a location in space. In a given frame of reference with an agreed upon origin, an object’s position can be expressed by a set of coordinates – three of them in a three-dimensional space, while its direction is expressed as a function of the angle between the reference point and the position. I take this opportunity to expand a little on the notion of frame of reference since it will be used repeatedly over the next few chapters. In physics, it boils down to three different parameters: the first is the origin, the centre of reference if you will, the second is scale though this only really matters for the purpose of taking measurements, and the third is the specification of axes so that one can orientate himself and pinpoint any location based on a given set of coordinates. When we think of the entire planet Earth and discuss distances separating two cars at rest then we are dealing with an inertial frame of reference because the distance between those cars doesn’t change unless one of them, or both, are being moved. Same thing when we sit at a coffee table with a friend. However, if your friend gets in one of the cars and drives it away then there are two ways to describe what is happening depending on the selected frame of reference. From your perspective, as an observer using the Earth coordinate system, he and the car are moving. From his perspective, using the car as a frame of reference, he is not moving but the rest of the planet is. This car + friend system still qualifies as an inertial frame of reference because it is moving uniformly and whatever happens within, such as the swatting away of a fly, could be described in relation with the system and as coordinates or motion within that system.

As for motion, it is the change in the object’s position between instant T0 and instant T1 . An object without motion is said to be at rest or stationary but, as I just alluded to, those terms only apply to the frame of reference being considered. So if you are sitting on your chair reading this you could be said to be stationary on planet Earth although you are hurtling through space around the sun and the solar system is itself orbiting the Milky Way galaxy so your stationariness is very relative.

Having introduced those terms, it is now fairly easy to describe kinetic and potential energies. The former is the energy embedded in an object due to its motion, so it is a function of the force applied to it and the displacement, i.e. an expression of work. Remember though that motion is a relative concept and depends on the frame of reference, and so is acceleration and the quantum of kinetic energy of an object.

In the same manner, potential energy is also relative. It is the energy an object holds on account of its position within the system. If we take the basketball and floor example, the further the ball is from the ground, the higher its potential energy, in this case potential gravitational energy to be precise. Which brings us to the various forms of energy.

c) The forms of energy

Energy doesn’t come in different shapes and sizes, that is for objects, but in our intellectual armoury it comes in different classes and form. I am listing the main forms below and will describe them in detail in Chapters 7 to 10. If you are interested in further exploration, the Wikipedia entry for energy lists a few more and I have enclosed the link in the final section of this chapter.

Nuclear energy is a result of the strong interaction between protons and neutrons, together called “nucleons”, the subatomic particles forming the nucleus of the atoms. The term is generally used as a byword for nuclear binding energy, the minimum amount of energy required to split the nucleus into its constitutive nucleons, though in theory it should also be extended to include nuclear potential energy, a function of the potential energy of the particles and therefore of their position with respect to one another.
Chemical energy is somewhat conceptually analogous to nuclear energy for it represents the differential in energy involved in the various chemical bonds, such as covalent bonds (refer to Section 2.b for details), before and after a chemical reaction. Since a chemical reaction involves the transformation of one set of chemical substances into another, we can add up the energy tied in chemical bonds before the reaction and subtract from it the potential chemical energy of the resulting substances to compute the chemical energy released or required by the reaction.
Electric energy is, in comparison, quite different from the preceding two in the sense that it isn’t embedded directly in the position or motion of electrically charged particles. Instead, it is the result of the motion of those charged particles, a measure of the work they are able to accomplish during a given period of time.
Magnetic energy might be the most difficult to define succinctly without having explained the nature of a magnetic field and the type of force it exerts on magnetic objects. So, for the time being, we will have to bookmark this and simply state that it is the energy stored in a magnetic field, which is created by the motion of electrically charged particles.
Mechanical energy is not another form of energy, it is the sum of the kinetic and potential energies of a given system, which obviously betrays the interplay between motion and position. This concept has been introduced to discuss and reason about the capacity to do work so one should think about it more as a framework.
Radiant energy is energy travelling away from the source in the form of photons or waves. Its nature can be electromagnetic, as is the case in light, or gravitational. Electromagnetic waves are essentially a coupling of electric and magnetic fields travelling outward.
Thermal energy relates to the motion of particles within a system, using that system as a frame of reference and therefore adjusting for its own motion. In a stationary system, this would be equivalent to the particle’s kinetic energy. The concept of thermal energy is closely related to thermal radiation and heat, these will be covered in Section 9.c.
Gravitational energy is the energy embedded by an object’s position in a gravitational field and is the direct result of gravity as one of the fundamental interactions. It is gravity’s very own potential energy. However, as we will see in Section 10.a there is an alternative way to think about gravity that challenges its description as a force and consequently the very notion of gravitational field and energy.

