Isothermal heating: purist and utilitarian views

The common thermodynamics example of reversible isothermal heating at temperature T requires the gas to maintain contact with a constant temperature reservoir at the same temperature as the gas. This is inconsistent with the often used view that heat is an energy transfer from higher to lower temperature. We discuss two ways to deal with this dichotomy, using what we call purist and utilitarian views, emphasizing the roles of language and logic in each. We suggest a way for teachers to address this issue in the classroom, and end with a review of related challenges to physics teachers associated with the terms heat and heating.