A Freshman Chemistry Thermodynamics Experiment: The Cyclic Rule Revisited Many freshman experiments fail to offer any conceptual challenge. Yet students can see the chemistry laboratory as more than a cookbook operation only if they do experiments beyond the cookbook format. An ordinary rubber band presents a simple thermodynamic system ideally suited to free-form studies.' When described in terms of the variables force (F), length (L), and temperature (T)-the analogs of P, V, and T for an ideal gas-the rubber hand falls subject to the cyclic rule in the farm
(JFIJL)T(JLIJT)F(JT/JF)L = -1 We seek an experimental verification of this relation, which seems to defy common intuition, and incidentally attain a painless introduction t o concepts of the partial differential calculus. The experiment was tested with a group of Harvard freshmen, working in pairs. They were told only that they were to determine the product of the three derivatives. They had then to devise same way to vary each pair of parameters while holding the third constant. Most soon arrived at procedures similar to the ones below. Measurement of (JF1JL)r: At constant temperature the elongation of a vertically-hung rubber band was measured as a function of force using either a set of weights or a beaker to which was added known volumes of liquids. Measurement of (aLIJT)p: A rubber hand was hung within a large-diameter glass tube wrapped with heating tape. Temperatures were set with a Variac. Constant force was insured by hanging a weight a t the end of the rubber band. Measurement of (ATIJF)L: Using an apparatus similar to that of the ( a L l a T ) experiment, ~ a rubber band was contracted by a rise of temperature. Weights were then added to bring the band back to its original length. Typical results with various rubher hands were as follows: (JFIiJL)T = 13000 dynlcm = l:l.:I g/cm (aLIaT)p = -0.05H:i cml°C (aT/dF),. = 0.00167 "Cldyn = 1.64 ' C l g and
(~FIJL)T(~LI~T)~(~TI~F)I, = -1.3 This experiment also affords many opportunities for the curious student. Many students found significant hysteresis effects, presumably due not to waiting long enough for equilibrium to he reached. Clearly visible in separate plots of length versus force in both extension and contraction, these effects may serve to motivate a discussion of non-equilibria thermodynamics. The negative value of (JL/JT)F is also very interesting. Several text@ give good discussions of why stretched rubber has a negative temperature coefficient of elongation and obeys an ideal gas-like equation. The theory of random chain conformations (analogous to random motions of molecules) gives the student an insight into the kinetic theory. The entropic nature of rubber's retractive force serves as an introduction to the Second Law. A few related exercises are the following: (1) Show mathematically that the cyclic rule holds for an ideal gas. (2) For ideal rubber ( J E I J L h E 0 (analogous with (JE1JV)r for an ideal gas). What happens to the work you put in when you stretch a rubher band? (3) Why is CF > CL (an analogy with Cp > CY for an ideal gas)? I am grateful to Professor L. K. Nash for helpful discussions. 'An exoeriment similar t o theonedescribed here is eiven hvCarroll. H. B.. Eisner.. M..and . Hensan. R. M.. Am. J. Phvs.. X I . 808 ( i 9 ~ 3 )which , seems to have rzcaped the notic; of chehists. 'Wall, F. T.. "Chem~ml'rhermodynamics." 3rd 4..Freeman, Snn Francisco, 1974, pp. 335 50. "Adnmson. A. W.. "Textbook of Physical Chemistry." Aendemic I'ress. New Yurk, 1973, pp. I021 45. Harvard University Cambridge, Massachusetts 02138
Bruce Dezube
Volume 56, Number 5. May 1979 1 313