This is a decent primer I think, just enough content to wet our appetite for the next chapters and to notice very clearly that energy is fungible. The form it is said to take reflects the way in which it is exerted or measured and does not necessarily suggest there are energies of a fundamentally different nature.

d) Energy conservation and transfer

Fungibility between forms of energy, transfer of energy within systems and between systems. This could appear confusing at first blush, yet in reality this is the exact opposite as long as we think of energy as a conserved quantity in an isolated system: it can be converted from one form into another, but neither can it be created nor can it be destroyed. This is the law of conservation of energy.

Let’s see how this works with our basketball. At instant T0, before we release the ball, in the ball-floor system the ball has no motion and therefore no kinetic energy, however it does have a relatively high potential energy due to its position away from the floor. This potential energy stems from the Earth’s gravitational field and if this field did not exist then the ball would have no gravitational potential energy and would not drop towards the ground unless pushed in that direction, or phrased in technical terms: unless work was applied to it in the form of mechanical energy. After a short moment, at instant T1, the ball has acquired momentum and therefore kinetic energy in an amount exactly equal to the loss in potential energy due to the reduction in the distance between the ball and the floor.

Before continuing on the description, it is important to introduce and define two technical terms with a very precise meaning in physics, especially as those terms are occasionally used in a much more flexible sense in everyday life. The first of those terms is momentum, it is the product of the mass and velocity of an object. The second is velocity, which is different from speed because it also captures the idea of direction or angle. Since multiplication is associative, momentum also embeds a directional aspect, which makes it a vector quantity. The formula for this is p = mv where v is the velocity, m the mass and p the momentum. Mass is expressed in kilogram (kg), velocity in metre per second (m/s) and momentum is therefore stated in kilogram metre per second (kg.m/s).

Back to our basketball. Shortly after impact, at instant T2 when the ball reaches its maximum deformation, the ball’s motion has stopped and its kinetic energy has been completely transferred to the floor material in the form of potential elastic energy. In the microseconds that follow, this potential energy will be transferred back as kinetic energy into the ball that will speed upward and slowly lose that kinetic energy as it gains height and increases its potential gravitational energy.

If the ball and floor were a perfectly isolated system then the bouncing would go on forever with the ball reaching the same position at the top of every bounce. However, this idealized system ignores the effect of the ball-floor environment, namely the friction of air and the heating of the floor at the time of impact; both of those entail a leaking or transfer of energy away from the ball-floor system.

From what we have learned thus far in this chapter, it is much easier to understand Newton’s laws of motion, first stated in his landmark work Philosophiæ Naturalis Principia Mathematica originally published in 1687. Let’s be clear, these laws were truly insightful for the time and not self-evident by any means since, from empirical evidence alone, all objects eventually come to rest. We now understand the explanation is of course because isolated systems are generally idealized ones used for computation purpose and theorizing, not real-life ones, unless you are in space. Friction, heat generation and gravity all cause the loss of momentum of an object, affecting its inertia – a concept first formulated by Galileo but essentially defined in Newton’s first law of motion.

This law states that unless a force is applied to it, a body at rest will remain at rest and if it is moving at a certain speed in a particular direction, its velocity will remain identical. So, what does this first law of motion really mean? If we think of one body as a simplified isolated system called System 1 consisting only of itself and as a point-like object acting as the origin in its own frame then, in that frame of reference, this body is at rest and has neither potential nor kinetic energy so the total energy of this isolated system is nil. It will remain so unless energy is being transferred into that system via the application of an external force. As long as this does not happen, within the context of its frame of reference, the energy of our isolated system will remain nil so it will not move. However, if an observer is at rest in a second system called System 2 which is moving in relation with System 1, then this observer will maintain her momentum as per her System 2 frame of reference, and it is the body in System 1 that will appear to be moving in a straight line. The classical illustration is a passenger in a train station who feels that the station is moving past the train, always a puzzling sensation. The important consequence of this law is that motion and rest are relative rather than absolute concepts.

The second law of motion quantifies the momentum of a body as the product of its mass and its velocity, with the formula p = mv as mentioned a few paragraphs prior. When rearranged, this yields the famous formula F = m.a where F is the net force, “a” is the acceleration and “m” is the mass. Note that acceleration is the derivative of speed with respect to time, i.e. it is the function representing the change in speed. And since speed is the rate of change of position with respect to time then acceleration is the second derivative of position with respect to time. On a graph representing speed on the y axis and time on the x axis, speed is the slope and acceleration is the curvature of the slope. A horizontal flat line means constant speed and no acceleration, a straight diagonal line means increasing or decreasing speed but no acceleration and a curved line implies both change in speed and acceleration or deceleration (which is the name for negative acceleration). In a body at rest in its own system, if no force is applied to a body with non-zero mass, then we have m*a = 0 which implies a = 0 and ties in with the first law because the speed remains constant (and that includes the scenario of being at rest).

