APPLICATIONS OF THERMODYNAMICS TO FLOW PROCESSES

The themiodynamics of flow is based on mass, energy, and entropy balances, which have been developed in Chaps. 2 and 5. The application of tliese balances to specific processes is considered in this chapter. The discipline imderlying tlie study of flow is fluid mechanics, which encompasses not only the balances of thermodynamics but also the linear-momentum principle (Newton s second law). This makes fluid mechanics a broader field of study. The distinction between thermodynamics problems and fluid-mechanics problems depends on whether this principle is required for solution. Those problems whose solutions depend only on mass conservation and on the laws of thermodynamics are commonly set apart from the study of fluid mechanics and are treated in courses on thermodynamics. Fluid mechanics then deals with the broad spectmm of problems which require application of the momentum principle. This division is arbitrary, but it is traditional and convenient. 

Flow processes inevitably result from pressure gradients witliin tire fluid. Moreover, temperature, velocity, and even concentration gradients may exist witliin the flowing fluid. This contrasts witlr tire uniform conditions tlrat prevail at equilibrium in closed systems. The distribution of conditions in flow systems requires tlrat properties be attributed to point masses of fluid. Thus we assume tlrat intensive properties, such as density, specific enthalpy, specific entropy, etc., at a point are determined solely by the temperature, pressure, and composition at tire point, uirinfluenced by gradients tlrat may exist at tire point. Moreover, we assume that the fluid exlribits tire same set of intensive properties at the point as tlrough it existed at equilibrium at tire same temperature, pressure, and composition. The implication is tlrat an equation of state applies locally and instantaneously at any point in a fluid system, and tlrat one may invoke a concept of local state, independent of tire concept of equilibrium. Experience shows tlrat tlris leads for practical purposes to results in accord with observation. 

The equations of balance for open systems from Clraps. 2 and 5 are summarized here hr Table 7.1 for easy reference. Included are Eqs. (7.1) and (7.2), restricted forms of tire mass balance. These equations are the basis for the themrodynanricanalysis ofprocesses in tlris and the next two clrapters. When combined with themrodynanric property statements, they allow calculation of process rates and system states. 

The appropriate energy balance is Eq. (2.32). With Q, Wj and Az all set equal to zero, 

The continuity equation, Eq. (2.27), is also applicable. Since m is constant, its differential fonnis  

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Hie applications of thermodynamics to flow processes usually are to finite amounts of fluid undergoing finite changes in state. One might, for example, deal with the flow of gas through a pipeline. If the states and thermodynamic properties of the gas entering and leaving the pipeline are known, then application of the... 

Two idealizations are imposed from the start to facilitate the application of S thermodynamic principles to flow processes ... 

The relationship we are about to describe is due to the work of Pierre Duhem (1861-1916) a French physicist who translated Gibbs work into French and was in his own rights a prolific author of thermodynamic studies. So far the applications of thermodynamic (except for the on-stream ammonia synthesis discussed above) have been for what are closed systems where it is possible to enclose the system with a boundary and separate it from the environment. Many of the synthetic applications in chemical engineering are carried out with on-stream processing rather than in a batch reactor, a system in which a continuous flow of reactants is processed and continuous product flows out of some sort of reaction chamber. While most laboratory synthesis is carried out in batch fashion, there are also static phenomena, which depend on adding an arbitrary amount of one... 

In equilibrium thermodynamics, entropy maximization for a system with fixed internal energy determines equilibrium. Entropy increase plays a large role in irreversible thermodynamics. If each of the reference cells were an isolated system, the right-hand side of Eq. 2.4 could only increase in a kinetic process. However, because energy, heat, and mass may flow between cells during kinetic processes, they cannot be treated as isolated systems, and application of the second law must be generalized to the system of interacting cells. 

From the previous Section it is expected that the application of the flow field will primarily affect the last two order parameters, i.e. the orientation and conformation of the chain. In the discussion of the nucleation dynamics, it is helpful to separate the contributions from the kinetic and thermodynamic processes. The first represents the fundamental timescale to form a nucleus, the prefactor, and the second describes the driving force for the phase transition based on the position of the system in the phase diagram. 

Development of the "flow" MEIS with the form reminding the models of nonequilibrium thermodynamics seems to be a very promising direction in equilibrium modeling of physical and chemical systems. Application of these models opens prospects for simpler analysis and solution of many complex problems related to the calculations of processes considered to be irreversible in principle. Certainly the flows in MEIS are interpreted statically as the coordinates of states. Thermodynamic interpretations are naturally extended to the kinetic coefficients that relate these flows with forces. Correctness of such interpretations is confirmed by the application of MP, being the theory of equilibrium states, as the terms for MEIS description. 

In Chap. 2 the first law of thermodynamics was applied to closed systems (nonflo processes) and to single-stream, steady-state flow processes to provide specifi equations of energy conservation for these important applications. Our purpos here is to present a more general equation applicable to an open system or to control volume. 

The theory treating near-equilibrium phenomena is called the linear nonequilibrium thermodynamics. It is based on the local equilibrium assumption in the system and phenomenological equations that linearly relate forces and flows of the processes of interest. Application of classical thermodynamics to nonequilibrium systems is valid for systems not too far from equilibrium. This condition does not prove excessively restrictive as many systems and phenomena can be found within the vicinity of equilibrium. Therefore equations for property changes between equilibrium states, such as the Gibbs relationship, can be utilized to express the entropy generation in nonequilibrium systems in terms of variables that are used in the transport and rate processes. The second law analysis determines the thermodynamic optimality of a physical process by determining the rate of entropy generation due to the irreversible process in the system for a required task. 

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