Cementing the foundations of thermodynamics: Comparison of system-based and surroundings-based definitions of work and heat

The distinction between system-based and surroundings-based definitions of thermodynamic heat (q) and work (w), particularly pressure-volume work, in irreversible processes is introduced and cleanly drawn. A systematic presentation of system-based q and w is given for the first time. This development complements the authors' earlier presentation of surroundings-based work and heat. Either set of definitions can and has been used to develop the laws of thermodynamics. Both sets of definitions are used to analyze examples presented by Kivelson and Oppenheim (KO). It is seen for two KO processes that w(sys-based) and w(surr-based) are not equal. This not uncommon result does not violate the first law because the two q values are also different. One of the KO examples corresponds to a 'quasistatic' process, which is reversible from the point of view of the system but not from the point of view of the system plus surroundings taken together, and, therefore, not reversible overall. A number of reasons are given for preferring surroundings-based definitions of w and q to system-based definitions. Perhaps the most important is the fact that w(sys-based) does not always satisfy the theorem of maximum work in a constant temperature process. Finally, an explanation is presented for why the common use of two different sets of definitions for w and q has not led to greater confusion in the past