Relationship between heat capacities derived by different but connected approaches

Deriving the same result with different approaches is not only an interesting experience but is also useful in teaching. Several connected derivations of the relationship between heat capacities, including a novel method, demonstrate this. It is proved that C-P - C-V >= 0, in all cases, even for water in the temperature range of 0 - 4 degrees C. Throughout this paper, it is argued that teaching content and concepts is not enough to provide a good education. It is more important to provide students with the experience of how methods solve problems in order to provide them with the ability to develop new concepts and to solve problems in their own research. (C) 2020 American Association of Physics Teachers.