Transfer of matter

If the T and P of a multiphase system are constant, then the quantities capable of change are the iadividual mole numbers of the various chemical species / ia the various phases p. In the absence of chemical reactions, which is assumed here, the may change only by iaterphase mass transfer, and not (because the system is closed) by the transfer of matter across the boundaries of the system. Hence, for phase equUibrium ia a TT-phase system, equation 212 is subject to a set of material balance constraints ... 

NOTE Electrolytes differ from metallic conductors in that the current is carried by ions, not by electrons (ion from the Greek word meaning to go ), so the passage of an electric current through an electrolyte is always accompanied by the transfer of matter. 

In a nuclear power plant, heat must be transferred from the core to the turbines without any transfer of matter. This is because fission and neutron capture generate lethal radioactive products that cannot be allowed to escape from the core. A heat-transfer fluid such as liquid sodium metal flows around the core, absorbing the heat produced by nuclear fission. This hot fluid then flows through a steam generator, where its heat energy is used to vaporize... 

Mass transfer is a kinetic process, occurring in systems that are not at equilibrium. To understand mass transfer from a thermodynamic perspective, consider the isolated system shown in Figure 1. The system is bounded by an impermeable insulating wall which prevents the transfer of matter, heat, or mechanical energy between the system and the external environment. The system is subdivided into... 

A control volume is a volume specified in transacting the solution to a problem typically involving the transfer of matter across the volume s surface. In the study of thermodynamics it is often referred to as an open system, and is essential to the solution of problems in fluid mechanics. Since the conservation laws of physics are defined for (fixed mass) systems, we need a way to transform these expressions to the domain of the control volume. A system has a fixed mass whereas the mass within a control volume can change with time. 

In reacting systems, transfer of matter and heat occurs by bulk flow and diffusion or conduction. Usually transfer in an axial direction is appreciable by bulk flow only. In a rectangular region the various elements of a material balance in one dimensional flow are,... 

Two immiscible fluids, in contact with each other, share a common surface, called the interface. Operations involving transfer of matter or of heat across an interface are very common in chemical industry. In such operations a large interfacial area per unit volume is necessary if the desired transfer is to be obtained rapidly in equipment of finite size. Three common methods of providing a high ratio of interfacial area to volume are now discussed. 

As the system is at equilibrium at con stant temperature and pressure, any infinitesimal transfer of matter between Phase A and Phase B occurs with a change of zero in... 

Diffusion The transfer of matter or heat as a result of molecular motion. This motion causes net transport from regions of high concentration (or heat) to regions of lower concentration. In the absence of gradients, this motion is random and causes no net transport. Also see Eddy diffusion. 

Already, you should be thinking to yourself But the particles in solids really don t move that mnch and you are certainly correct. They do move or translate in the liquid state of that same solid, however, and don t forget about rotation and vibration, which we will see in subsequent chapters can be very important in solids. But along this line of thinking, we can simplify the First Law of Thermodynamics, which in general terms can be written for a closed system (no transfer of matter between the system and surroundings) as... 

In many cases, the transport of substrates to the cells and that of metabolites from the surface of the cells to the culture medium are carried out at rates characterised by time constants of the same order of magnitude as those of the biological reactions. Transport or transfer of matter must thus be included in an analysis of the behaviour of a bioreactor as well as the kinetic rates [59, 60]. 

Heat flow, whether by radiation, conduction, convection, or the bulk transfer of matter, introduces temperature as another variable. Thus, for systems in motion, thermal similarity requires kinematic similarity. Thermal similarity is described by... 

A curreni of electricity In an electronic conductor is due to a stream of electrons, particles of. subatomic size, and ihe current causes no net transfer of niatrer. The flow is. therefore, in a direction contrary to what is conventionally known as Ihe direction of the current. In electrolytic conductors, flic carriers are charged particles of atomic or molecular size called ions, and under a potential gradient, a transfer of matter occurs. 

