JCE 1997 (74) 286 [Mar] An Exceptional = Theoretical Process Belandria replies

From: Subject: JCE 1997 (74) 286 [Mar] An Exceptional Theoretical Process Belandria replies Date: Mon, 12 Jul 2010 23:26:43 -0400 MIME-Version: 1.0 Content-Type: text/html; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Content-Location: http://webdelprofesor.ula.ve/ingenieria/joseiraides/publicaciones/exceptionaltheoreticalprocessbelandriareplies.htm X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.5512 JCE 1997 (74) 286 [Mar] An Exceptional = Theoretical Process Belandria replies

An = Exceptional=20 Theoretical Process Belandria replies

Jose Iraides Belandria
Universidad de los = Andes,=20 Merida, Venezuela

I appreciate this opportunity to demonstrate that = there is=20 no fundamental problem with my paper as some readers = believe.=20 Instead it shows a transformation that fits general=20 thermodynamic restrictions and exhibits an internal = entropy=20 coupling that generate an unexpected behavior not seen = in=20 conventional thermodynamic systems.=20

To analyze letters on my article I am going to = answer first=20 comments that are common across all letters and then = comments=20 that are specific for each author.=20

A general comment related to feasibility considers = that the=20 process described in Figure 1 of the article is not = permitted=20 by thermodynamic laws. In this respect thermodynamics = suggests=20 that for a process to be feasible temperature must be = greater=20 than 0 K, energy must be conserved, and the total = entropy=20 change of the universe should be equal to or greater = than zero=20 (15). I have demonstrated in the article = that the=20 process sketched in Figure 1 fits the above = requirements.=20 Therefore, its operation meets general thermodynamic=20 requisites and it should be feasible.=20

In any case, an intuitive view of the dynamics of = the=20 process suggests that once the adiabatic film covering = the=20 metal partition is removed, transition starts with a=20 spontaneous heat transfer between tank A and = B,=20 caused by a temperature gradient across the metal = separation.=20 Simultaneously, compression begins at a controlled = rate to=20 keep isothermal conditions in A. Then = transformation=20 may continue to reach the final state according to = prediction.=20

It is convenient to say that the process shows a = set of=20 conditions where internal entropy is simultaneously = created=20 and destroyed in different parts of the universe. This = is an=20 interesting behavior suggesting the existence of an = internal=20 entropy coupling not seen before in common systems. = Under=20 these conditions the process is more efficient than a=20 conventional reversible operation.=20

Now, the important fact here is that this = unexpected=20 universe may exist because it meets general = thermodynamic=20 requirements. Otherwise, articulation of thermodynamic = laws=20 should be reviewed to consider this case.=20

Another common comment considers that the process = of Figure=20 1 is not allowed by thermodynamics because it is = impossible=20 that the isothermal compression process with internal = entropy=20 coupling requires less work than a conventional = reversible=20 isothermal compression for the same initial and final = state.=20

To this objection, it is interesting to detect that = by=20 linking together a nonreversible isothermal = compression with a=20 heat transfer between two tanks it is possible to find = a=20 feasible set of conditions where the nonisothermal = compression=20 work input is less than the work required by a common=20 reversible isothermal compression for the same initial = and=20 final states.=20

This result is unexpected from the point of view of = classical thermodynamics, but irreversible = thermodynamics=20 suggests that such a behavior may occur as a = consequence of=20 the simultaneous production and destruction of = internal=20 entropy in different parts of the universe. Here an = oriented=20 heat transfer between tank A and tank B = produces=20 or creates enough internal entropy to drive a = simultaneous=20 nonreversible isothermal compression in tank A = with=20 destruction of internal entropy. Some authors believe = that=20 production of internal entropy causes a loss in = capacity to do=20 work (1, 3). Then, by analogy, destruction of = internal=20 entropy may increase the ability of the system to = produce=20 work. In this context the net result of simultaneous=20 production and destruction of internal entropy is a = gain in=20 capacity of the system to do work relative to the=20 corresponding reversible isothermal compression. = During the=20 operation energy is conserved and the total entropy = change of=20 the universe is greater than zero, fitting general=20 thermodynamic requirements.=20

