Austria

002

Zentralfriedhof, Vienna, Austria

48° 8 ′ 58 ″ N, 16° 26 ′ 28 ″ E

A Scientist Among the Composers

If you need an excuse to visit the beautiful Austrian capital, then use the Zentralfriedhof (Central Cemetery) as your reason. Although the cemetery may not be one of the most famous attractions in Austria, it is the final resting place of many celebrated Austrians (and others), including Beethoven, Brahms, Schubert, four Strausses, and a host of other artists and politicians. But the grave that’s waiting for scientific visitors is the one with a fundamental equation of thermodynamics written upon it.

That grave belongs to Ludwig Boltzmann, the Austrian physicist who created statistical mechanics (which helps to explain how the fundamental properties of atoms, such as mass or charge, determine the properties of matter) and showed that the laws of mechanics at an atomic level could explain the second law of thermodynamics (roughly that heat cannot flow from a cool body to a hotter body) via Boltzmann’s Equation (see Equation 2-1).

Equation 2-1. Boltzmann’s Equation

Boltzmann lived during the 19th century (he died just after the turn of the 20th) and firmly believed that matter was composed of atoms and molecules. Despite the fact that Dalton (see Chapter 55) had described atomic weights in 1808, there was still debate about the existence of atoms. But Boltzmann used what others considered to be an unproven theory to apply, to great effect, probability theory to the physical world through statistical mechanics.

Along with James Clerk Maxwell (see Chapter 35) and Josiah Willard Gibbs, Boltzmann was one of the most important physicists of the 19th century. His grave (Figure 2-1) is a testament to his importance, with his famous equation cut into the stone and featuring an imposing bust of the scientist. He is buried alongside members of his family.

Figure 2-1. Boltzmann’s grave; courtesy of Martin Röll (martinroell)

The cemetery itself is enormous—2.4 square kilometers in size with around three million people buried there, making it one of the largest cemeteries in Europe. One area contains the tombs of notables, of which Boltzmann is the only scientist.

While you are in Vienna, there’s also a small museum in Freud’s former home that is worth a visit.

Practical Information

The number 71 tram has multiple stops at the Zentralfriedhof. Boltzmann’s grave is in section 14C of the cemetery, which is closest to the Zentralfriedhof Tor 2 stop.

Statistical Mechanics and Entropy

The relationship between the macrostates (such as volume, temperature, and pressure) and the microstates (the location, mass, and velocity of individual atoms) of a material is fundamental to statistical mechanics, and Boltzmann laid its foundations. The macrostates are easily measured; the microstates are not.

Externally, a bottle full of air might be described by a small number of macrostates—its exact volume, temperature, and pressure could be measured, for example. But inside the air, the molecules are moving around and bumping into each other, and for any fixed macrostates the microstates are constantly changing. Nevertheless, there’s a relationship between the micro and macro.

Boltzmann’s entropy can be thought of as a measure of the degree of chaos inside the bottle, or a measure of the number of different ways the molecules of air can arrange themselves to achieve the same volume, pressure, and temperature.

Imagine a pack of 52 playing cards dropped on the floor. You can think of them as having one macrostate: the number of playing cards that are face up. That macrostate, like volume, temperature, and pressure, can be easily measured. But for any specific number of face-up cards, there are many different combinations of individual face-up cards: that is, for any macrostate there are many possible microstates (each card has its own microstate specifying whether it is up or down).

If all the cards are face up, then there’s little chaos: each card’s microstate is known. The same applies if all are face down. The most chaos occurs at the midpoint of these two extremes: when 26 cards are face up and 26 cards are face down. Then there are 495,918,532,948,104 possible microstates.

Boltzmann’s famous equation (as interpreted by Max Planck) uses the number of possible microstates, W, for any given set of macrostates. The constant k is known as Boltzmann’s constant. The resulting value, S, the entropy, is actually a macrostate just like volume, temperature, or pressure and can be calculated for an ideal gas (for more on ideal gases, see page 211).

For any given volume, temperature, and pressure, the entropy, S, is a measure of how uncertain we are about the internal state of the gas.

Boltzmann’s equation is engraved on his tomb because it is the fundamental link between the microscopic world of moving, colliding atoms and the macroscopic world of temperatures, pressures, and volumes.