Thermodynamic Stuff Equations

In this chapter we develop expressions that relate heat and work to state functions those relations constitute the first and second laws of thermodynamics. We begin by reviewing basic concepts about work ( 2.1) that discussion leads us to the first law ( 2.2) for closed systems. Our development follows the ideas of Redlich [1]. Then we rationalize the second law ( 2.3) for closed systems, basing our arguments on those originally devised by Carath odory [2-4]. Finally, by straightforward applications of the stuff equations introduced in 1.4, we extend the first and second laws to open systems ( 2.4). 

THERMODYNAMIC STUFF EQUATIONS 55 2.4 THERMODYNAMIC STUFF EQUATIONS... 

In 2.2 and 2.3 we presented the first and second laws for closed systems. In practice these would apply to such situations as those batch processes in which the amount of material in the system is constant over the period of interest. But many production facilities are operated with material and energy entering and leaving the system. To analyze such situations, we must extend the first and second laws to open systems. The extensions are obtained by straightforward applications of the stuff equations cited in 1.4. We begin by clarifying our notation ( 2.4.1), then we write stuff equations for material ( 2.4.2), for energy ( 2.4.3), and for entropy ( 2.4.4). These three stuff equations are always true and must be satisfied by any process, and therefore they can be used to test whether a proposed process is thermodynamically feasible ( 2.4.5). 

But when these criteria are met, the thermodynamic stuff equations are powerful and versatile. In particular, they can be implemented without knowing the detailed mechanisms by which a proposed process is to accomplish its task. This occurs because the first and second laws establish equivalences between process variables (Q and W) and changes in system variables (such as u, h, and s). 

How do we use the thermodynamic stuff equations to test the feasibility of a proposed process ... 

In 2.4 we presented differential forms of the thermodynamic stuff equations for overall mass, energy, and entropy flows through open systems. Usually, such systems, together with their inlet and outlet streams, will be mixtures of any number of components. Individual components can contribute in different ways to mass, energy, and entropy flows, so here we generalize the stuff equations to show explicitly the contributions from individual components these generalized forms contain partial molar properties introduced in 3.4. 

Thermodynamic stuff equations are internal constraints on the variables that describe open systems. Therefore, in 3.6.2 and 3.6.3 we show how those constraints enter determinations of the number of independent quantities needed to analyze open steady-flow systems. 

We now turn to processing situations in which heat effects are of primary importance examples include chemical reactors and separators that exploit phase partitioning. Thermodynamic analysis of these situations invoke the stuff equations in particular, steady-state heat effects are computed from (12.3.5). To obtain the partial molar enthalpies that appear in (12.3.5), we need enthalpies as functions of composition so in 12.4.1 we show how enthalpy-concentration diagrams can be constructed from volumetric equations of state applied to binary mixtures in phase equilibrium. Then we apply the energy balance (12.3.5) to multicomponent flash separators ( 12.4.2), binary absorbers ( 12.4.3), and chemical reactors ( 12.4.4). 

To understand robber elasticity we have to revisit some simple thermodynamics (the horror. the horror ). Let s start with the Helmholtz free energy of our piece of rubber, by which we mean that we are considering the free energy at constant temperature and volume (go to the review at the start of Chapter 10 if you ve also forgotten this stuff). If E is the internal energy (the sum of the potential and kinetic energies of all the particles in the system) and 5 the entropy, then (Equation 13-26) ... 

Finally, we discussed the primitive steps in beginning an analysis that will determine how a system responds to processes. Those primitive steps culminate either in a two-picture diagram for closed systems or in a one-picture diagram for open systems. In addition, for open systems we identified forms of a general balance equation that apply to any kind of stuff that may cross system boundaries. With all these primitive concepts in place, we can begin the uphill development of thermodynamics. 

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