The design of heterogeneous chemical reactors falls into a special category because an additional complexity enters into the problem. We must now concern ourselves with the transfer of matter between phases, as well as considering the fluid dynamics and chemistry of the system. Thus, in addition to an equation describing the rate at which the chemical reaction proceeds, one must also provide a relationship or algorithm to account for the various physical processes which occur. For this purpose it is convenient to classify the reactions as gas-solid, gas-liquid and gas-liquid-solid processes. The present chapter will be concerned with gas-solid reactions, especially those for which the solid is a catalyst for the reaction. 

Analogies have been developed between heat transfer and fluid friction (i.e., energy and momentum analogies) [5-7]. Similarly, analogies have been developed for systems having a transfer of matter by diffusion accompanied by heat transfer [8-10], Our discussion here is limited to flow in a tube. 

One of our recently-developed systems is a good example of adapting laboratory methods to ln-sltu field measurements. We developed this system to measure the exchange of CO2 between the atmosphere and the surface of the earth. The transfer of matter and energy from a... 

The meaning and also the limitation of the term possible variations must be considered. For the purposes of discussion, we center our attention on Equation (5.2) and consider a heterogenous, multicomponent system. The independent variables that are used to define the state are the entropy, volume, and mole numbers (i.e., amount of substance or number of moles) of the components. The statements of the condition of equilibrium require these to be constant because of the isolation of the system. Possible variations are then the change of the entropy of two or more of the phases subject to the condition that the entropy of the whole system remains constant, the change of the volume of two or more phases subject to the condition that the volume of the whole system remains constant, or the transfer of matter from one phase to another subject to the condition that the mass of the whole system remains constant. Such variations are virtual or hypothetical,... 

When we consider a one-component, two-phase system, of constant mass, we find similar relations. Such two-phase systems are those in which a solid-solid, solid-liquid, solid-vapor, or liquid-vapor equilibrium exists. These systems are all univariant. Thus, the temperature is a function of the pressure, or the pressure is a function of the temperature. As a specific example, consider a vapor-liquid equilibrium at some fixed temperature and in a state in which most of the material is in the liquid state and only an insignificant amount in the vapor state. The pressure is fixed, and thus the volume is fixed from a knowledge of an equation of state. If we now add heat to the system under the condition that the temperature (and hence the pressure) is kept constant, the liquid will evaporate but the volume must increase as the number of moles in the vapor phase increases. Similarly, if the volume is increased, heat must be added to the system in order to keep the temperature constant. The change of state that takes place is simply a transfer of matter from one phase to another under conditions of constant temperature and pressure. We also see that only one extensive variable—the entropy, the energy, or the volume—is necessary to define completely the state of the system. 

Thus, the enthalpy is a function of the entropy and the Helmholtz energy is a function of the volume, and each function may be used in place of the other variable. However, the Gibbs energy is a constant for any closed system at constant temperature and pressure, and therefore its value is invariant with the transfer of matter within the closed system. 

A system which does not allow transfer of matter between the system and the surroundings. 

If there is a difference in chemical potential, the transfer of energy occurs as transfer of matter. Chemical potential is a measure of the tendency of the species to leave the phase, to react or to spread throughout the phase through chemical reaction, diffusion, etc. 

CLOSED SYSTEM. CLOSED PHASE. No transfer of matter across boundaries of system... 

Generalising for any system containing n components in p phases the conditions governing the transfer of matter between phases are ... 

Further insight regarding the concept of the chemical potential may be obtained as follows Consider a two-phase, one—component system at fixed temperature and pressure for which G - niPi + n p, and suppose that at some instant > px. The system can then not be at equilibrium instead, some spontaneous process must occur which ultimately results in the equalization of and. At constant T and P this can occur only by a transfer of matter from one phase to the other. Let there be a transfer of - dnx - + dn > 0 moles from phase 1 to phase 2 then dG — (p — p1)dn1, where we have set dnx = dnx. Since we assumed p > the preceding relation shows that dG < 0 for this case i.e., the transfer of matter from the phase of higher chemical potential to the phase of lower chemical potential occurs spontaneously. Thus, a difference in chemical potential represents a driving force for transfer of chemical... 

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