Behavior exhibited by this process implies that=20 irreversibility under internal entropy coupling = conditions may=20 enhance the ability of a system to do work relative to = an=20 equivalent reversible operation for the same change of = state.=20 I have further confirmed this by designing a feasible=20 thermodynamic cycle with internal entropy coupling = resulting=20 in a cycle of greater efficiency than an equivalent = Carnot=20 cycle operating between the same temperature levels = (6,=20 7, J. I. Belandria, unpublished). This finding is = unusual=20 and reveals an extraordinary feature of internal = entropy=20 coupling systems that suggests the possibility of = designing=20 feasible thermodynamic cycles more efficient than = conventional=20 classical ones by introducing steps involving = simultaneous=20 production and destruction of internal entropy.=20

All the letters estimate the final pressure reached = by a=20 conventional reversible isothermal compression at 1500 = K using=20 as work input the value required in Figure 1 and find = 3.086=20 atm. They argue correctly that a reversible = compression cannot=20 reach the final pressure of 4 atm obtained by the = system=20 sketched in Figure 1. This is true because the process = described in the article is more efficient than a = conventional=20 reversible isothermal compression as a consequence of = the=20 simultaneous production and destruction of internal = entropy,=20 as I explained earlier.=20

Some letters express opinions in relation to = specification=20 of the final state. For example, Nash wonders "where = the=20 author gets his figure for the final pressure in tank=20 A". Tykodi says "he assumes an impossible = condition in=20 the final state for his illustrative process".=20

Olivares and Colmenares state that "the final = pressure of=20 405.32 kPa used by Belandria is unattainable". And = Freeman=20 considers that "he has simply postulated initial and = final=20 conditions without providing data about the change".=20

To get the final pressure I set up a thermodynamic = model=20 for the whole process using eqs 33 to 42 and = investigated the=20 changes of state permitted by thermodynamic laws, = keeping=20 energy constant and the total entropy change of the = universe=20 equal to or greater than zero. Surprisingly, I = detected a set=20 of conditions allowed by general thermodynamic = restrictions=20 where internal entropy is simultaneously created and = destroyed=20 in different regions of the universe, and the work = required=20 for the nonreversible isothermal compression is less = than the=20 value expected from classical thermodynamics. Then I = selected=20 at random one of these exceptional changes of state = and=20 designed the process shown in Figure 1 of the article. = I have=20 found that there is an infinite set of such states and = several=20 transformations that permit an internal entropy = coupling=20 process.=20

The model indicates that the total entropy change = of the=20 universe is less than zero for temperatures in tank = A=20 below 940.14 K, keeping constant other variables. = Therefore,=20 the process is not allowed by thermodynamics in this = range of=20 temperature. Here, internal entropy destruction in = tank=20 A is greater than production of internal = entropy by=20 heat transfer.=20

For temperatures in tank A above 940.14 K = the total=20 entropy change of the universe is greater than zero = and the=20 process should be allowed by the second law of = thermodynamics.=20 It is possible to see that for temperatures between = 940.14 K=20 and 4948.20 K the process shows an interesting and = unexpected=20 behavior suggesting an internal entropy coupling. In = this=20 range, internal entropy is simultaneously produced and = destroyed in different regions of the universe, and = the=20 nonreversible compression in tank A is more = efficient=20 than a reversible isothermal compression. At 940.14 K = the=20 production of internal entropy is equal to destruction = of=20 internal entropy and efficiency reaches its maximum = value. A=20 thermodynamic cycle operating in the region of almost=20 cancellation of internal entropy shows a greater = efficiency=20 than an equivalent Carnot cycle working between the = same=20 temperature levels (6, 7, J. I.=20 Belandria, unpublished).=20

For temperatures in tank A greater than = 4948.20 K,=20 internal entropy is created in all regions of universe = and the=20 system operates according to classical thermodynamics=20 expectations.=20

From this analysis it seems that in some relatively = simple=20 interconnected systems, general thermodynamic = restrictions may=20 allow the theoretical existence of a region with = simultaneous=20 creation and destruction of internal entropy. Under = certain=20 conditions close to equal production and destruction = of=20 internal entropy, the process exhibits a = superefficiency, as=20 Tykodi expresses. In this transformation, thermal = death is=20 retarded or avoided by the internal entropy coupling = process,=20 keeping variation of the total entropy of the universe = as low=20 as possible.=20

