Thermodynamic systems closed

A thermodynamic system (closed system) is one that interacts with the surroundings by exchanging heat and work thru its boundary an isolated system is one that does not interact with the surroundings. The state of a system is determined by the values of its various properties, eg, pressure, volume, internal energy, etc. A system can be composed of a finite number of homogeneous parts, called phases, or there can be a single phase. For some applications, it may... 

Consider two distinct closed thermodynamic systems each consisting of n moles of a specific substance in a volnme Vand at a pressure p. These two distinct systems are separated by an idealized wall that may be either adiabatic (lieat-impemieable) or diathermic (lieat-condncting). Flowever, becanse the concept of heat has not yet been introdnced, the definitions of adiabatic and diathemiic need to be considered carefiilly. Both kinds of walls are impemieable to matter a permeable wall will be introdnced later. 

In order to obtain a qualitative view of how the transition regime differs from the continuum flow or the slip flow regime, it is instructive to consider a system close to thermodynamic equilibrium. In such a system, small deviations from the equilibrium state, described by thermodynamic forces X, cause thermodynamic fluxes J- which are linear functions of the (see, e.g., [15]) ... 

Figure 3.1 Schematic representations of thermodynamic systems a) isolated system, b) closed system and c) open system...

Most thermochemical calculations are made for closed thermodynamic systems, and the stoichiometry is most conveniently represented in terms of the molar quantities as determined from statistical calculations. In dealing with compressible flow problems in which it is essential to work with open thermodynamic systems, it is best to employ mass quantities. Throughout this text uppercase symbols will be used for molar quantities and lowercase symbols for mass quantities. 

Heat Content or Enthalpy. A thermodynamic property closely related to energy. It is defined by H = E + PV where E is the internal energy of the system, P is the pressure on the system and V is the volume of the system. Often it is used in differential form as in. AH = AE + PAV for a constant pressure process... 

Exercise. In particular this situation obtains if the equation refers to a closed thermodynamic system. The corresponding matrix S oo) = is known from equilib-... 

In many cases, the study of kinetics concerns itself with the paths and rates adopted by systems approaching equilibrium. Thermodynamics provides invaluable information about the final state of a system, thus providing a basic reference state for any kinetic theory. Kinetic processes in a large system are typically rapid over short length scales, so that equilibrium is nearly satisfied locally at the same time, longer-length-scale kinetic processes result in a slower approach to global equilibrium. Therefore, much of the machinery of thermodynamics can be applied locally under an assumption of local equilibrium. It is clear, therefore, that the subject of thermodynamics is closely intertwined with kinetics. 

Consider a material or system that is not at equilibrium. Its extensive state variables (total entropy number of moles of chemical component, i total magnetization volume etc.) will change consistent with the second law of thermodynamics (i.e., with an increase of entropy of all affected systems). At equilibrium, the values of the intensive variables are specified for instance, if a chemical component is free to move from one part of the material to another and there are no barriers to diffusion, the chemical potential, q., for each chemical component, i, must be uniform throughout the entire material.2 So one way that a material can be out of equilibrium is if there are spatial variations in the chemical potential fii(x,y,z). However, a chemical potential of a component is the amount of reversible work needed to add an infinitesimal amount of that component to a system at equilibrium. Can a chemical potential be defined when the system is not at equilibrium This cannot be done rigorously, but based on decades of development of kinetic models for processes, it is useful to extend the concept of the chemical potential to systems close to, but not at, equilibrium. 

Thermodynamic systems are parts of the real world isolated for thermodynamic study. The parts of the real world which are to be isolated here are either natural water systems or certain regions within these systems, depending upon the physical and chemical complexity of the actual situation. The primary objects of classical thermodynamics are two particular kinds of isolated systems adiabatic systems, which cannot exchange either matter or thermal energy with their environment, and closed systems, which cannot exchange matter with their environment. (The closed system may, of course, consist of internal phases which are each open with respect to the transport of matter inside the closed system.) Of these, the closed system, under isothermal and iso-baric conditions, is the one particularly applicable for constructing equilibrium models of actual natural water systems. 

The general relationships involved for a single chemical reaction in a closed system are shown schematically in Figure 1, where the degree of advancement at point e corresponds to chemical equilibrium. Point t represents a state of the system corresponding to spontaneous chemical reaction. While the invariant condition of the closed system considered is the equilibrium state, e, this generally is not the case for a thermodynamic system open to its environment. For such a system, the time-... 

Carbon System. A diagram has not been given for the carbon system since the major feature is simply a conversion of predominant C02 to predominant CH4 with the half-way point at pE(W) = —4.13. At this pE value, where the other oxidation states exhibit maximum relative occurrence, the equilibrium concentration of HCOO" is just 6 X 10-10M, that of CH20 only 5 X 10 17M and that of CH3OH only 10 14M. Formation of solid carbon is thermodynamically possible close to pE = —4.13, but its inclusion does not change other relationships significantly. 

