The Combined First and Second Law Statement Reversible Work

15 THE COMBINED FIRST AND SECOND LAW STATEMENT REVERSIBLE WORK 

Here To is the surroundings temperature, discussed below. If the process in the box is an oil refinery, Eq, 2.57 will have dozens of terms for flows of material, heat and work in and out. If it is a simple binary distillation column it will have one material flow in and two out, with heat exchange at two different temperatures, and (generally negligible) work flows for some pumps. Chemical engineers often use Eq. 2.57 for simple applications like the distillation column, although there is no reason (except for complexity) that it could not be applied to an oil refinery. 

If we now restrict out attention to reversible processes, for which i.Sin eversibie = 0. we Can say that the dW must be the work that the process in the box would consume or produce if it had the same flows of mass and heat in and out, and it were reversible. We can solve for that reversible work amount as 

The two Ts that appear here are Tin, the temperature at which heat flows in or out across the system boundary, and To the reservoir temperature - the lowest temperature of an unlimited reservoir of heat or cooling, normally the temperature of the nearest large body of water that can supply or accept heat, or of the atmosphere, or of an industrial plant s cooling water system. The reversible work in this equation is the 

FIGURE 2.12 The flow diagram for a very general process, that exchanges multiple flows of mass, heat and work with its surroundings, and may change internally with time. 

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