Exchange of matter

The diffcrrential form of the first law as applied to a dosed system, for which there is no exchange of matter between the system and its surroundings, is given by... 

Consider a closed system (i.e., one in which there is no exchange of matter between the system and its surroundings) where a single chemical reaction may occur according to equation 1.1.3. Initially there are ni0 moles of constituent At present in the system. At some later time there are n moles of species At present. At this time the molar extent of reaction is defined as... 

The major function of cutin is to serve as the structural component of the outer barrier of plants. As the major component of the cuticle it plays a major role in the interaction of the plant with its environment. Development of the cuticle is thought to be responsible for the ability of plants to move onto land where the cuticle limits diffusion of moisture and thus prevents desiccation [141]. The plant cuticle controls the exchange of matter between leaf and atmosphere. The transport properties of the cuticle strongly influences the loss of water and solutes from the leaf interior as well as uptake of nonvolatile chemicals from the atmosphere to the leaf surface. In the absence of stomata the cuticle controls gas exchange. The cuticle as a transport-limiting barrier is important in its physiological and ecological functions. The diffusion across plant cuticle follows basic laws of passive diffusion across lipophylic membranes [142]. Isolated cuticular membranes have been used to study this permeability and the results obtained appear to be valid... 

Biological systems are open to the exchange of matter with their environment. If species from the medium (either nutrients or pollutants) travel towards the membrane and a net increase in their concentration arises in the cell, then an uptake process is occurring. Apart from the obvious importance for the organism itself, there is an impact on the medium (e.g. regulating the fate of pollutants in the environment). 

The distribution of residence times gives information on how long various elements of fluid spend in the reactor, but not on the detailed exchange of matter within and between the elements. For a reaction with rate linear in concentration, the extent of reaction can be predicted solely from knowledge of the length of time each molecule has spent in the reactor. The exact nature of the surrounding molecules is of no importance. Thus the distribution of residence times yields sufficient information for the prediction of the average concentration in the reactor effluent. 

However at a critical distance from equilibrium, the system must choose between two possible pathways, represented by the bifurcation point Ac. The continuation of the initial pathway, indicated by a broken hne, indicates the region of instability. The concentration of the species A and the value of A assume quite different values, and the more so, the further from equilibrium. An important point is that the choice between the two branching directions is casual, with 50 50 probability of either. The critical point Ac has particular importance because beyond it, the system can assume an organized structure. Here the term self-organization is introduced as a consequence of the dissipative structures, dissipative in the sense that it results from an exchange of matter and energy between system and environment (we are considering open systems). 

The systems considered here are isothermal and at mechanical equilibrium but open to exchanges of matter. Hydrodynamic motion such as convection are not considered. Inside the volume V of Fig. 8, N chemical species may react and diffuse. The exchanges of matter with the environment are controlled through the boundary conditions maintained on the surface S. It should be emphasized that the consideration of a bounded medium is essential. In an unbounded medium, chemical reactions and diffusion are not coupled in the same way and the convergence in time toward a well-defined and asymptotic state is generally not ensured. Conversely, some regimes that exist in an unbounded medium can only be transient in bounded systems. We approximate diffusion by Fick s law, although this simplification is not essential. As a result, the concentration of chemicals Xt (i = 1,2,..., r with r sN) will obey equations of the form... 

The change in exergy resulting from a change from State 1 to State 2 without any exchange of matter with the dead-state environment is given by... 

The visible matter of galaxies is concentrated in mainly three components stars, interstellar matter, and stellar remnants. Since the early days of galaxy formation there is a vivid exchange of matter between the stellar component and the interstellar matter. Stars are formed in local concentrations of the ISM, the molecular clouds they live for a certain period of time while burning their nuclear fuels and they die... 

For an open system, an additional contribution to the energy due to the exchange of matter dUm occurs... 

If the reaction proceeds in a closed system where there is no exchange of matter with the outside, we have... 

When the fluctuations are due to the exchange of matter between the parts, Eq. (12.6) yields... 

Consider a system enclosed by diathermic walls. As explained in Sec. 1.1, these enclosures prevent exchange of matter but do permit changes in state of the system by manipulations of the surroundings. An example of this situation is provided by a Bunsen burner that is placed below a flask containing ice, water and vapor the diathermic glass walls of the beaker permit the ice to melt in response to the application of a flame exterior to the system (ice, water, steam) and boundary (flask). 

In open systems, which are characterized by an exchange of matter with the surrounding medium, the evolution towards stable thermodynamic equihbrium may appear to be impossible in principle. However, the spon taneous evolution of such systems leads also to some state with its proper ties being dependent on the boundary conditions for the system. We shall consider, in general, that the system exists in a dynamic equilibrium if the imposed boundary conditions are compatible with such equilibrium. The latter means that, for example, the system may achieve a stationary state implying no change in the matter concentration and/or temperature field distribution in time. The typical and limit example of the dynamic equihbrium is indeed the stable thermodynamic equilibrium. 

Operation of such systems is only possible when they have exchange of matter with the environment, i.e. when they are open with respect to the initial reactants and final products i.e. the systems exist in a thermodynamically non equihbrium state. Evidently, the non equihbrium state of open sys terns can only be maintained due to the occurrence of thermodynamic driving forces which are responsible for generation of matter and/or energy flows. 

Figure 4.2. Schematic representation of closed (a, b), open (c) and isolated (d) systems. In system (a) a volatile substance can be exchanged between water and the gas phase. The total quantity of matter within the system remains constant. In system (b) the water phase is closed toward the gas phase no exchange with the gas phase occurs H2CO or NH3 are treated as nonvolatile species. In the open system (c) exchange of matter with the environment occurs for example, a water in equilibrium with the atmosphere is characterized by a constant partial pressure of COaCPco )- System (d) represents an isolated system. No exchange of matter and energy occurs with the environment. (Metaphorically, the system is like a thermos bottle.)...

We notice that the inequality (3.21) applies equally to open systems. For open systems only differ from closed systems in the exchanges of matter and energy, which take place with the surroundings. The transport of entropy d S for open systems includes the term dQjT together with others related to the transport of matter. On the other hand the production of entropy by chemical reactions in the bulk of the system remains unaltered. We shall return to a more detailed study of open systems in the last volume of this work. 

A closed system is one in which no exchange of matter between system and surroundings is permitted. 

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