I believe that an improved approach to teaching thermodynamics can be created by starting with the atomic theory of matter and then explaining the connections between this theory and macroscopic thermodynamic phenomena. This micro-to-macro approach arguably began in the late 19th century when a small group of scientists, namely Rudolf Clausius, James Clerk Maxwell, and Ludwig Boltzmann, successfully developed the kinetic theory of gases, which eventually became the key bridge from classical thermodynamics to statistical mechanics. The prediction of heat capacity played a crucial role in this effort, and an interesting related story was the absence of heat capacity predictions for monatomic elements. Why was this? To me, the reason had to do with the structural difference between a sphere and an atom. Check out the below video in which I lay out my argument.
Addendum: It’s a real challenge trying to understand what the early theorists were truly thinking as they developed thermodynamics. I wish each had written an autobiography to share their thoughts, thoughts that were not suitable for publication but still, their own thoughts on what nature looked like. Especially Gibbs!
Regarding the heat capacity of gas atoms, it’s not that they attempted and made a mistake, it’s that they never attempted to begin with, and this is what struck me when I read their papers. I believe that the main reason for this is that they couldn’t conceive of an atom that didn’t spin, or have energy associated with spin. They couldn’t conceive of an atom comprised of mostly empty space, with all the mass concentrated in the center nucleus.
For an excellent in-depth analysis of the development of the kinetic theory of gases, I highly recommend Stephen Brush’s Kinetic Theory of Gases, The: An Anthology of Classic Papers with Historical Commentary.
I delve into the successful development of the kinetic theory of gases, which successive chapters on Clausius, then Maxwell, and finally Boltzmann, in my book.