3.4: The First and Second Laws of Thermodynamics

In the chapters to follow we will frequently explain chemical and physical changes by invoking the associated changes in potential energy and we will refine the idea, making it more specific and useful to make predictions concerning the direction of spontaneous changes. Presently, however, we want to put the ideas we have already covered in a larger context. In so doing, we convey one of the bedrock principles in all of science: the First Law of Thermodynamics. While this law can be stated in a variety of ways, the most accessible and useful for our purposes is as follows: energy is conserved; it can be transformed from one form to another, but it is neither created nor destroyed by physical and chemical processes. Often referred to as the Conservation of Energy, this concept can provide a helpful logical framework when analyzing systems undergoing change. In this chapter we have shown several examples of energy conversion, but we have not emphasized the conservative nature of those changes. We do so below, using the example of a  pendulum to describe the reversible change of potential to kinetic energy. 

 

 

 

Figure 3-12. A simple pendulum with its arm directed at an outward angle; if held still in this position, the bob would possess potential but not kinetic energy. Releasing the bob would allow it to fall, causing it to lose potential energy but gain kinetic energy.

 

 

 

 

In your mind’s eye, picture a pendulum that is held motionless such that its arm is not pointing straight down (Figure 3-12). You will recognize that in this state the bob of the pendulum has potential but not kinetic energy. As soon as you release the bob it begins to move, increasing in speed as it moves to the lowest point along its trajectory. As it does so, its potential energy is gradually converted to kinetic energy and, at its lowest point, all of the potential energy that was available to drive its motion is exhausted and the kinetic energy is at a maximum; the bob is moving at its greatest speed. The maximum speed it can attain is limited by the potential energy it had initially; the closer it was to the bottom of its trajectory, the lower will be its maximum speed when it gets there. After it passes the nadir of its path, its speed decreases as kinetic energy is reconverted back to potential energy. When the kinetic energy is eventually exhausted and the potential energy is maximized, the bob stops moving momentarily as it reverses direction, then begins to fall back down along its path, beginning the cycle again. 

The above illustrates the conversion of energy, from potential to kinetic and then back to potential again. Because, in accord with the First Law, energy cannot be destroyed, we would expect that the potential energy attained at the end of this sequence would be exactly the same as it was at the beginning, which is to say, that its height after one cycle will be exactly the same as it was initially. This is clearly an oversimplification and experience tells you that the amplitude of the bob’s trajectory, that is the height it attains in each cycle, will gradually decrease and the bob will eventually come to rest at its equilibrium position with the arm oriented straight down. At that point it would certainly appear that energy was lost because, when the bob rests in that position, it has neither kinetic nor potential energy. This leads us directly to the Second Law of Thermodynamics, one version of which states that no transformation of energy is ever 100% efficient, that is, some energy is always “lost” to heat. In this case friction, arising from the pendulum’s pivot point as well as to air resistance, causes a small amount of energy to be “lost” during each potential-to-kinetic and kinetic-to-potential conversion. Of course, the First Law tells us that the energy is not destroyed, thus energy “lost” is not the same as energy destroyed. It can be accounted for in the form of the heat that is generated by the friction, but that heat is not available to drive the pendulum’s motion so it eventually comes to a standstill.

Despite its seemingly prosaic form, the implications of the Second Law are truly profound. It gives us a guide to the directionality of change in the universe. For example, if you hold a book in your outstretched arms and drop it, the potential energy of the book is initially converted to kinetic energy and, upon landing, it is dissipated as heat. Nothing in the First Law would prevent that sequence of events from “running backwards”, that is, having the heat and sound caused by the book’s landing to somehow become focused and thereby induce the floor to push the book back up into your hands. Energy would not be created by that event, so it would not violate the First Law. It is the Second Law that states that only the forward scenario is possible because once potential energy is dissipated as heat it is no longer available to do useful work. The Second Law also makes it impossible to create machines that are 100% efficient, that is, a device that accomplishes an amount of work equal to the energy expended. Despite many attempts to design and build such perpetual motion machines, all have been shown to be either hoaxes or unworkable.

We will explore more aspects of the Second Law as they relate to various topics throughout this book. For example, it is helpful when explaining why mixtures of oil and water separate, how diffusion across a membrane can accomplish useful work in a cell, and why water evaporates at temperatures far below its boiling point. For the time being, however, keep the following tongue-in-cheek versions of the First and Second Laws in mind: with respect to any energy conversion, the First Law states that you can’t win, you can only break even, meaning you can’t get more energy or work out of a system than you put in; the Second Law states that you can’t even do that.

Thermodynamics In A Nutshell:

The First Law of Thermodynamics: energy is neither created nor destroyed.

The Second Law of Thermodynamics: in the conversion of one type of energy to another, some energy is always dissipated as waste heat.

It is truly difficult to overstate the importance and usefulness of these two principles. We are loathe to appeal to authority in matters of science, but it is nevertheless helpful to consider one accomplished scientist's thoughts on the centrality of these ideas to physical science. To wit, a quote from Albert Einstein: 

A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended is its area of applicability. Therefore the deep impression which classical thermodynamics made upon me. It is the only physical theory of universal content concerning which I am convinced that within the framework of the applicability of its basic concepts, it will never be overthrown. [12]

 

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Notes and References.

[12] Albert Einstein, Autobiographical Notes (1947)