Specific heats (C v) of saturated and compressed liquid and vapor carbon dioxide

1986 ◽  
Vol 7 (6) ◽  
pp. 1163-1182 ◽  
Author(s):  
J. W. Magee ◽  
J. F. Ely

The present paper is occupied with an experimental investigation into the variation of the specific heat at constant volume of carbon dioxide attending change of absolute density. The investigation is in continuation of a previous one, in which Carbon Dioxide, Air, and Hydrogen were the subjects of a similar enquiry over low ranges of density. It appeared to me desirable to extend the observations more especially in the case of carbon dioxide, because of the extended knowledge we already possess of its isothermals, and the fact that its critical temperature is within convenient reach. Other physical properties of the gas have also received much attention of recent years. It is also readily procured in a nearly pure state. The observations recorded in this paper extend, in the one direction, to densities, such that liquid is present at the lower temperature; and in the other, to a junction with the highest densities of the former paper. A plotting of the new observations is in satisfactory agreement with the record of the old. It reveals, however, the fact that the linear nature of the variation of the specific heat with density, deduced from the former results, is not truly applicable over the new, much more extended range observation. For convenience the chart at the end of this paper embraces the former results, and the present paper is extended to include the entire results on the variation of specific heat with density where the range of temperature, obtaining at each experiment, is approximately the same: that from air temperature to 100° C.


In a recent number is a criticism under the above title by Sir R. T. Glazebrook, of some figures given by me in a paper with the same title. I am accused of not giving Holborn and Henning's own figures, because I State that part of my curve is filled in from the researches of Swann, and of Holborn and Henning. As Swann and Holborn and Henning are not in agreement, it seems evident that one set figures cannot be used without some adjustment to the other set. These discrepancies were dealt with by the British Association Committee (of which Sir R. T. Glazebrook later became a member) in their 1908 Report, and the figures I give are in fairly close agreement with theirs for the low temperatures. I State in my paper (p. 492) that I find Holborn and Henning about 7½ percent. too low at 800°C. for air and steam, and I assume that the same error applies to the carbon dioxide. (Prof. Callendar suggests their error may be as much as 10 per cent. at 1400°C.) I have, therefore, distributed this error over the range for which I have used Holborn and Henning's figures. On this account it may be anticipated "that the figures at the higher temperatures are higher than the corresponding figures due to Holborn." I believe it is usual, when quoting the results of other workers, to attach their names to the figures quoted; this I have not done.


Although our knowledge of the energy-content of solid bodies has been greatly extended by the theoretical investigations of Planck, Einstein and Debye, and by the experiments of Dewar, Nernst and others, the problem in the cases of gases, and especially of vapours, is still far from a satisfactory solution. With the object of providing accurate data for a theoretical study of the energy-content of molecules in gases, the experiments described in this paper were commenced in 1911 in the laboratory of the Physikalisch-Chemisches Institut of the University of Berlin. I desire to express my thanks to Prof. Nernst for the interest he showed in this work, and for many useful suggestions he made during the period 1911-1913, in which I worked in his laboratory. Since air and carbon dioxide have been the object of some very careful investigations by previous experimenters, it was decided that a re-investigation of the ratio of the specific heats, c p / c v , of these gases would be appropriate at the commencement of the research. Other gases, for which the constants are less accurately known, such as ammonia, sulphur dioxide, nitrous oxide and nitrogen, are at present under investigation by a method similar to that described in the present communication. The present results were published in an abstracted form in 1913.


The investigation of the ratio of the specific heats, c p / c v = γ , of hydrogen described in the present communication was undertaken during the summer of 1923 by the method previously used with air, carbon dioxide, oxygen and nitrogen. The gas used was electrolytic hydrogen, supplied by the British Oxygen Company, and was purified in the same way as the oxygen in the previous experiments, except that the four U-tubes now contained quicklime, caustic soda, and two tubes of calcium chloride, in the order given. Phosphorus pentoxide was, as before, used for the final drying of the gas. The globe A, fig. 1 in the paper of 1924, was, before the commencement of the experiments, filled with pure nitrogen from previous measurements. The purified hydrogen was passed directly into the globe until the nitrogen had been completely displaced, and there was thus no danger that an explosive mixture of hydrogen and oxygen could be formed, which might have been ignited by contact with the thin platinum wires of the bolometer, or, at least, might have formed moisture by slow reaction in contact with the platinum.


In a previous paper an account was given of experiments to determine the specific heats of carbon monoxide up to a temperature of 1800° C. by the sound velocity method. The principle of the method employed was the setting up in a heated tube of a stationary train of sound waves; the source of the wave system being a quartz crystal vibrating piezo-electrically at a known frequency.


The question of the dependence of the specific heat of carbon dioxide upon its density having been investigated, so far as is described in Part II., the further question remained over as to whether the specific heat of a gas is dependent upons range of temperature over which the gas is heated. The question was evidently within the power of the steam calorimeter to answer, provided arrangements were ride for varying the lower limit of temperature—the initial temperature. To vary upper limit by resorting to vapours other than steam would, on the large scale on which operations were being conducted, have been costly and troublesome, though not attended with any inaccuracy, as the experiments of Wirtz on the Heats of several vapours, determined by the method of condensation, appear show. It is to be observed, indeed, that the use of vapours other than water would .ow of operations being conducted upon smaller quantities of the gas, as it would be sy to find liquids whose vapours possessed a latent heat one-half or one-fourth as eat as that of water; and a construction necessitating but little loss of vapour at experiment could be easily contrived. In this case, also, it would be necessary provide a means of varying the initial temperature. Chiefly on the grounds of supense I decided upon the use of steam in conjunction with a means of altering the initial temperature. It appeared probable, too, that the alteration of the initial temperature between 10° and 100° would disclose the chief points of interest in these of the gas under consideration, the critical temperature lying within this range.


In a recent number is a paper by Mr. W. D. Womersley bearing the above title, in which an account is given of a determination of specific heats of the gases named, employing a calorimeter designed by the late Prof. B. Hopkinson. Mr. Womersley’s experiments extended over the range 1000° C. to 2000°, and he states that the lower parts have been filled in from the researches of Swann and Holborn and Henning.


The experiments described in this memoir were made in continuation of those carried by Dixon, Campbell and Parker on the velocity of sound in gases at high temperatures. Our object was to determine the velocity of sound in the vapours of the low-boiling inflammable liquids ether, methyl and ethyl alcohols, pentane, hexane and benzene, and in condensable gases such as ethylene and ammonia. Corrigendum . As a preliminary we desire to take this opportunity of making a correction (which Prof. J. R. Partington has pointed out to us) in the calculation of the ratio of the specific heats from the velocity of sound in “free” nitrogen, carbon dioxide, methane and ethane, given in the former paper. For instance, by the use of round figures, the values of γ between 0° and 500°C. derived from the velocity of sound in free nitrogen were made 0·002 too high, a difference which appreciably affects the value of C v calculated from it; and similarly the values γ for carbon dioxide between 0° and 300°C. were made too low. The Tables XI, XIII, XIV and XV printed on pages 23 and 24 of that memoir have therefore been recalculated, the new gas constant R = 1·9875 being used, and should read as follows


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