There are many touchstone examples we have discussed that have drawn our attention to critical features of not only the concepts and their connections, but what it means to understand them.
Included in these touchstone examples are
- An ideal gas in an external gravitational field. How do we think about the kinetic energy and temperature varying with height? Theoretically, intuitively, and empirically.
- The free expansion of a non-ideal gas. How do kinetic and inter-molecular potential energies change? How does temperature change? Why? How are these changes related?
- A gaseous systems composed of boson and fermions in near classical regime. How do kinetic energies compare?
Ralph Baierlein in "Thermal Physics" writes the following in a section called "Temperature recapitulated" in a subsection called, "Temperature is deeper than average kinetic energy":
"The misconception that introduces this subsection is propagated with the best of intentions: to make temperature easier to understand. The root of the conceptual error lies in this: a belief that the purpose of absolute temperature is to tell us about a physical system's amount of energy. That is not the purpose of the temperature notion. Rather, temperature is intended to tell us about a system's hotness, its tendency to transfer energy (by heating). All physical systems are capable of heating or cooling others. The purpose of temperature is to rank the systems with respect to their ability to heat one another."