The way most teach the ideal gas laws is wrongheaded and irrational: they are presented out of nowhere with no inductive basis and no context. The fault is not the fault of all teachers and all schools. The fault is with the pedagogists and philosophers who pushed the Platonic and Deweyian points of view that are destroying us today. Theses people are the evil ones, not all the teachers and schools. Heck, I used to not know better, either. Thank goodness, to paraphrase Newton, I can stand on the shoulders of giants.
We should be learning the gas laws inductively and contextually, and in an integrated fashion: integrating sense observations with concepts and principles, integrating ideas with ideas to form a more general principle, integrating ideas with other ideas (gas laws with physics and thermodynamics and the work of engines and human biology and mathematics), integrating ideas with the needs and values of human life.
We should be learning in a way briefly presented in The Historical Gas Laws by Jeff Altig of New Mexico Tech. The article does not use the common approach: throw the laws in your face and say “surprise!” Nor does the articles use the other common “rationalistic” approach of deducing the laws from some abstract principle(s) about which you know nothing — the approach of ancient cult leaders who “just know” the higher mysteries which you will never know (until you can pretend you do, thereby attaining the rank of cult leader), and who present you with ideas to memorize and blindly follow. (A “rationalistic” approach is not rational because it detaches reason from the evidence of the senses, treating reason as some faculty that merely makes things up. Then where does this knowledge come from? And then why is reason so efficacious in the world? No good answer is ever given, nor can ever be given.) Rather than engaging in such insults to your independence and intellect, the article presents the ideal gas laws inductively by showing how they were developed. It gives some original data from experiments done long ago, too.
Context for the gas laws and integration of them with other areas of though is provided in Dr. Michael Fowler’s Evolution of the Atomic Concept and the Beginnings of Modern Chemistry. Dr. Michael Fowler knows that physics should be taught from a historical perspective (which thereby makes it inductive and contextual). In Teaching Heat: the Rise and Fall of the Caloric Theory, he says:
In my experience, there is much to be gained from teaching physics with some historical perspective. Unfortunately, the trend in physics textbooks these days is in the opposite direction. Thirty years ago, most standard texts included some discussion of how and when basic concepts in physics developed. Recent editions of these same books, much heavier and more colorful, have dropped that material in favor of endless detailed instruction on how to solve textbook problems. This may be, in part, a necessary response to less well prepared students, and possibly teachers, but the new texts, despite four color artwork on shiny paper, are rather dreary. My solution is simply to use the text as a source of problems and for back up reading, to use a fair amount of historical material (and demonstrations) in class, and to post my class notes on the web. Homework assignments include calculations based on historical experiments (for example: Estimate the mechanical equivalent of heat using Rumford’s cannon-boring data and Watt’s estimate of one horsepower.) Most of the students enjoy this approach.
I strongly believe that it is not a waste of time to discuss some earlier theories that turned out to be wrong. In fact, these earlier theories are often close to the students’ current thinking, so challenging them as to why those ideas were finally abandoned can stir the critical faculties and lead to better understanding. A case in point is the caloric theory of heat. Of course, the students are vaguely aware that it’s not right, but their intuitive ideas of heat, based on everyday experience, have probably led them to construct an operational model not too different from the caloric one, so we go ahead and discuss heat from this naïve point of view, and mention the first recorded systematic experiments on heat and heat flow. For example, Ben Franklin measured heat flow down rods of different materials by seeing how long it took to melt wax, and thereby compared the thermal conductivities of different materials, a matter of real practical importance in designing stoves, for example. Franklin believed some weightless (or almost weightless) caloric fluid was flowing down those rods. Recall he’d thought the same thing about electricity—there was some electric fluid flowing when an object was being charged electrically—and there he was absolutely correct. Like the electric fluid, Franklin believed the caloric fluid would flow from one object to another, but overall there was always the same amount of fluid: it was conserved. That is the basic Caloric Theory.
I agree: teaching inductively preserves the integrity and independence of each student’s mind, and trains the student in using reason and logic properly.
Update (2-12-15, 1:35 AM): If you think “math is useless,” “science is useless,” “when am I ever going to use that?,” watch Night Crossing. And please think about its abstract meaning for human life in general, your life in particular. Don’t get caught up in the particulars and be “concrete bound,” i.e., non-conceptual! Think large, live large; be not someone blinded above and to the sides by a narrow canyon, be a man on a mountain.