Edited by RALPHK. BIRDWHISTELL
textbook forum
University of West Florida Pensacola. FL 32504
Temperature, Cool but Quick Stephen M. Cohen Noningham University. University Park, Nottingham NG7 2RD, United Kingdom1 The Maxwell-Boltzmann distribution of molecular speeds has long been an important aspect of teaching the kinetic theory of gases in both general and physical chemistry courses. Yet I would like to call attention to a serious and ooteotiallv misleadine ambieuitv " in manv. .. if not most. textbooks, in the light of the development of supersonic jets w e r the vast 30 \,ears,and the use of these iets bvchemisrsfor the pasi decade. Standard textbook kinetic theory notes that a t low temperatures, the Maxwell-Boltzmann distribution of gas molecules is narrow, with most molecular speeds near zero. At higher temperatures, the speed distribution widens, with the consequence that the average molecular speed increases (I). This is tvoicallv shown bv a nlot of "fraction of molecules" (or "probahilit;" or " m i k j v e r s u s "molecular speed". The ambinuitv occurs when dealine with suoersonic iet experiments: N ~ Wused widely in milecular spectroscopy experiments, this technique changes a high-pressure gas's random molecular motion into directed motion, when expanded out of anozzle into a near-vacuum, producing ajet of cold, isolated gas molecules moving at locally supersonic speeds. These gas molecules are translationally cold-often less than 1 K-because the Maxwell-Boltzmaun distrihution of the molecules in the jet is extremely narrow, and yet the distribution is disolaced oositive to the usual cold eas peak near zero speed ( 2 , 3 ) ,as shown in the figure. Therefore, temperature should not he regarded as inextricable from average molecular speed. Instead, i t should he regarded solely as related to the width of the Maxwell-Boltzmaun distribution, not to the distribution's position, such that a wide flat curve indicates high temoerature, and a tall, sharp peak shows low temperatire, regardless if auerage speed. If the view described above seems rather hazy or unclear, perhaps the following analogies will help. If we take a chunk of drv ice and hurl it a t high sneed. the d w ice will remain u . . cold (with a narrow Maxwell-Boltzmann distribution) even though it is traveling very rapidly. Similarly, if we swing a bucket of liquid nitrogen around in a circle, the liquid nitroeen retains its narrow soeed distribution even thoueh the iiquid's molecules are moving a t a high speed. If objections arise because the examples put forth are condensed phases, not gaseous, then consider that the earth's atmosphere is whirling around with the earth's rotation at an equatorial speed of around 1700 km h-', but still retains a MaxwellBoltzmann distribution corresponding t o a mean temperature of only -285 K at sealevel (4). Likewise, asupersonic jet
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'Current address: Department of Chemistry, Wiess School of Natural Sciences, P.O. Box 1892, Rice University, Houston, TX 77251.
1038
Journal of Chemical Education
molecular speed/ km s-' Maxwell-Boltzmann distribution tor He at 10 K and 100 K, and for a 10 K wpersoni~jet of He traveling at 1.9 km s-'; k = Boltzmann constant, c = molecular speed. m = mass of He atom = 6.6466 X lo@' kg.
of gas travels a t a high velocity, up to 2 km s-', yet has a narrow Maxwell-Boltzmann distribution (.2.) . My proposal is by no means new; Levy suggested this view of temoerature several vears aeo (5.6). . . . vet - all the textbooks examined (I, 7-12), except for one, completely ignore it. The hook that does very briefly discuss "a gas in macroscopic motion" (13)was written by, among others, Rice, who was a colleague of Levy. A defense could be made that the Maxwell-Boltzmann distrihution uses relatiue molecular speed as the independentvariable, yet none of the textbooks made note of this. Of course, had such a distinction been made, the next question would be "Relative to what? Other molecules? The container"? Obviously, if the textbooks note that the molecular soeeds eraohed are relative to some sort of averaee molecular speeb in the group, the problem is solved. ~ u far t easier solution would be to remark w o n the relative widths of the Maxwell-Holtzmann distribut~ons,and not their positions. Such arnbieuirv in basic textl~onksin uniustifiable when we consider how i t could arbitrarily limit the ideas and creativity of students by steering them away from certain areas of research, especially when we consider the growth in the use of the supersonic jet in chemistry, an experimental technique that is likely to become more, and not less, important in future research.
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Literature Clted i l l Br0wn.T. L ; LeMay, H. E.,J,. '"Chemi8try:The Central Hall: Englewood cliff^, NJ. 19m gp 276-7. (21 Levy, D. H.Ann.Rsu.Phys. Chem. 1980,31,197.
seiend"'3rded.: prenticp-
(81 Sudh$,Aa.;Sehulz,P.: Krajn0vich.D.; Shen,Y. R.: Lee,Y.T. Adu.LossrChom. 1978, 5. $08. (4) Wesst, R. C.. Ed. "Handbook af Chemistwsnd Physics". 55th ed.: C R C Cleuehnd, OH, 1974. (51 Levy, D. H. NouScientist 1981.89.15. (61 Levy, D. H. Science 1981,211,263. 171 Alherty,R.A.:Daniels.F."PhysicslChemistw".5thed.,SIvernion:Wiley:NewYark, 1980: pp 4661. 181 Atk1ns.P. W. "Physical Chemistw",3rd ed.: Oxford Univ.:Orford, 1986.~~8-9,64750.
(91 Bromherg, J. P. '"Phwical Chemistry": Allyn and Bamn: Baston, 1980. pp 41621. (101 Haltzclaw,H.F.,Jr.:Rohinson,W.R.;Nehergall,W.H."GencralChemistry'~7thed.; Heath: Lexington,MA, 1984:pp26b7. ( I l l McQuarrie, D. A,: Rock. P. A. "General Chemiatw"; Freeman: New York, 1984: pp 178-80. (121 Mortimer. C. E. "Chemistry': 5th ed.: Wedsworih: Belmont, CA, 1983: pp 2W-2. (13) Berry, R. S.: Rice, S. A,: Rors, J. "Phyaicd Chemistry; Wiley: New York, 1980: pp 1056-8.
Volume 63
Number 12
December 1986
1039
