Process impossible

Assigning monetary values to other considerations may be difficult or impossible. Process flexibility and equipment availability may be critical. For instance, to accommodate beneficial trade considerations it may be desirable to manufacture a product in another country, whereas a route that uses locally available equipment may be selected. Financial projections may be necessary to decide whether... 

So refined is a production process that supervised operators who are not chemists or even scientists can carry it out. Their workplace may be so far from the development laboratories that frequent oversight by the researchers is impossible. Process chemists therefore compose clear, comprehensive instructions covering each reaction, work-up, and purification. 

It has now been demonstrated how considerations of work and heat changes in cyclical processes combined with a statement of the Second Law lead to the development of a quantity that can distinguish possible from impossible processes under certain conditions. The next step is to combine this with a statement of the First Law to get our first look at a fundamental equation . 

Why in the world would we be interested in such a strange kind of impossible process It s simple, really. The reason the reversible process (defined as a continuous succession of equilibrium states) is important in the thermodynamic model is that it is the only kind of process that our mathematical tools of differentiation and integration can be applied to - they only work on continuous functions. Once our crystal of diamond leaves its state of equilibrium at 25 °C, practically anything could happen to it, but as long as it settles back to equilibrium at 50 °C, all of its state variables have changed by fixed amounts from their values at 25 °C. We have equations to calculate these energy differences, but they refer to lines and surfaces in our model, and that means that they must refer to continuous equilibrium between the two states. 

All the deviations from ideahty are now captured in the activity coefficient, and since solutes obey Hemy s law as their concentrations approach zero, a a and Ka 1 as WA 0. The activity coefficients of a solute can be estimated by Debye-Hiickel theory using interionic forces to estimate aggregation. That said, this is an exceedingly difficult if not impossible process for solutions containing multiple species. As a result, it is normally assumed that Ka = 1 and the conditions under study amount to an ideal dilute solution. This assumption also negates the practical difficulties with measuring activities of solutions, because under ideal, dilute conditions the activity of the solute is numerically equal to its (more readily measured) concentration. 

Finally, it may be remarked that when we speak of a possible or impossible process the notion of time s passage is implicit. It is a question of whether a state A can precede or succeed another state B, in an adiabatic enclosure. The decision which of these states is later than or earlier than the other is based primarily on the subjective time sense of the human observer— which is not to say however that, once the second law has been seen to be true for all isolated systems, we cannot choose one such system as defining the time direction for all the rest. This can be done without reducing the law to a tautology. ... 

An impossible process is a change that cannot occur under the existing conditions, even in alimiting sense. It is also known as an unnatural or disallowed process. Sometimes it is useful to describe a h)q)Othetical impossible process that we can imagine but that does not occur in reality. The second law of thermodynamics will presently be introduced with two such impossible processes. 

The spontaneous processes relevant to chemistry are irreversible. An irreversible process is a spontaneous process whose reverse is an impossible process. 

It is true that reversible processes and purely mechanical processes are idealized processes that cannot occur in practice, but a spontaneous process can be practically reversible if carried out sufficiently slowly, or practically purely mechanical if friction and temperature gradients are negligible. In that sense, they are not impossible processes. This book will reserve the term impossible for a process that cannot be approached by any spontaneous process, no matter how slowly or how carefiiUy it is carried out... 

Consider the process depicted in Fig. 4.1(a) on the next page. The system is isolated, and consists of a cool body in thermal contact with a warm body. During the process, energy is transferred by means of heat from the cool to the warm body, causing the temperature of the cool body to decrease and that of the warm body to increase. Of course, this process is impossible we never observe heat flow from a cooler to a warmer body. (In contrast, the reverse process, heat transfer from the warmer to the cooler body, is spontaneous and irreversible.) Note that this impossible process does not violate the first law, because energy is conserved. 

These processes would not be impossible if we could control the trajectories of large numbers of individual particles. Newton s laws of motion are invariant to time reversal. Suppose we could measure the position and velocity of each molecule of a macroscopic system in the final state of an irreversible process. Then, if we could somehow arrange at one instant to place each molecule in the same position with its velocity reversed, and if the molecules behaved classically, they would retrace their trajectories in reverse and we would observe the reverse impossible process. 

The second law establishes no general relation between entropy changes and heat in an open system, or for an impossible process. The entropy of an open system may increase or decrease depending on whether matter enters or leaves. It is possible to imagine different impossible processes in which dS is less than, equal to, and greater than dq/ Tb. 

In an isolated system, an equilibrium state cannot change spontaneously to a different state. Onee the isolated system has reached an equiUhrium state, an imagined finite change of any of the independent variables consistent with the eonstraints (a so-ealled virtual displacement) corresponds to an impossible process with an entropy deerease. Thus, the equiUbrium state has the maximum entropy that is possible for the isolated system. In order for 5 to be a maximum, dS must be zero for an infimtesimal ehange of any of the independent variables of the isolated system. 

For such questions, we cannot refer to the first law of thermodynamics. The first law does not distinguish between possible and impossible processes the first law only describes the changes of energy in a thermodynamic system if a specified process develops. The first law is the energy account of thermodynamics, i.e. the bookkeeping that monitors the conservation of energy. 

According to classical thermodynamics, any process occurring in an isolated system is connected with an increase in entropy according to the Clausius inequality, a spontaneous process reducing the entropy in an isolated system is an impossible process. 

To understand this apparently contradictory notion of the concept impossible process , it can be useful - even if only roughly - to look into a specific example of the Boltzmann relation (4.34). Assume an isolated system containing 1 mol of ideal gas in thermodynamic equilibrium in state (1). What is the probability that a spontaneous change of state will reduce the entropy content of the system by AS = 1 J/K ... 

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