Rajesh Kumar

Optimizing life, one day after the next

A Simplistic Model for Energy - Part I

29 Mar 2006

In response to my friend, Tewodros Mamo's question, what is energy?

You know it. I know it. Everything in engineering and science is a model. We have models because nothing in this universe of ours can be proved absolutely. Not even the fundamental laws of nature, fundamental as they may be. What was thought to be fundamental—the three basic laws of thermodynamics—even those break down miraculously when we go down to the pico scale.

Take molecular diffusion for instance. The current theories we have today for osmosis and diffusion of ideal gases are still again, only models. Never provable in any number of finite steps. The truth is that diffusion is nothing but nature's model for a perpetual motion machine of the second kind. It is nature's manifestation of energy. Today, we term this energy as kinetic energy: a wholesome sum of a molecule's vibrational, rotational and sway energies. But kinetic energy is once again the mean of the Boltzmann's distribution, given by

$$\overline{K.E.} = \frac{3}{2}kT$$

But it does not stop there. The variable $$T$$ is absolute temperature on the Kelvin scale. High school teaches us that temperature is related to, but not the same as heat. But heat is the flow of thermal energy. There we go. The energy term again. No matter what we try to do, we end up with this bad boy term: e for energy.

It therefore only sounds reasonable to model our definition of energy around the following commonly observable manifestations:

Let's take the arguably simple example of an organic semiconductor embedded in an integrated photonic circuit with the aid of transport and carrier proteins. For the electron to have enough energy to traverse the circuital loop, it requires energy. And where does it get this energy from? Simple. From the ATP contained within the organic selenide crystal.

We are now at a stage where we can discuss energy, not as a mathematical abstraction, but as a more theoretical idea that provides us with a lucid framework that will allow us to summarize all of mechanics, both classical and quantum, in a very beautiful manner.

We have all been taught, at some point or the other, the quintessential definition for energy. I can still recall my Grade 7 science teacher, Mrs. Suma, going: "energy is the ability to do work." Yawn. What a boring definition. Not only is it boring, but wrong too! Work precedes energy and not vice versa. People never could imagine the concept of energy; only changes, or deltas, or differentials, whatever you want to call it. People then came to relate this change in energy to be equal to the amount of work done.

$$W = \Delta{}E = \int{F \cdot{} ds}$$

I can spend all day pushing against a brick wall and still perform no theoretical work, as no displacement is achieved. But energy I have expended nonetheless, which is quite evident from the copious amounts of sweat produced by my body. What does this tell us? The answer is exceedingly simple.

Energy is a function. Not any function, but a state function.

That's true. It doesn't matter how the energy got there. Or why it got there. Or where it came from. All that matters to the pragmatic engineer is that it's there. I can add to it, subtract from it, and do all sorts of arithmetic with it, without even knowing what the heck it is. James Watt engineered the first steam engine even though he wrongly imagined heat to be a fluid-like substance, then called the caloric, to flow spontaneously from a hot object to a cold object as dictated by the second law of classical thermodynamics. He didn't have to know what energy was, he didn't have to know how heat was transferred, or what the medium was, or anything for that matter. All he had to know was that when a hot body was placed in thermal contact with an other cold body, the colder object became hotter and the hotter object became colder. Period. That was the end. And the steam engine was invented.

In lecture yesterday, we were taught that energy can also be visualized as a vector, the poynting vector, moving as an electromagnetic wave in 3-dimensional space. That is

$$\underline{S} = \underline{E} \times \underline{H}$$

where S, H and E are energy, electric field and magnetic flux density vectors respectively. The cross-product yields a vector that is neither in the direction of E nor H, but is perpendicular to both.

Now, this offers an interesting perspective on the whole notion of energy. The very fact that energy can be a called a vector tells us something about its intrinsic properties.

to be continued…

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