Ludwig Boltzmann
and
His Discoveries
Overview
Ludwig Boltzmann was an Austrian theoretical physicists of 19th century who made remarkable contributions in the fields of kinetic theory, statistical mechanics and thermodynamics. He was one of the great pioneers who helped us understand what heat really was. He showed us the importance of the laws of thermodynamics based on which the entire universe operates.
Let us learn about Boltzmann’s discoveries and his remarkable contributions to physics in this post.
Early Years
Boltzmann was born in Vienna, Austria in 1844. He studied mathematics and physics at the university of Vienna. He received his doctorate in 1866.
Boltzmann worked as mathematical physics professor at various universities including University of Graz, University of Vienna and University of Munich. It was at the University of Graz, he developed most of his work on the statistical mechanics of physics.
What is heat?
For centuries, one of the big questions that remained unresolved in physics was what is heat? Physicists (wrongly) believed that the heat was a result of the flow of an invisible fluid called ‘calorie.’ When water is heated by burning coal, physicists of those days believed that ‘calorie’ flowed from coal into water. Even, Sadi Carnot, the French physicist and engineer, published his steam engine theory, in 1824, based on the assumption that calorie existed.
It was James Joule, English physicist, who suspected the validity of calorie theory when he noticed that flowing electric current produced heat in the wires and that friction generating enormous heat. But Joule too could not answer what heat really was.
In 18th century, Daniel Bernoulli, Swiss mathematician and physicist, theorized that the kinetic energy from the random motion of the particles of fluids could be the reason for macroscopic attributes of fluids such as temperature and pressure. Since he was well advanced for his time, his ideas languished for almost hundred years.
Rudolf Clausius, German physicist and mathematician was the one who restarted the debate on the kinetic energy of gas particles in the year 1857, and he showed that kinetic energy from the random motion of the constituent particles of a gas could be responsible for the internal heat energy.
Scottish theoretical physicist James Maxwell, who believed in the atomic nature of matter, mathematically analyzed the kinetic energy of gases based on statistical methods.
Like James Maxwell, Boltzmann too believed in the atomic and molecular nature of matter. In fact, Maxwell was Boltzmann’s hero.
Kinetic Theory &
Statistical Mechanics
And later in 19th century, James Maxwell, believing in atomic nature, further developed kinetic theory of gases using statistical method. Boltzmann extended Maxwell’s ideas in developing kinetic theory not only for gases but also for liquids and solids. They proved that the macroscopic properties of gases, liquids and solids are related to the average kinetic energy of their individual microscopic entities.
For instance, the temperature, pressure and internal energy of gas in a container are related to the average kinetic energy of the molecules of the gas. Kinetic energy arises from the random motion of the molecules either due to linear motion or from the spin of each molecule. As it is impossible to keep track of the position, velocity and spin of each molecule of the gas in a container which may contain billions and billions of molecules, Maxwell and Boltzmann adopted statistical method to figure out the average kinetic energy the gas.
The key takeaway from their works is that the energy that we feel as heat arises from the random motion (and collisions) of molecules in gases or liquids. In the case of solids, it is the vibration of the molecules or atoms we feel as heat.
Entropy
In order to understand Boltzmann’s contribution in explaining the laws of thermodynamics, especially the second law, we first need to take a look at the concept of entropy.
What is entropy? To put it in simple words, entropy is a measure of disorder in a system. In 1877, Boltzmann was the first to define entropy mathematically using statistics.
For instance, consider a new deck of playing cards. The pristine deck normally has all the 52 cards ordered by rank-and-suit precisely as in the picture below. Obviously, the new deck has low randomness. To put it in entropy terms, the new deck has low entropy.
Before you start a game with a new deck, you certainly want to shuffle it so that the randomness increases. Once you shuffle it, the disorder increases and so does the entropy.
Below is the equation Boltzmann discovered to quantify the entropy of a system using statistical method.
In this equation, s is the entropy of a system, k is Boltzmann constant, and W refers to the number of all possible distinguishable microstates (arrangements) for a given macro-state.
So, the entropy of a closed system is proportional to the logarithm of the number of possible distinguishable microstates for a given macro-state.
Laws of Thermodynamics
Why does heat flow from hot to cold and not in the reverse direction? The laws of thermodynamics, especially the second law, has the answer. Let us quicky review the laws of thermodynamics.
Thermodynamics deals with subject of how heat energy exchange occurs. Though there are four laws of thermodynamics, first two laws are particularly important.
The first law of thermodynamics deals with conservation of energy. It states that energy can neither be created nor destroyed; but it can only be converted from one form of energy to another. In this process, total energy remains constant all the time.
The second law states that the entropy of a closed system always increases.
Boltzmann stated that the second law is a direct consequence of the probabilistic nature of the world; only increasing entropy is extremely a high probability than a decreasing entropy in a system.
The arrow of time and the heat flow from hot to cold are because of the fact that increasing entropy is more probable. This amazing insight came from Boltzmann.
The End
In 1906, Boltzmann, the amazing theoretical physicist sadly, succumbed to his disease. The equation that he discovered remains engraved on Boltzmann’s tombstone.
One of the universal constants in physics (k) is named after his him. It is the Boltzmann constant.
Key Takeaways
- What is heat? It is a form of energy. It arises in gases and liquids because of the random motion of its constituent molecules and random collisions. In solids, it is the vibration of their molecules or atoms that is the source of heat.
- The theory of kinetic energy of gases, based on statistical methods, proves that the macroscopic properties like temperature, pressure and internal energy are from the kinetic energy of its constituent molecules.
- The first law of thermodynamics deals with the conservation of energy.
- The second law of thermodynamics deals with how heat energy propagates. Heat energy flows from the hot to cold, not in the reverse, as the entropy of a closed system can only increase.
- Boltzmann mathematically quantified the entropy of a closed system.
- Boltzmann showed that the second law of thermodynamics ( entropy of a closed system can only increase) was a consequence of the probabilistic nature of entropy; only increasing entropy was much more probable than decreasing entropy.
References
- Einstein’s Fridge by Paul Sen
- Cosmic Numbers by James D. Stein
- https://en.wikipedia.org/wiki/Ludwig_Boltzmann
- Britannica, The Editors of Encyclopaedia. “Ludwig Boltzmann”. Encyclopedia Britannica, 1 Sep. 2023, https://www.britannica.com/biography/Ludwig-Boltzmann. Accessed 6 February 2024.
- Britannica, The Editors of Encyclopaedia. “Statistical mechanics”. Encyclopedia Britannica, 15 Dec. 2022, https://www.britannica.com/science/statistical-mechanics. Accessed 10 February 2024.
- https://plato.stanford.edu/entries/statphys-Boltzmann/