ABSTRACT
The language of work is not problematic. However, the language of heat has endured long-standing and continuing language difficulties. The concept of work is familiar from classical mechanics, where it is defined as the force applied to an object multiplied by the resulting displacement along the direction of that force. The common thermodynamics example of reversible isothermal heating of a gas at temperature requires the gas to maintain contact with a constant temperature reservoir at the same temperature as the gas. Utilitarians use thermodynamic equations developed using purist thermodynamics, but with utilitarian approximations and interpretations in mind. This chapter provides a summary of the purist and utilitarian views of reversible isothermal volume changes. For any thermodynamic system, there are three relevant types of equilibrium: mechanical equilibrium, chemical equilibrium, and thermal equilibrium. Thermal equilibration between two objects with initially different temperatures requires that the hotter object heat the cooler one until they are both at the same temperature.