In some letters Nash, Tykodi, and Olivares and = Colmenares=20 comment about entropy destruction. Tykodi opines that = "there=20 is never entropy destruction". Nash asks "if we should = give=20 credit to entropy destruction" and Olivares and = Colmenares=20 follow Prigogine's statement that "we can therefore = say that=20 absorption of entropy in one part, compensated by a = sufficient=20 production in another part of the system is = prohibited".=20

To this question, irreversible thermodynamics = suggests the=20 possibility of simultaneous creation and destruction = of=20 internal entropy in relatively complex systems. These=20 transformations have been detected in multireaction = and=20 biological systems, thermodiffusion, and active = transport of=20 ions, and in thermomechanical closed systems=20 (58). In these systems there is at = least a=20 process that creates internal entropy coupled to a=20 simultaneous transformation that destroys internal = entropy.=20 The destruction of internal entropy is not expected to = take=20 place by itself in a single process but can be made to = occur=20 by coupling it with another simultaneous process that = creates=20 enough internal entropy to compensate internal entropy = destruction.=20

Freeman, Nash, and Olivares and Colmenares discuss = the=20 creation of internal entropy across a metallic = partition.=20 Freeman says that reference to creation of entropy in = the=20 metal partition "smacks of witchcraft" because an = object with=20 no mass and no heat capacity cannot create entropy. He = explains that there is an increase in entropy as a = result of=20 energy flow through the partition, but the increase = arises=20 from the difference in temperature on the two sides of = the=20 partition. Nash indicates that "the increase in=20 S_univ is a simple consequence of the = flow of=20 heat from a hotter body A to a cooler = B". And=20 Olivares and Colmenares calculate the creation of = internal=20 entropy due to heat flow through the metallic = partition,=20 concluding incorrectly that there is no creation of = internal=20 entropy in this transition.=20

Now, in my article, system M is the metal = partition=20 of negligible mass surrounded by an imaginary surface=20 representing the boundaries of system M. = Surrounding=20 system M are tanks A and B at = different=20 initial temperatures. Therefore, there is a heat flow = from=20 tank A to B through limits of system = M.=20 System M is receiving heat Q_a = at a=20 constant temperature T_A and = expelling it to=20 a source at a variable temperature = T_B=20 without accumulation of energy or entropy. It is = evident, as=20 Nash and Freeman say, that there is a creation of = entropy that=20 may be attributed to heat flow from A to = B=20 arising as a consequence of the difference in = temperature on=20 the two sides of the partitions. I would like to say = that the=20 entropy balance expressed by eq 27 of the article is = based on=20 this consideration and I have assumed for convenience = that=20 internal entropy creation is located within the = boundaries of=20 system M.=20

On the other hand, Olivares and Colmenares try to = make=20 rigorous demonstrations to estimate the creation or = production=20 of internal entropy in the process of Figure 1 and = find=20 erroneously that there is no production of internal = entropy by=20 heat flow through the partition.=20

They attempt to evaluate entropy flow through the = metal=20 partition using eq 17 of their comments. They did not = realize=20 that their procedure evaluated the variation of = entropy inside=20 the metal partition rather than the entropy flow = generated by=20 heat transfer from tank A to tank B. = Next, they=20 concluded that eq 19 represents entropy flow across = the metal=20 partition. Indeed, eq 19 takes into account the = variation of=20 internal entropy inside the partition and does not = represent=20 the entropy flow caused by heat transfer from tank = A to=20 tank B through barrier boundaries. This is = demonstrated=20 when they calculate the entropy change of the metal = partition=20 and obtain eq 20, which is identical to eq 19, = confirming my=20 hypothesis. When eqs 19 and 20 are introduced in the = entropy=20 balance expression given by eq 21, they obtain zero = production=20 of internal entropy. Obviously, Olivares and = Colmenares are=20 not correct because everybody knows that internal = entropy is=20 produced when heat transfer takes place across a = finite=20 temperature difference. Freeman, Nash, and = conventional=20 engineering thermodynamic textbooks confirm opinion = suggesting=20 that entropy should be produced by the flow of heat = from=20 A to B through a metal partition = (4,=20 5).=20

