Why Does Ice Melt? The Answer Lies in Physics.

In this installment on the history of atom theory, physics professor (and my dad) Dean Zollman discusses the contributions of Max Planck seeking an explanation for why energy goes only one way (for example, ice starts to melt in a warm room instead of becoming even colder). – Kim

By Dean Zollman

Ernest Rutherford’s discovery of the nucleus provided a basic structure for the atom. However, to explain some of the observations of the 19th century required additional discoveries. In particular, the light emitted from atoms could not be explained by a simple model of an electron orbiting a nucleus. (Recall that each element emits a unique set of colors when the element is heated or, for gases, has electricity passed through it.) To get the additional tools to explain this phenomenon, we need to back up to the end of the 19th century and follow a thread that was developing simultaneously with the study of radioactivity and the nucleus.

During the last half of the 19th century, some physicists were attempting to explain the behavior of matter, primarily gases, by applying Newton’s Laws to particles in the gases. Some of them were assuming that matter was made of small solid objects (atoms) that bounced off each other. This bouncing and motion could be described by using the principles that Newton had laid out. Others thought that while the basic known laws of mechanics would still work, it was better to approach the issue from the perspective on energy. All of this research is called statistical mechanics and is still an active area of research.

One observation that statistical mechanics needs to explain is the one way energy naturally flows. If I put a cup of ice on a table in a warm room, the ice always gets warmer. It never becomes even colder by transferring its internal energy to the room, which would then become even warmer. To make the ice colder, we must intervene (e.g. put it in the freezer).

In the 19th century, physicists were divided over whether this observation was a fundamental law of physics based on energy considerations or something based on the average (statistical) behavior of the particles making up the ice and surrounding air. (Statistical wins in the long run.)

Black Bodies That Aren’t Black

Max Planck in 1878 (public domain via Wikimedia Commons)

Max Planck (1858-1947) began considering these arguments in the 1880s. At that time, he was an advocate of the energy perspective and thought that the concept of atoms was not consistent with one-way flow of energy. He had written that “in spite of the great successes of the atomistic theory in the past, we will finally have to give it up and to decide in favor of the assumption of continuous matter.” (Quoted in Kragh, Physics World, December 2000)

To develop an explanation for the behavior of energy flow, Planck began looking for ways to combine mechanics and electrodynamics, the theory that describes electromagnetic phenomenon. A particular problem that Planck tackled was that of the so-called black body radiation. The physicist’s black bodies are rather poorly named because they are not necessarily black. These objects do absorb all electromagnetic radiation (including light) that strikes them. But a good absorber of radiation is also a good emitter. So the body may appear to be any color depending on the energy being emitted by it. Stars, including the sun, and a potter’s kiln are examples of black bodies that are definitely not black.

An artist’s rendition of what we might see when looking at the spectrum of a radiating black body that would be somewhat orange. The horizontal scale is wavelength in nanometers. Human eyes see only about 400 to 700 nanometers, so this drawing shows much more than we can see (via Wikimedia, licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license).

Each black body has a characteristic color that depends on its temperature. But not all of the light is emitted at that one color. Instead, light of many colors (and therefore energies) is emitted. The distribution of colors determines how we perceive the object. When the burner on your electric stove is glowing red, it is emitting more red light than other colors but is still emitting some of the other colors.

By the late 19th century, physicists had investigated the colors emitted by many different objects. They could draw graphs of the intensity of light versus wavelength or frequency, which is related to color. The problem was that there was no good theoretical background to explain these curves. By applying statistical methods and electrodynamics to the material in a black body, Planck was attempting to create such a foundation.

The black body radiation curves that Planck was seeking to explain. T in the graphs is the temperature associated with the object, called the black body temperature (public domain via Wikimedia Commons).

Two nice interactive graphs are available on the web. To see an interactive graph with as indication of the color that we see for stars as the temperature changes, go to McGraw Hill Education. To “create” similar graphs for a variety of object including an oven, light bulb, and the sun go to PhET Interactive Simulations. You will need to zoom in to see the graphs for the earth and the oven.