The third law is possibly the catchiest-sounding of the three: for every action, there is an equal and opposite reaction. This is why forces are also called interactions and, like relative motion, force is relative depending on which side you are on. If we think of two objects interacting – say my hand pushing on a wall without it moving, then the hand-wall system is at rest, which suggests there is no net force being applied to this system. Since we know the hand is pushing the wall we therefore need an opposite force of equal magnitude and opposite direction to be applied by the wall to cancel it out, as per the first law.

e) Units of measure

To wrap this chapter up, I thought it might be interesting to list a few units of measure relating to energy. As chance would have it, several of them will come in handy over the next four chapters. Note that SI stands for the International System of Units and was the topic of Section 1.f.

The newton is the SI unit of force and is defined as the amount that will accelerate one kilogram of mass one meter per second squared 1 kg⋅m⋅s^-2. As mentioned in the previous section, F = m.a where “m” is the mass and “a” the acceleration, in adequation with Newton’s second law of motion. Since acceleration is the derivative of speed, which is expressed in m/s or m.s^-1, then the Force “F” is expressed in m.s^-2. No surprise, it is named after Isaac Newton.
The joule is the SI unit of energy and is named after 19th-century physicist James P. Joule. It is defined as the work done by a force of 1 Newton displacing a mass by exactly 1 metre in the direction of that force. There is no need to specify the mass because it is already included in the concept of the force, which here is set at 1 Newton and since the definition says nothing about time then the acceleration value will simply change in inverse proportion to the mass – it will take longer to move a larger mass by one meter when applying a fixed force. The unit is symbolized by the letter J and J = N.m where “N” is the Newton unit; accordingly J is expressed in kg⋅m²⋅s^-2
The watt is the SI unit for the rate of energy transfer, also known as power, and is equal to 1 joule per second (1 kg⋅m²⋅s⁻³). To compute the quantity of energy based on power we simply need to multiply by a time unit and the kilowatt-hour is commonly used by electricity producers to reflect the quantity of energy produced by one kilowatt of power for one hour – you can check this on your utility bill. The unit is named after James Watt, the 18^th century chemist and engineer who improved (but did not quite invent) the steam engine.
Staying with the electrical, the ampere is the unit for electric current, which is a rate of flow, and the coulomb (denoted by the letter “C”) is the formal unit of electric charge defined as the amount of electrical energy delivered by a current of 1 ampere in 1 second. Flipping this around, 1 ampere is 1 coulomb moving through every second. C is set by the International System of Units at the constant value of 1/(1.602176634×10⁻¹⁹) * e with “e” being the electric charge carried by a proton (also known as elementary charge). Andre-Marie Ampere and Charles-Augustin de Coulomb were both physicists.
The volt is the difference in electric potential between two points dissipating one watt of power when the current conducted is equal to one ampere. The way you may want to think about this is as a water pipeline where voltage is the force of the water current (or its pressure), watt would be the quantity of water passing through and the ampere is the rate of flow, which is the surface area of the interior of the pipeline (or for a river it would be the cross-section area represented by its depth and width at the point where it is being measured). Since the volume of water going through is the pressure multiplied by the rate of flow (1W=1V*1A), then the pressure is the quantity of water divided by the rate of flow (1V=1W/1A). In particle physics, energy is often measured in electronvolt (“eV”), defined as the work required to move an electron through an electrical potential difference of one volt (eV = e*V). The volt is named after Alessandro Volta who invented the namesake voltaic battery.
The ohm, represented by the symbol “Ω”, is the SI unit of electrical resistance and is defined as the resistance between two points of a conductor when an electric potential difference equal to 1 volt produces a current of 1 ampere. This can be formulated as Ω = V/A. And if we substitute 1V for 1W.A^-1 then Ω = W.A^-2. Using the water pipe analogy, the resistance inserted in the pipeline multiplied by the rate of flow creates pressure, i.e. Ω*A = V. We do fall on our feet. And Georg Ohm was an early 19^th-century physicist who used some of Volta’s discoveries for his own research.

Clearly, as a scientist, you know you have made it in life when a unit of measure is named after you, though this is traditionally a posthumous badge of honour.

f) Trivia – Heat and power units

Other units used for heat are calories and BTU, short for British Thermal Units. The former is the amount of energy required to increase the temperature of one litre of water by one degree Kelvin or Celsius whereas the latter unit was based on a similar idea but for one pound of water by one degree Fahrenheit.

The maths work out as follows: 1cal = 4.184J and 1 BTU ≃ 1055 J or 252.2 cal.

When it comes to engine outputs, the horsepower is the unit of choice. The imperial horsepower written as “hp” is equal to about 745.7 watts while the metric version abbreviated as “cv” is a tad lower at around 735.5 watts. The term of horsepower originated from James Watt when trying to market his improved steam engine as being much more powerful than draft horses. So yes, in a way, horsepower came from a Mr Horse whereas the word calorie originates from the Latin “calor”, meaning “heat”.