From this wrong conclusion, Olivares and Colmenares = consider that no entropy coupling exists and the = process is=20 not allowed by thermodynamic laws because the internal = entropy=20 destroyed in tank A is not compensated by = production of=20 internal entropy. This is not true, and whatever = conception we=20 select to analyze the process of Figure 1, we find = that=20 creation of internal entropy should occur as a = consequence of=20 heat transfer across a finite temperature difference. = Also,=20 when they calculate the total entropy production of = the=20 universe with eq 25 they find 5.83 JK^-1. By = a=20 simple balance if -2.16 JK^-1 is destroyed = in tank=20 A, then 7.99 JK-1 should be created in some = other=20 place. According to the discussion, such creation must = be=20 attributed to heat flow across the metal partition = because=20 nothing else produces entropy in my process. Therefore = they do=20 not solve the "paradox" affecting general validity of=20 Prigogine's formulation as they say.=20

Next, they comment that my eq 27 used to estimate = creation=20 of internal entropy is not correct and does not have=20 thermodynamic foundations. To this I would say that = such an=20 equation comes from a simple entropy balance in a = metal=20 partition and its surroundings. Some thermodynamics = textbooks=20 present similar entropy balances in related cases,=20 demonstrating the validity of my calculations = (4,=20 5).=20

Tykodi comments that for system A to stay = isothermal=20 during compression means that the work interaction = with the=20 surroundings must be mechanically reversible. = Similarly=20 Battino and Wood say that "the only way the = compression in=20 A may occur isothermally is via a reversible = process".=20 In relation to this, most laboratory and industrial = isothermal=20 operations are irreversible. Some conventional = textbooks show=20 examples of irreversible isothermal processes = invalidating the=20 above argument (9, 10). By controlling = compression=20 force and heat transfer we may reach irreversible = isothermal=20 conditions without serious difficulties.=20

Now, I am going to discuss specific comments of = each=20 letter. Tykodi points out that my notation could be = improved=20 by using IUPAC rules. This may be true, but when I = wrote this=20 paper I had in mind engineering convention and I used = it for=20 simplicity and customary reasons. In any case, results = and=20 consequences of my work are independent of any = arbitrary or=20 conventional notation system.=20

In a third point Tykodi assumes that I treat the = uptake of=20 heat by system B as a reversible process. = Indeed, when=20 I analyze tank B I do not make any previous = assumption=20 about reversibility, but entropy balance suggests that = transition in B occurs without production or=20 destruction of internal entropy. Since production of = internal=20 entropy is zero in B, then it appears that an = event in=20 tank B occurs as if it were reversible as = Tykodi=20 thinks.=20

Tykodi indicates that the only irreversible part of = my=20 process is the heat transfer across the finite = temperature=20 between systems A and B. This picture is = not=20 correct because the process in tank A is also = an=20 attainable nonreversible isothermal compression as = explained=20 previously.=20

Then he lists results for an imagined process = consisting of=20 a reversible compression in tank A, a = reversible=20 heating in tank B, and an irreversible heat = transfer=20 between A and B. Such values are correct = for his=20 assumption but not for the process described in my = article,=20 composed of a nonreversible isothermal compression in = tank=20 A, a constant volume heating in tank B, = and an=20 irreversible heat transfer between A and = B=20 across a metal barrier. His calculation does not = consider the=20 internal entropy coupling occurring in the cited = process.=20 Tykodi believes that entropy can only be produced and = never=20 can be destroyed. This statement is true in all = systems=20 described by classical thermodynamics, but my process = is an=20 interesting exception of this behavior.=20

He argues that final state cannot be reached = adiabatically=20 from initial state for my selected path. To this = consideration=20 I have explained that the process fits general = thermodynamic=20 requirements. Therefore, the overall adiabatic path = selected=20 is allowed by thermodynamics and may represent an = exception of=20 Caratheodory's theorem for adiabatic processes = (11).=20

