DONALD F. HORNIQ
856
Here one has T2 > T I , or in our notation T > To. The relaxation of the vibrational temperature for this case is shown in curves A and C of Fig. 1 in reference 3. To check how well the theory agrees with experiment one could transform the usual data of density us. shock strength or density US. distance behind the shock wave into T v i b us. time and compare these data with the temperature relaxation curve calculated from eq. 23. It should be pointed out again that the above theoretical results have been derived for a system of harmonic oscillators. Work is now in progress to extend these calculations to a system of anharmonic oscillators. The question as to whether it is possible to carry over this result of an exactly defined vibrational relaxation temperature to the anharmonic oscillator case must await the completion of this study. The use of state variables in shock wave studies obviates the need for detailed information about tJhe level population in the analysis of the data. To
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obtain some detailed information about the relaxation of vibrational non-equilibrium distributions and, in particular, about the efficiency of intermolecular energy exchange involving molecules in the higher vibrational levels it is, however, desirable to have such information. This suggests that some thought should be given to the instrumentation of shock tubes with spectroscopic equipment. At high shock strength, where higher vibrational energy levels will be excited, such a study might yield some interesting data on vibrat,ional and dissociation energy lag and on the efficiency of intermolecular energy transfer. Acknowledgments.-I have benefited greatly from the opportunity to discuss the contents of this paper with E. W. Montroll. I also wish to acknowledge some helpful correspondence with Professor R. G. w. Norrish of Cambridge University in regard to his work on vibrationally excited oxygen. I am indebt,ed to Mrs. J. Kimrey for her assistance with the calculations presented in Section 3.
ENERGY EXCHANGE I N SHOCK WAVES BY DONALD F.HORNIG* Metcalf Chemical Laboratories, Brown University, Providence 12,R. I . Received January 50, 19.57
Shock waves provide a means to change temperature, flow velocity and other variables in gases in as little as 10 to 15 collisions. Studies in the shock front region show that translational equilibration occurs in about the distance predicted by the Navier-Stokes equation, a few mean free paths. Rotational equilibration seems to require from 1-5 collisions, except in hydrogen, where 300:ollisions are required. Shock waves have also been used to study vibrational equilibration a t Because gases can be heated to high temperatures in a few collisions, they are also a useful tool temperatures up to 6000 in the study of chemical reactions and have been applied to the kinetics of dissociation reactions.
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It has been pointed out already in this symposium that shock waves have become an important new tool in the study of vibrational relaxation in gases. They have, in fact, become useful in the study of all kinds of energy exchange as well as in the study of fast chemical reactions. In each case the basic reason is tha,t they afford a means to change the pressure and temperature in a gas over a wide range in a very short time. The formation of a shock wave readily can be understood in terms of a hypothetical experiment in which we imagine a tube of gas with a piston inserted a t one end. If the piston is slightly accelerated, the gas ahead of it is slightly compressed, and the disturbance propa.gates down the tube a t the velocity of sound. If the piston is again accelerated, another pressure pulse moves down the tube but a t a higher velocity than the first. The reason is that although the second disturbance also moves a t sonic velocity, it is moving in a gas which is itself in motion a t the first piston velocity and which has been slightly heated by the first compression. Therefore, it gains on the first disturbance and eventually catches up with it. If the piston is accelerated to a finite velocity, each successive disturbance catches up with the preceding disturbances so that down the tube a discontinuity in pressure and temperature is formed, behind *
Department of Chemistry, Prinrrton University, Princeton, N. J.
which the compressed and heated gas moves a t the velocity of the piston. The shock tube affords an easy experimental means of achieving this result.'-3 The gas under investigation is confined in one section of a tube, a t a pressure usually ranging from a fraction of a mm. to a few atmospheres. This section is serarated by a suitable diaphragm from a high pressure section filled with a gas, preferably a light gas such as H 2 or He, a t a pressure normally between 1 and 100 atmospheres. When the diaphragm is broken, either by spontaneous bursting or vhen pricked with a needle, the high pressure ga.s expands into the low pressure gas, acting as the piston in the preceding discussion and setting up a shock wave in the low pressure gas. In order to understand the properties of a shock wave which make it useful for the study of energy exchange it is convenient to consider it in a coordinate system in which the shock wave is at rest and the gas is flowing by. This situation is illustrated in Fig. l. The gas enters at the left at the velocity of propagation of the shock wave, M times the velocity sound, c, in the initial gars and (1) W. Payman and W. Shepherd, Proc. Rou. Soe. (London), 8 1 8 6 , 293 (1946). ( 2 ) W. Bleakney, D. I
