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  Home > JCE Print > Journal of Chemical Education > Issues > 1997  > March  >
Chemical Education Today
Letters
An Exceptional Theoretical Process
Robert D. Freeman
Oklahoma State University, Stillwater, OK 74078

Cover
March 1997
Vol. 74 No. 3
p. 281

Full Text
I am puzzled by several aspects of the paper by Belandria on "...Internal Entropy Coupling" (J. Chem. Educ. 1995, 72, 116­118). I'll skip comment on obvious problems with significant digits; otherwise, I am questioning not the author's calculations but his interpretation.

Belandria postulates that the metal partition separating chambers A and B has "negligible mass" and negligible heat capacity; I have no quibble with that. Later, he interprets his results as indicating that "there is a creation of entropy in the metal partition M during the process." While there certainly is an increase in entropy in the process, I would argue that the metal partition has nothing to do with "creating entropy", except the obvious function of being a partition between two chambers.

To elaborate: the entropy in chamber B increases because it receives energy ("heat") and its temperature rises; nothing else happens in B, so calculation of energy and entropy change is straightforward given the initial and final temperatures. The situation in chamber A is more complicated; since compression of the gas in A is "nonreversible" but otherwise unspecified, the work done on the gas can not be calculated directly but must be inferred from the energy ("heat") transferred to B. On the other hand, the entropy change of the gas in A can be calculated because entropy is a state function, and data (p,T,n) are given.

Now, let us examine the entropy changes. The entropy of the gas in B increases (because the temperature rises and the volume is constant); the entropy of the gas in A decreases (because the temperature is constant and the volume decreases). The entropy change of the "universe" is just the sum of the changes in A and B: Delra SU = Delta SA + Delta SB = -11.53 + 17.39 = 5.83 J/K (Belandria's numbers).

But what about Belandria's "creation/destruction of entropy"? Application of this term could be justifiable in the case of chamber A, wherein the decrease in entropy of the gas based on (p,T,n) data is greater than the decrease based on "heat flow" to chamber B (but see below). However, reference to "creation of entropy" in metal partition M smacks of witchcraft. There is an increase in entropy as a result of energy flow through the partition, but the increase arises from the difference in temperature on the two sides of the partition and the partition is an innocent bystander in the process. Use of the term "creation" in this context not only raises troublesome questions (e.g., how can an object with no mass and no heat capacity "create entropy"?), it diverts attention from the real origins of the changes in entropy. Further, the term "creation" has a number of connotations that are undesirable in a scientific discipline. I believe that the terms "creation/destruction of entropy" are an unfortunate choice and cause more problems than they cure.

Another puzzling aspect of this paper is Belandria's claim that the process described is somehow "more efficient" than a corresponding reversible process. Just before his "Conclusion", he states "the reversible work required for the same isothermal compression process is 17,288 J"compared to 14,054 J for his irreversible process. This seems to me a totally invalid comparison: if such a reversible isothermal compression were done, the heat generated (17,288 J) would (i) raise the temperature of chamber B well above the posed equilibrium value of 1500 K, violating the second law (direction of heat flow), or (ii) raise the temperature of both chambers above 1500 K, violating the posed conditions of the process. The question to be asked, it seems to me, is: given the posed initial conditions, let the gas in A be compressed isothermally and reversibly to a final pressure such that the heat produced in A is exactly that required to produce the given results in B (i.e., 14,054 J); what is the final pressure? I obtain 312.7 kPa, compared to 405.32 kPa for Belandria's irreversible process.

Finally, the result quoted above14,054 J for the irreversible process and 17,288 J for the reversiblerings a warning bell. One of the standard results of thermodynamics is that getting from state X to state Y can be accomplished with minimal work if the reversible path is taken. Yet Belandria tells us that in his process the reversible path requires more work. How can that be? Well, he tells us nothing about the work done on the gas in A; he has simply postulated the initial and final conditions in chamber A without providing data about the change. It is clearly implied (second paragraph under "The Process") that all of the "nonreversible" work done on the gas is converted to "heat" which flows to chamber B, so that this "heat" flow into B is a direct measure of the postulated "nonreversible" work. It is simply not possible for this amount of work to accomplish the stated compression of the gas in A.

Belandria's postulated data violate the second law; consequently, none of his results can be considered valid.

I see no merit in this paper other than its being used as an "debugging" assignment for a thermodynamics class: Find what's wrong.

More Information
*  Citation
Freeman, Robert D. J. Chem. Educ. 1997 74 281.
*  Keywords
*  History
Created:
Last Updated:
July 29, 1999
June 23, 2005
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