At the end of his letter Tykodi opines that = referees did=20 not review the article well. For me it is difficult to = think=20 that referees of a universally known journal did not = read my=20 work carefully and critically. I guess that reviewers = felt=20 that the article was interesting enough to be = published=20 independent of notation and nonconventional ideas that = may=20 generate an stimulating discussion about thermodynamic = topics.=20

Now, I will consider Nash's comments. He states in = his=20 first paragraph that "the change of state taking place = in tank=20 A is nothing but the isothermal compression of = an ideal=20 gas from 1 to 4 atm". To this I would like to say that = the=20 change of state taking place in tank A is = something=20 more than a conventional solitary isothermal = compression.=20 Indeed, the process illustrated in Figure 1 of my = article=20 represents an internal entropy coupling system in = which an=20 oriented heat transfer between tank A and tank = B=20 produces enough internal entropy to drive a = simultaneous=20 reversible isothermal compression in tank A = with=20 destruction of internal entropy. During the process = heat is=20 released to tank B, where the temperature = varies from=20 373 to 1500 K and both tanks are covered externally by = an=20 adiabatic wall. From this outline it is possible to = visualize=20 that the process described in Figure 1 is not = equivalent to a=20 conventional isothermal compression as Nash considers. =

It is obvious, as he explains, that the minimum = work=20 required "by nothing but an isothermal compression at = 1500 K=20 from 1 to 4 atm" is -17.3 kJ. This performance = corresponds to=20 a conventional reversible isothermal compression = releasing=20 heat to a constant-temperature heat reservoir at the = same=20 temperature of the system equal to 1500 K. Classical=20 thermodynamics postulates that the above value is the = minimum=20 work required for the best isothermal compression = system=20 designed by man for the given change of state.=20

However, if we link an irreversible isothermal = compression=20 with a heat transfer between two tanks as described in = Figure=20 1, it is possible to find a feasible set of conditions = where=20 the work input is less than the work required by a=20 conventional reversible isothermal compression. In = this sense,=20 I have demonstrated that under internal entropy = coupling it is=20 possible to design a feasible irreversible isothermal=20 compression with a work input of -14,054 J, which is = less than=20 the -17,289 J required by a reversible isothermal = compression=20 for the same initial and final states. This result is=20 unexpected from the point of view of classical = thermodynamics=20 as Nash claims, but irreversible thermodynamics = suggests that=20 this behavior may occur as a consequence of the = internal=20 entropy coupling process as explained earlier.=20

Nash tries to use the process in a closed cycle to = conclude=20 that the process described in my article violates the = second=20 law of thermodynamics, but he makes a wrong assumption = that=20 invalidates his reasoning. He writes "imagine tank = A as=20 the cylinder of a Carnot engine in thermal contact = with an=20 immense heat reservoir at 1500 K. Beginning at 1 atm, = let the=20 author's notional irreversible isothermal compression = proceed=20 to 4 atm with work input of -14.05 kJ. Let the gas = then resume=20 its original state by a reversible isothermal = expansion=20 yielding a work output of 17.3 kJ". Here, Nash is = imagining a=20 process different from the one described in Figure 1 = of my=20 article. It is possible to see that tank A = cannot be=20 used as the cylinder of a Carnot engine in thermal = contact=20 with a heat reservoir at 1500 K as Nash thinks. It can = be seen=20 that during the process heat is transferred from tank = A=20 to tank B, which is a nonisothermal heat sink = and its=20 temperature varies from 373 to 1500 K. Also, both = tanks=20 A and B are covered externally by an = adiabatic=20 wall. Therefore, the cycle imagined by Nash does not = fit the=20 requirements of the geometry of the process described = in the=20 paper and his cycle does not work. It is evident that = the=20 process does not violate the second law of = thermodynamics=20 because the total entropy change of the whole universe = is=20 greater than zero.=20

He continues and calculates the entropy change for = his=20 conventional reversible compression and finds a value = of=20 -9.369 J K^-1 and concludes that the = difference=20 between the value given in my article and his value is = the=20 entropy destroyed, equivalent to -2.15 J = K^-1. He=20 calculates the total entropy change for the = conventional=20 isothermal compression using the work input of Figure = 1 and a=20 final pressure of 3.086 atm and obtains a value of = 7.99 J=20 K^-1 for his compression model, which is = different=20 from the system represented in Figure 1, where the = total=20 entropy change of the universe is equal to 5.83 J=20 K^-1. Therefore, there are not discrepancies = in my=20 conclusion, as he asserts, because all my calculations = are=20 correct and consistent with the system expressed in = Figure 1;=20 and his results are valid only for his system, which=20 represents a different situation.=20

