Stuff equations generalized

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. 

The temperature outside the system boundary is ext- Fleat Q may cross the boundary, shaft work Wg/j may act through the boundary, and the boundary itself may be deformed by boundary work W. Material may enter the system through any number of feed streams a and leave through any number of discharge streams p. 

Material balances. The overall mass balance on the system is written in (2.4.3). The 

Energy balance. The overall energy balance for open systems appears as (2.4.15) in 2.4. Here we neglect the boundary energy L/j, and introduce partial molar quantities for each component i, so (2.4.15) becomes 

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Although the general stuff equations (2.4.3), (2.4.10), and (2.4.21) are always true, they may not always be useful. To be useful, sufficient information must be available from calculations or measurements. Specifically, to test whether a process satisfies the first law, we must have either (a) complete specifications of the initial and final states of the system, or (b) values for both the heat and the work. To test whether the second law is satisfied, we must know the value for the heat then we would use (2.4.21) to compute dSggfi and determine whether the second part of the second law is obeyed. 

For open systems, the first and second laws are particular forms of the general stuff equation presented in 1.4. The first law represents an energy balance on a system, and it asserts that energy is a conserved quantity. Similarly, the second law represents an entropy balance, but the second law asserts that entropy is not conserved through the actions of dissipative forces, entropy is created (but never consumed) during any irreversible process. 

Consider an open system having any number of inlets a and any number of outlets p. For such a system, the general stuff equation (1.4.1) can be written in terms of the number of moles of species i,... 

For the system in Figure 1.6, the boundary allows transfer of some quantity which, for generality, we call stujf. By identifying all ways by which the amount of stuff may change, we obtain a general balance equation, which we call the stuff equation [11],... 

In general the stuff equation is a differential equation and its accumulation term can be positive, negative, or zero that is, the amount of stuff in the system may increase, decrease, or remain constant with time. In a particular situation several kinds of stuff may need to be inventoried examples include molecules, energy, and entropy. 

The stuff equation applies to both conserved and non-conserved quantities. Conserved quantities can be neither created nor destroyed so, for such quantities the stuff equation reduces to a general conservation principle... 

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. 

The name stuff equation for the general balance equation is not ours, but we are embarrassed to report we don t know who originated the idea. 

In many applications the quantities we can actually measure or manipulate are the heat and work effects on the external side of the system boundary. We call these Qgj f and Wgj f) they would be measiued at a point on the boxmdary at which the surroxmd-ings have temperature and pressxue ext- These external heat and work effects would differ from the heat and work effects felt by the system whenever the system boundary possesses a finite mass that could store energy. In such cases, the second part of the first law for closed systems generalizes (via the stuff equation (1.4.1) and Figure 1.7) to... 

In addition to material and energy balances, we may also perform an entropy balance on the system in Figure 2.11. But since entropy is not conserved (entropy can be generated in the system and its boundary), we must appeal to a more general form of the stuff equation, namely (1.4.1). The balance can be written as a generalization of the first part of the second law (2.3.8), in which terms are now included to account for entropy carried by the streams ... 

This is the general form of the stuff equation for an open system containing a total of C species, some or all of which are engaged in chemical reactions. 

If during a process the rates of accumulation, generation, and consumption are all zero, then the process is said to be in steady state with respect to transfer of that particular stuff. In such cases the general differential balance (1.4.1) reduces to a simple algebraic equation... 

All volume-explidt equations of state should satisfy this limit. For gases composed of small rigid molecules such as nitrogen and carbon dioxide at ambient and higher temperatures, properties are generally within 1% of their ideal-gas values for pressures up to roughly 10 bar. So the stuff you are now breathing is essentially an ideal gas. 

Surely these equations satisfy the requirements for the status of law-like propositions. They describe what happens in all like cases of double replacement reactions, that is they apply generally ceteris paribus, to instances or samples of these material stuffs. Other things being equal clauses are more or less explicitly tacked on. For instance, in the later stages of the universe the Hubble expansion will open up such great distances between the surviving ions that no chemical reactions will occur. The ions will be there, but no products will come to be. 

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