A Revolutionary Formula

Planck’s attempts were at first not very successful. He would get part of the curve right but not all of it. In the autumn of 1900, he tried a new idea. He thought of the light-emitting object as containing a large number of electrically charged oscillators. Each oscillating charge would emit radiation. There is nothing new so far. James Clerk Maxwell had shown that oscillating charges emit electromagnetic radiation. (In a couple of months, we will see how this fact came to haunt physicists.) Now, Planck added a twist. Instead of emitting any frequency, Planck’s oscillators could emit only multiples of some fundamental frequency. Mathematically, energy of the emitted light is expressed as

Energy =n x h x (frequency of light)

The symbol n is an integer number. Today, we refer to h as Planck’s constant.

With this additional hypothesis, Planck was able to match the intensity versus frequency spectrum for black bodies at all temperatures.

Max Planck’s Nobel portrait (public domain via Wikimedia Commons)

Creating a formula to match an observation is not such a big deal. However, the idea underlying Planck’s assumption started a revolution is physics. His assumption says the light energy is emitted in discrete amounts. If we have an electrically charged object that is oscillating with a frequency f, the object can emit light with energies of only n times h times f. All other frequencies are somehow forbidden. Light comes out of the object is discrete small packets. Those packets are now called quanta or photons. From this beginning, quantum mechanics was built and changed our fundamental understanding of the nature of matter. Historians of science discuss whether Planck understood the importance of his discovery. Some argue that his formula worked, but Planck had little understanding as to why. Others think that he did see the deep meaning that allows only certain energies to be emitted. Of course, there are historians who are in between these two views.

By the time Planck received the Nobel Prize, much progress had been made in using Planck’s hypothesis to describe a variety of phenomena. In his Nobel lecture, Planck stated that science “owes [current knowledge] to the unceasing progress of the researchers who have put the quantum of action to the service of their investigations. A. Einstein made the first breakthrough in this domain.” We will look at Einstein’s contribution to this progress next time.

A few side notes:

Many textbooks state the Planck discovered quanta because he was trying explain something called the “ultraviolet catastrophe.” In fact, I introduced Planck’s result to my classes in this way for many years. The “catastrophe” was that some equations predicted that black bodies should emitted an infinite amount of radiation at low wavelengths (high frequencies). This does not seem to be the case. Instead Planck was bringing to together various known laws of physics and needed one new hypothesis.

In 1878, Philipp von Jolly (1809-1884), Planck’s physics teacher at the University of Munich, told the young Max Planck to pursue some other discipline. Jolly believed that there was nothing new to be discovered in physics and “all that remains is to fill a few holes.” Planck was interested in understanding nature as it was, so he studied physics anyway and created some monstrous holes that still need to be filled.

Planck’s fourth son, Erwin, was involved in the July 20, 1944, attempt to assassinate Hitler. A few years ago, this event was depicted in the film Valkyrie. Erwin Planck was executed in January 1945 for his role in the attempt.

Dean Zollman is university distinguished professor of physics at Kansas State University where he has been a faculty member for more than 40 years. During his career he has received four major awards — the American Association of Physics Teachers’ Oersted Medal (2014), the National Science Foundation Director’s Award for Distinguished Teacher Scholars (2004), the Carnegie Foundation for the Advancement of Teaching Doctoral University Professor of the Year (1996), and AAPT’s Robert A. Millikan Medal (1995). His present research concentrates on the teaching and learning of physics and on science teacher preparation.

Previously

What Are Things Made of? Depends on When You Ask.

Ancient Greeks Were the First to Hypothesize Atoms

The Poetry of Atoms

Atom Theory in Ancient India

Religion, Science Clashed over Atoms

Medieval Arabic Scholarship Might Have Preserved Scientific Knowledge

Rediscovering a Roman Poet – and Atom Theory – Centuries Later

Reconciling Atom Theory with Religion

Did Atom Theory Play a Role in Galileo’s Trouble with the Inquisition?

Did Gifted Scientist’s Belief in Atoms Led to His Obscurity?

Does Atom Theory Apply to the Earthly and the Divine?