Other specific comments appear in Battino and = Wood's=20 letter. They assume a reversible compression in tank = A=20 and a reversible heating process in tank B and=20 calculate correctly the required pressure and total = entropy=20 change of such a system. Then, they estimate the heat=20 transferred from tank A considering a = reversible=20 isothermal compression and find 17,289 J. Next they = compare=20 this value with 14,054 J taken by tank B and = ask "what=20 happens to the excess heat?" Well, the numbers are=20 incompatible because they compare heat intake of tank = B=20 with heat release from a reversible isothermal = compression in=20 tank A. They should make comparison using the = actual=20 heat released by the nonreversible isothermal = compression=20 described in the article, which is 14,054 J. In this = case, the=20 numbers are compatible.=20

They said finally that there are no surprises here = and no=20 exceptions to the laws of thermodynamics. In relation = to this,=20 I have explained my ideas in the beginning of this = rebuttal=20 letter.=20

Olivares and Colmenares start their letter = considering that=20 the process is physically unfeasible because according = to=20 classical thermodynamics for a reversible isothermal=20 compression in tank A, pressure should be equal = to or=20 less than 312.71 kPa. As I explained earlier, the = process=20 meets general thermodynamic requirements. Then it = should be=20 feasible, being more efficient than a conventional = reversible=20 compression. The internal entropy coupling process = allows the=20 existence of a path with a final pressure greater than = the=20 value expected from simple mechanical arguments, and = the=20 system does more work than a reversible process = between the=20 same states.=20

They continue to explain that a total entropy = change=20 greater than zero does not imply that a process will = in fact=20 occur because it depends on the dynamics of = transformation.=20 They suggest as an example that the formation of water = from=20 its elements at 25 =B0C and 1 atm is highly favored=20 thermodynamically; however, it does not take place=20 spontaneously unless a catalyst or a spark initiates = reaction.=20 Now, if we analyze intuitively the dynamics of the = process=20 described in Figure 1 of my article, it can be deduced = that=20 the process starts spontaneously when the adiabatic = film on=20 the metal partition is removed. The removal of the = adiabatic=20 film is the act or impulse that initiates a = spontaneous heat=20 transfer from tank A to tank B because = of the=20 temperature difference across the metal barrier.=20 Simultaneously, compression starts at a controlled = rate to=20 keep isothermal conditions in A. Then, the = system may=20 continue to reach a final state according to model = prediction.=20 In any case, experimental evidence would be necessary = to=20 verify my hypothesis; but theoretically, the process = starts.=20

Next, they said that I failed to recognize that = entropy=20 production is not an additive property as they show in = eq A7.=20 Although this may be generally true, for the process = it is=20 additive as I will now show. They find in eq 29 a = value of=20 5.83 J K^-1 for total entropy production = according=20 to their reasoning. Now, if I assume additivity, the = total=20 entropy production for the whole universe will be = obtained=20 summing up my eqs 21, 25, and 27 and I get 5.83 J=20 K^-1, which is the same value found by them. = Since=20 the values coincide my hypothesis is correct.=20

Other specific comments appear in Freeman's letter. = He=20 considers that the term creation/destruction has a = number of=20 connotations and should not be used in a scientific=20 discipline. In this respect I think that any term used = to=20 describe a process must have a physical or intuitive = feeling=20 to understand better its behavior. I have selected for = the=20 article a name that reflects the nature of a process = involving=20 simultaneous creation and destruction of internal = entropy. The=20 term creation/destruction gives us a stimulating view = of some=20 special transformations of nature and describes at = different=20 levels the events taking place in the article, where = many=20 interpretations are possible.=20

