9: The Energy

Figure 9.1
energy and an isentropic set

Now our prototypical biological cell has closed its entry orifice, we need to handle the situation it is facing with care. It is important we carefully distinguish the mechanical chemical energy we have just used to increase the internal energy by taking on a specific number of moles of chemical components from the nonmechanical chemical energy that the entity is about to absorb through its entry aperture in Stage II. It further increases its internal energy so that it can manipulate those same components.

Since this situation is fraught with difficulty, we first need to note very carefully what is happening to the piston in Figure 9.1, so that we can carefully distinguish the mechanical chemical energy entering through the entry orifice from the nonmechanical chemical variety, entering through the aperture, that our entity is about to use. Both contribute to the cell and the surrounding population's total stock of internal energy.

We need to prepare ourselves to deal with memes, information, and the various modes of vibration available to our biological entities. We can then return to dealing with their trajectory through the circulation of the generations.

First, we notice the rock and the earth. That rock focuses our attention on the mass aspect of the chemical components we have just taken on, and clarifies the nature and properties of the strictly mechanical chemical energy aspect we have just exploited.

Sir Isaac Newton changed the world by proving that all material objects attract each other with a force that is proportional to their masses, m, and inversely proportional to the square of the distance between them, 1/r2. This is a gravitational form of energy we can measure through his inverse square law … and it is also strictly mechanical. That does not mean other aspects are irrelevant. It simply means we can hold them in abeyance.

The rock in Figure 9.1 is ready to fall down to the earth under gravitational attraction. That is its potential. Those two bodies—i.e. the rock and the earth—therefore follow the laws of planetary motion. Although this does not yet say anything about the nonmechanical chemical behaviours and modes of vibration our biological entity is about to use, nothing in this universe can happen without those laws of planetary motion. There is no energy—whether it be mechanical or non-mechanical—without them. Biological entities certainly use both those types, but it is important to recognize the distinction between them, and so their very different ways of contributing to internal energy, or we will never unmask evolution.

We now look at the piston or system on the left hand side of Figure 9.1. Its walls are ‘adiabatic’, i.e. they are impervious to heat, a word taken from the Ancient Greek a- for ‘not’ and diabatos for ‘passable’ or ‘crossable’,

The volume of the gas in our adiabatic vessel is at its largest possible value. That entire volume is being utilized as the gas contained in it diffuses throughout the entire extent. The system's temperature is also low. All the molecules are interacting equally with each other in each unit of time throughout the available space. None are being favoured. The piston's entropy is therefore at the largest possible value. It is as much like the surroundings as possible.

If we now pick up the big rock and place it on top of our piston, we create the situation on the right. Since our piston's walls are adiabatic, then the entirety of the mechanical energy the rock creates as it seeks to fall down under gravity has two immediate consequences: (a) we compress the gas and reduce its volume; and (b) we increase its temperature. And when we increase the temperature, we are also increasing the quantity of nonmechanical chemical energy inside the system. The molecules vibrate more quickly which is a thermal form of energy, and an addition to the internal energy. (We of course also (c) increase its pressure. We shall consider pressure and its nonmechanical consequences later, as well as the volume changes it causes. For now, we focus on the mechanical source of the various effects).

Placing that rock on the piston produces two contrasting effects. FIRSTLY: whenever something confines itself to a restricted subset of its available possibilities, potentials, or available volume, then its entropy has decreased. It has become less like the surroundings. Therefore, putting a rock on our gas inside our perfectly adiabatic (no-heat-shall-be-lost) piston decreases its entropy.

HOWEVER, the gas in our piston has also increased its temperature as its molecules increase their vibrations, which is again to increase in its nonmechanical energy. The molecules are not just under pressure, they are moving around more quickly. They are colliding with each other an increased number of times per second, which is to increase their temperature. They collide with greater energy, more frequently, internally interacting a greater number of times in each possible moment. In this case, that is the form of internal energy known as thermal energy. This increase in nonmechanical energy they have experienced, because of the rock bearing down on them mechanically, also increases their entropy. But since the walls are adabiatic, there is no heat because there is no passage out to the surroundings.

In this specific case, therefore, the amount by which the entropy decreases because the volume has decreased exactly matches the amount by which the entropy increases because the temperature has increased. Since these two exactly match each other, the system's entropy stays exactly the same as it increases in its internal energy and switches between the mechanical and nonmechanical forms of energy. And as long as no heat passes across those walls, then although these two states in the diagram at first sight appear very different, they are in other ways the same (“things that are equal to the same thing are also equal to each other”). They belong to the same ‘isentropic set’.

This system's entropy may have stayed the same, but it has still undergone a very important change in state. This change is that it has become compressed, and its nonmechanical energy stock has increased, along with its internal energy. Something has therefore changed. And what has changed is that the system's total energy stock has increased by the exact amount of planetary motion imposed through the work being done by the rock, as it follows the laws of planetary motion and presses down under gravity.

We have successfully converted the entirety of the mechanical and gravitational energy that the rock makes available, by insistently falling, into a given stock of internal and nonmechanical energy expressed in a thermal form that we have successfully captured inside the system. We have captured it as the increase in molecular motion. This is the microscopic and quantum expression of the events taking place outside it in the rock and the planet. Those external laws are Newton's three laws of motion.

The net consequence is that we have successfully converted some macroscopic and gravitational–planetary mechanical energy of motion into the microscopic internal and now thermal form of energy as a microscopic motion, while leaving the entropy both (a) in the system, and (b) throughout the universe the same (at least ... as long as those walls do not manifest an iota of heat, which is in practice impossible!).

