Work from Nonequilibrium Systems

Abstract

It is common belief that in an adiabatic process, the first law asserts that a system can do work “at the expense of its internal energy” (Truesdell 1979). However, this is what Carnot’s general axiom precisely negates. If everything is at the same temperature no work can be done. Work is not associated with any single step in the Carnot cycle, but with the cycle itself. Hence, both adiabatic and isothermal processes are necessary to produce work.

Fermi (1956) uses Kelvin’s statement

A transformation whose only final result is to transform heat into work that has been extracted from a source at the same temperature throughout is impossible.

of the second law to show that work can be attributed to a single step in the Carnot cycle, as if it was a purely mechanical concept! Fermi’s interpretation is exemplary of the confusion in the interpretation of the first law as a purely mechanical law. He emphasizes the word only and cites as an example the isothermal expansion of a gas that absorbs heat at a single temperature thereby performing work. According to Fermi, the complete transformation of heat into work is not in violation of Kelvin’s statement because the gas occupies a larger volume at the end of the expansion. If this were the case we could carry out this process indefinitely thereby converting the heat absorbed entirely, and completely, into work. Rather, it is the net work that the first law is concerned with, and in order to calculate it, the system must be brought back to its initial state. The net change in the internal energy is zero but not the work which is equal to the difference between the heat absorbed at the boiler and the heat rejected at the condenser. The presence – and necessity – of the condenser is the last vestige of caloric theory. The possibility of doing work must be paid back by returning to the original state. This is precisely the role of the condenser. Only the net gain is pertinent.