Freeman states that another puzzling aspect is my = claim=20 that the nonreversible compression process is more = efficient=20 than a reversible isothermal compression for the same = initial=20 and final states. He says this is an invalid = comparison=20 because if such a reversible compression were done the = heat=20 generated would raise the temperature in tank B = above=20 1500 K or raise the temperature of both chambers, = invalidating=20 the posed conditions of the process. To this argument = I would=20 say that my intention is to compare the process taking = place=20 in tank A in my model with a conventional = reversible=20 isothermal compression occurring in a tank surrounded = by an=20 isothermal heat reservoir. This tank is not connected = to tank=20 B as Freeman thinks. I found that the = nonreversible=20 isothermal compression in Figure 1 of my article = requires a=20 work input of -14,054 J. Now, if gas is compressed = between the=20 same states under isothermal reversible conditions in = a tank=20 immersed in an isothermal heat reservoir it would = require a=20 work input of -17,289 J. Evidently, the process taking = place=20 in tank A is more efficient than the = corresponding=20 isothermal reversible compression occurring in a tank=20 releasing heat reversibly to isothermal surroundings. = This=20 seems to me a reasonable comparison to measure the = efficiency=20 of the process.=20

He comments that the question to be asked is "given = the=20 posed initial conditions, let the gas in A be=20 compressed isothermally and reversibly to a final = pressure=20 such that the heat produced in A is exactly = that=20 required to produce the given results in B. = What is the=20 final pressure?" He finds 312.7 kPa, compared to = 405.32 kPa=20 found in the process. Obviously, these results mean = that the=20 compression process represented in Figure 1 is more = efficient=20 than a reversible isothermal compression. This = behavior is a=20 consequence of the internal entropy coupling process=20 previously explained.=20

Freeman also says that it is not possible to = accomplish the=20 stated compression of the gas in A. However, I = have=20 demonstrated that the process fits general = thermodynamic=20 requirements and should be feasible through the path=20 described.=20

Finally, Freeman states that there is no merit in = this=20 paper other than its being used as a debugging = assignment. I=20 would be happy if this paper were used as a debugging=20 assignment, because I feel people will find a new = vision of=20 the universe and thermodynamic fundamentals. I = consider that=20 this paper has drawn attention from readers around the = world=20 generating an interesting discussion about the = existence of=20 internal entropy coupling processes and the = implications of=20 their extraordinary behavior. The article has = interesting=20 aspects and presents a stimulating situation that = deserves to=20 be discussed at different levels. I think this is = relevant=20 whatever interpretation we assign to it.=20

Literature Cited=20

1. Smith, J. M.; Van Ness, H. C. Introduction to = Chemical Engineering Thermodynamics; McGraw Hill: = New=20 York, 1975.=20

2. Modell, M.; Reid, R. C. Thermodynamics and = its=20 Applications; Prentice Hall: Englewood Cliffs, NJ, = 1974.=20

3. Balzhiser, R. E.; Samuels, M. R.; Eliassen, J. = D.=20 Chemical Engineering Thermodynamics; Prentice = Hall:=20 Englewood Cliffs, NJ, 1972.=20

4. Sandler, S. I. Chemical and Engineering=20 Thermodynamics; Wiley: New York, 1977.=20

5. Prigogine, I. Introduction to Thermodynamics = of=20 Irreversible Processes, 3rd ed.; Interscience: New = York,=20 1967.=20

6. Belandria, J. I. XLIV Meeting ASOVAC; Coro, = Venezuela,=20 1994.=20

7. Belandria, J. I. I Congress of Mechanical = Engineering;=20 M=E9rida, Venezuela, 1994.=20

8. Dickerson, R. E. Molecular = Thermodynamics;=20 Benjamin: New York, 1969.=20

9. Abbott, M. M.; Van Ness, H. C. = Thermodynamics: Theory=20 and Problems; McGraw Hill: New York, 1969.=20

10. Daniels, F.; Alberty, R. A. Physical=20 Chemistry; Wiley: New York, 1966.=20

11. Spalding, D. B.; Cole, E. H. Engineering=20 Thermodynamics; Edward Arnold: London, 1967.

Citation: Belandria, Jose = Iraides. An=20 Exceptional Theoretical Process Belandria replies = J. Chem.=20 Educ. 1997 74 286.

Keywords:

March = 1997
Vol.=20 74 No. 3
p. 286

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