(67d) In the Spirit of Carnot: Theoretical Limits to Steady-State Productivity

Although this talk will not be about thermodynamics, it is useful to recall the spirit of the classical Carnot analysis of heat engines. The Carnot analysis tells us that, for specified constraints (upper and lower operating temperatures), there is a limit to how much of a supplied entity (heat) can be converted into a desired product (work). Although highly idealized Carnot engines cannot be realized in practice, they nevertheless play an essential role in the analysis, not least in establishing that the derived bound on conversion of heat to work is sharp: To the extent that Carnot engines might be approximated in the limit by real engines, the theoretical Carnot bound on conversion can be realized arbitrarily closely. This is of enormous importance, for the Carnot analysis offers a theoretical benchmark against which all engines, subject to the same operating constraints, can be measured.

Process designs (like engine designs) are finally judged on practical grounds, but the Carnot story is an instructive one, suggesting a spirit in which reactor-separator synthesis might be approached. Can we know when a candidate steady-state design is, in some theoretical sense, efficient in its production rate relative to all other designs consistent with the same commitment of resources? In particular, is there a theoretical limit to what might have been produced from the same feed in any steady-state design that utilizes the same reactor size as the candidate design, that respects the same pressure-temperature bounds within reactor units, and that respects the same constraints on the production of unwanted side products? More generally, for specified temperature-pressure bounds in reactor units is there a minimum reactor size, independent of design, that is required to achieve a target productivity, and, if so, how might it be calculated? And are there certain universal Carnot-like configurations that invariably achieve maximum productivity subject to process constraints?

Some thoughts on these questions will be presented.