24 Chapter 1. What the ancients knew[[Student version, December 8, 2002]]
The remarkable thing about Equation 1.11 is that it holdsuniversally:Any gas, from hydrogen
to vaporized steel, obeys it (at low enough density). All gases (and even mixtures of gases) have
thesame numerical valueof the constantkB(and all agree about the value of absolute zero). In
fact, even the osmotic work formula, Equation 1.7, involves this same quantity! Physical scientists
sit up and take notice when a law or a constant of Nature proves to be universal (Section 1.3).
Accordingly, our first order of business in Part II of this book will be to tease out the deep meaning
of Equation 1.11, and its constantkB.
T 2 Section 1.5.4′on page 26 makes more precise this book’s use of the unit “mole,” and relates it
to other books’ usage.
The big picture
Let’s return to this chapter’s Focus Question. Section 1.2 discussed the idea that the flow of energy,
together with its degradation from mechanical to thermal energy, could create order. We saw this
principle at work in a humble process (reverse osmosis, Section 1.2.2 on page 10), then claimed
that life, too, exploits this loophole in the Second Law of thermodynamics to create—or rather,
capture—order. Our job in the following chapters will be to work out the details of how this
works. For example, Chapter 5 will describe how tiny organisms, even single bacteria, carry out
purposeful motion in search of food, enhancing their survival, despite the randomizing effect of
their surroundings. We will need to expand and formalize our ideas in Chapters 6 and 8. Then
we’ll be ready to understand the self-assembly of complicated structures in Chapter 8. Finally,
Chapters 10–12 will see how two paragons of orderly behavior, namely the motion of molecular
machines and nerve impulses, emerge from the disorderly world of single-molecule dynamics.
Before attempting any of these tasks, however, we should pause to appreciate the sheer immen-
sity of the biological order puzzle. Accordingly, the next chapter will give a tour of some of the
extraordinarily ordered structures and processes present even in single cells. Along the way we will
meet many of the devices and interactions to be discussed in later chapters.
Key formulas
Each chapter of Parts II–III of this book ends with a summary of the key formulas appearing in that
chapter. The list below is slightly different; it focuses mainly on formulas from first-year physics,
which will be used throughout the book. You may want to review these using an introductory
physics text.
1.First-year physics: Make sure you recall these formulæ from first-year physics, and what all
their symbols mean. Most of these have not been used yet, but they will appear in the coming
chapters.
momentum = (mass)×(velocity).
centripetal acceleration in uniform circular motion =rω^2.
force = rate of transfer of momentum.
torque = (moment arm)×(force).
work = transferred mechanical energy = (force)×(distance) = (torque)×(angle).
pressure = (force)/(area).
kinetic energy =^12 mv^2.