This is how the Greek physicist and mathematician Constantin Carathéodory helped to define energy. Energy is the substance that enters into an (admittedly imaginary) adiabatic or non-heat-losing system when it receives an input of mechanical work, with that work being the movement of a mass through a given height in a given gravitational field, and so being a consequence of planetary motion, converting from macroscopic to microscopic, and as internal energy.

But by the first law of thermodynamics, we could in fact have used any process whatever to move that piston down, and the result would have been just the same. We would have got exactly the same increase in internal energy. We could for example have used a magnet, an electric motor, or a diesel engine instead of a rock (or let a mechanical model lion chase down a mechanical model lamb) and it would have made no difference to the end result in our piston, for this is the interconvertibility of energy. In the diagram, it is a conversion between the mechanical and the thermal, the latter being a form of nonmechanical energy expressed as the increased vibrations of molecules. But it is still how all possible energy is defined and quantified. It is how we know what energy is; and how we know what it can do. Every stock of nonmechanical energy is equivalent to some stock of the mechanical variety, with the nonmechanical variety not generally being visible, because it induces internal changes in state as changes in internal energy. The mechanical variety of energy tends to induce external changes in state.

A mathematical aside

Carathéodory's definition states: “An extensive property exists whose increment is the work received by a system while surrounded by an adiabatic wall”. That extensive property is, of course, energy.

And since we have here the conversion of a given quantity of mechanical energy or work, δW, into a specific quantity of heat, δQ, through a specified transformation within the system, dU … then the quantity of heat engendered between the system and the surroundings is equal to both that change in state and the distance that piston moves, because of that weight, for that work done. Although it involves and implies the laws of planetary motion, this is known as the first law of thermodynamics: δQ = dU + δW.

If the piston in our system in Figure 9.1 is truly adiabatic and moves perfectly, then it is possible to remove the rock and allow the system to return to its original state. It will lose in its internal energy and its temperature will fall back to the original. It will increase its volume and decrease its pressure. And once it is back in its original state, we can put the rock straight back onto it again, recompress that piston, and once again increase its internal energy. We can now go back and forth and do this time and again, all without loss. We will always do exactly the same amount of work involving the same quantity of mechanical energy; and we will always get the same amount of nonmechanical heat energy. It is always fully interconvertible. The most important aspect is that we do something outside the system to increase the internal energy, and can then also extract that increased internal energy for use elsewhere, transferring between the mechanical and nonmechanical through various complementary and complementing changes in state. Work is the transfer between different forms of energy, while heat is the specific transfer of internal enery from a higher to a lower temperature.

Figure 9.2
energy and a rocket

The realization that the microscopic world is very different from the macroscopic one (i.e. quantum physics) is one of the so-called twin pillars of modern, as against “classical”, science (the other being relativity). Figure 9.2 now introduces some microscopically based nonmechanical chemical energy, along with some of the consequences of the changes in pressure and in volume that that nonmechanical energy tends to cause, and that biological entities exploit. Those resulting pressure-volume effects from arise from the microscopic interactions of internal energy, and tend to be mechanical when observed macroscopically.

The valve in Figure 9.2 is initially closed. The gas is initially compressed. It is in a low entropy state. When, as in the middle, the valve is opened, the volume immediately increases and the pressure decreases. Since, however, the far end is closed, there is no mechanical effect from those changes. There is no external change in state. Therefore, the potential rocket does not move. That nonmechanical chemical energy contained in those molecules, and in their ability to expand, has not yet been converted into mechanical form. The internal energy remains the same, but the entropy increases because the valve has been opened.

Gases have a natural tendency to transform. This is also a notable characteristic of biological organisms, and it is what entropy measures.

Rockets exploit the nonmechanical chemical potential that gases and fuels contain. Gases and fuels express their transformation potential, which is their entropy, by spontaneously expanding. If we now open the far end, the gas has an indefinite volume into which it can transform itself and expand. The rocket can now move by actualizing the gas's pressure and indefinite expansion potentials. The molecules implicitly follow those same laws of planateray motion, but expressed in quantum and probability terms. They exit the rear; propel themselves outwards as an exhaust; and the rocket exploits their implied momentum to carry itself forwards macroscopically and mechanically. The mechanical work the rocket is now doing is again exactly equivalent to the nonmechanical chemical reactions from the gas now acting as the fuel. The changes in pressure and in volume that the gas goes through convert the fuel's microscopic and nonmechanical chemical potential into the macroscopic and mechanical energy of the moving rocket. The pressure and volume changes that the molecules create by undertaking a set of microscopic transformations are again equivalent to a macroscopic mechanical effect … and all in accordance with the energies of the laws of planetary motion that they implicitly obey, but in their quantum probability and microscopic manner. The entire chemical change in state, which is the nonmechanical chemical energy, is the increase in entropy. It creates the indefinite expansion in volume which is then converted into the thrust of mechanical energy. And since the temperature outside the rocket is lower, there is also a heat effect as the temperature falls. The same microscopic to macroscopic principles hold for electrical and other forms of nonmechanical energy, all of which are various modes of vibration for the microscopic particles concerned.

And now that we understand how to convert energy from one form to another, and how to absorb it into a system whilst still leaving its entropy exactly the same, we are ready to see our prototypical cell open its entry aperture and enter the next stage of its biological cycle. It is of course going to convert the nonmechanical energy contained in the incoming solar radiation pressure emitted by the sun into the internal nonmechanical chemical energy it requires to survive and reproduce. It is going to undertake some extremely important internal changes in state and reconfigurations, courtesy of the implied laws of planetary motion.