Closed Systems Closed systems exchange energy with their environment through their boundaries, but they do not exchange matter. The simplest example is the nonadiabatic batch reactor. These systems also tend towards a thermodynamic equilibrium with time, again characterized by maximal entropy, or the highest possible degree of disorder. 

Studies of linear systems and systems without "intermediate interactions show that a positive steady state is unique and stable not only in the "thermodynamic case (closed systems). Horn and Jackson [50] suggested one more class of chemical kinetic equations possessing "quasi-ther-modynamic properties, implying that a positive steady state is unique and stable in a reaction polyhedron and there exist a global (throughout a given polyhedron) Lyapunov function. This class contains equations for closed systems, linear mechanisms, and intersects with a class of equations for "no intermediate interactions reactions, but does not exhaust it. Let us describe the Horn and Jackson approach. 

The heat capacities that have been discussed previously refer to closed, single-phase systems. In such cases the variables that define the state of the system are either the temperature and pressure or the temperature and volume, and we are concerned with the heat capacities at constant pressure or constant volume. In this section and Section 9.3 we are concerned with a more general concept of heat capacity, particularly the molar heat capacity of a phase that is in equilibrium with other phases and the heat capacity of a thermodynamic system as a whole. Equation (2.5), C = dQ/dT, is the basic equation for the definition of the heat capacity which, when combined with Equation (9.1) or (9.2), gives the relations by which the more general heat capacities can be calculated. Actually dQ/dT is a ratio of differentials and has no value until a path is defined. The general problem becomes the determination of the variables to be used in each case and of the restrictions that must be placed on these variables so that only the temperature is independent. 

The discontinuous stirred reactor (Batch Reactor, BR, Fig. 2.1(a)) corresponds to a closed thermodynamic system, whereas the two continuous reactors (Continuous Stirred Tank Reactor, CSTR, Fig. 2.1(b), and Plug Flow Reactor, PFR, Fig. 2.1(c))... 

The physical laws of conservation of mass, momentum, and energy are commonly formulated for closed thermodynamic systems,2 and for our purposes, we need to transfer these to open control volume3 formulations. This can be done using the Reynolds Transport Theorem.4... 

In physics and chemistry we call an ensemble of substances a thermodynamic system consisting of atomic and molecular particles. The system is separated from the surroundings by a boundary interface. The system is called isolated when no transfer is allowed to occur of substances, heat, and work across the boundary interface of the system as shown in Fig. 1.1. The system is called closed when it allows both heat and work to transfer across the interface but is impermeable to substances. The system is called open if it is completely permeable to substances, heat, and work. The open system is the most general and it can be regarded as a part of a closed or isolated system. For instance, the universe is an isolated system, the earth is regarded as a closed system, and a creature such as a human being corresponds to an open system. 

Figure 29.2 displays three situations at constant temperature, T and pressure, P. In diagram (a) we have a single closed phase (labelled a) which contains two components labelled 1 and 2 whose chemical potentials are and but the thermodynamic system is such that no matter can be transferred across the boundaries of the system. Hence adapting equation (29.6) to apply to this case, the change in free energy, dG a) for the system is given by ... 

In an irreversible process, in conformity with the second law of thermodynamics, the magnitude that determines the time dependence of an isolated thermodynamic system is the entropy, S [23-26], Consequently, in a closed system, processes that merely lead to an increase in entropy are feasible. The necessary and sufficient condition for a stable state, in an isolated system, is that the entropy has attained its maximum value [26], Therefore, the most probable state is that in which the entropy is maximum. 

No information can be deduced about the entropy variation in the intermediate range of reaction rates however, the process is not isentropic because equation n. C. 2. does not go to zero. Considerarions from irreversible thermodynamics show that the entropy must always rise in a closed thermodynamic system when irreversible reaction processes take place (25). 

Evidently, the uncatalyzed direct thermal decomposition is simply too unattractive from both a thermodynamic and kinetic viewpoint to be seriously considered for a practical process. Work has therefore focussed on methods for increasing the reaction yields under more moderate process conditions. Unfortunately, thermodynamics cannot be violated but thermodynamic limitations can be sidestepped, and kinetic limitations can be overcome using catalysts. Four principle types of techniques are being investigated for improved yields including upset equilibrium systems, closed cycle loops, open cycle loops, and electrochemical methods. The advantages and disadvantages of these will now be discussed more fully. 

In this section we study closed systems (closed to mass transport but not energy transfer) held at constant temperature. In statistical mechanics these systems are referred to as NVT systems (because the thermodynamic variables N, V, and T are held fixed). We shall see that the Helmholtz free energy represents the driving force for NVT systems. Just as an isolated system (an NVE system) evolves to increase its entropy, an NVT system evolves to decrease its Helmholtz free energy. 

Stochastic models for biochemical reaction systems in terms of the CME are not an alternative to the differential equation approach, but a more general theoretical framework that deserves further investigation. In particular, the relation between the dynamic CME and the general theory of statistical thermodynamics of closed and... 

---