April 20, 2025
Is Energy "Lost" When It Changes Forms?

A while back, I had a series of interactions on FB which reveal common gaps in folks' understanding of energy conversions and conservation of energy.

The meme above sparked the conversation.

To dispense with a pet peeve of mine at the start, heat is a process of energy transfer, distinct from another process called work. What the meme should say is that the other energy is converted to thermal energy, a form of energy produced during the process of heating something up.

Numerous commenters refused to believe that heaters could be 100% efficient because they had learned that some energy is "lost" when it is converted from one form to another. It was clear what they meant is that a certain amount of energy would disappear, a clear violation of the law of conservation of energy. These commenters remind us that students will cheerfully hold conflicting ideas in their minds until teachers force examination of the conflict, and that describing energy as "lost" is perhaps not the best choice of words.

Some commenters referred to sound or light emitted from the heater as "wasted" energy. I countered that sound is just organized thermal energy, which would disorganize soon enough and warm the room. And that light from the element of a heater, if it did not go out a window, would be absorbed by the air or by surfaces in the room, and converted to thermal energy. Now we had begun to get to the heart of the matter.

There is no law of physics that requires energy to be "lost" or "wasted" during energy transfers. Earth has been orbiting the Sun for over 4 billion years, with continuous transfers of kinetic energy to gravitational potential energy and back. The second law of thermodynamics refers specifically to entropy, the concept that not all of the thermal energy available to a heat engine can be converted to mechanical energy. As a practical matter, devices with moving parts (and that includes electrons moving in a wire) are subject to friction, which produces thermal energy from kinetic energy and reduces the efficiency of the device.

Most of us would agree that the purpose of a heater is to heat the air in a room. If that is our definition of the outcome, it's tough to argue that the heater is significantly less than 100% efficient. Even a vortex heater which emits no light and circulates air across its elements will itself be warmed, and that warmth will eventually dissipate to the room. To find sources of inefficiency, we would need to follow the source of the electrical current being used by the heater until the wires carrying it are not in the room. I suppose one could argue that thermal energy absorbed by objects in the room and not the air inside it constitutes loss. As is often the case in physics, the definition of what is inside the system vs. what is part of the environment outside the system determines the mathematical process and outcome.

September 19, 2024
Process-Based Physics Education

Principles or formulas? Content or process? Effective physics education focuses on all of these, and more.

A meme making the rounds of social media attributes the following quote to Richard Feynman: "Teach principles, not formulas. Understand, don't memorize." If Feynman actually said this, and and I cannot find a definitive source proving he did, it would be out of character for him to be so imprecise. I suspect there was context around this statement the meme is ignoring.

While it's certainly true that memorizing facts and formulas isn't a useful approach to learning physics, ignoring facts and formulas is equally stifling. Formulas are the concise and powerful outcome of our physical understanding of the world, and spoken-word principles don't give us the insights needed to put our knowledge to work.

As an example, let's consider Einstein's theory of special relativity. Its principles include two postulates—that physical laws are identical in all inertial reference frames, and that the speed of light is the same for all observers. Working the postulates into classical kinematics and dynamics yields additional principles, notably mass-energy equivalence and the existence of a spacetime continuum governed by time dilation and length contraction. Reading about the elasticity of space and time predicted the the theory of special relativity has been a source of wonder for physicists and layman alike. But why stop there?

Special relativity formulas rely on the same algebra most of us learned in high school.

With these formulas and a little Googling for values, we can learn why time dilation and length contraction are not readily observable at the typical speeds of terrestrial objects. Or we can determine that the energy produced by a typical nuclear power plant in a day can be obtained from about one gram of matter, the mass of a small paper clip.

A third important consideration, beyond principles and formulas, is the connection between the two: In other words, the answer to the question, "Where do formulas come from?" The time dilation formula above can be derived from the principles of special relativity using simple geometry.

Finally, it's worth getting to the bottom of how experimental inquiry, in this case the Michaelson and Morley experiment which established the invariability of the speed of light, leads to the development of new principles and formulas.

In all of these ways, revealing to students the processes of physics, and expecting them to draw evidence-based conclusions from data, from principles, and from formulas, builds in them the confidence needed to become rational problem solvers in their careers and in their lives. The curricula of the present-day AP Physics courses—their dependence on requiring students to "justify their answer," "explain their reasoning," "determine," and "calculate"—encourage students to engage in the processes of physics. Process-based activities and assessment can be infused into physics courses at all levels.

As "grist for the mill," memorization of principles and content is a good thing, so long as it doesn't end there. Processes (laboratory inquiry, derivation, applied reasoning) are the strands connecting content (principles and formulas) into a web of understanding.