The Specific Heat of Carbon Dioxide—Correction

1928 ◽  
Vol 24 (2) ◽  
pp. 290-290
Author(s):  
W. H. McCrea

In a recent paper in these Proceedings the writer suggested the possibility of a transition from one molecular form to another in CO2. The suggestion is embodied in the equation (10) and the resulting specific heats for low temperatures given. He greatly regrets that it was not till after those results were published that he found they gave a high and altogether impossible maximum in the specific heat curve for higher temperatures before it returns to the neighbourhood of the unmodified curve Cv′.

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.


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.


Although the heat capacity of iron at different temperatures has been the subject of a number of investigations in the past, it is only recently that iron of purity greater than 99.9 % has been available. Furthermore, in most previous determinations the property actually measured has been the total heat over a relatively large temperature range. Specific heats deduced from such measurements are liable to appreciable error, since if the total heat curve is smoothed, small fluctuations in the specific heat will be concealed, whereas if the actual observations are retained without smoothing, fluctuations which have no physical existence may appear in the result. Thus, suppose that the total heat is measured from 50 to 145 and from 50 to 155° C, the former being in error by 1 part in 1000 in excess and the latter the same amount in defect, the error in the specific heat over the range 145-155° C will be almost 2%. Evidently a real variation of 1 or 2% would be liable to pass unnoticed if any smoothing is undertaken, and conversely, fluctuations of this order may be introduced spuriously if the observations are used without smoothing. In general, calorimetry from high temperatures cannot be carried out to an accuracy of 1 part in 1000, and in any case, even this accuracy is insufficient at temperatures of the order of 1000° C.


A method of determining the specific heat of substances at low temperatures was described in a paper on “Studies with the Liquid Hydrogen and Air Calorimeter,” also in the abstract of a lecture delivered at the Royal Institution entitled“ Liquid Hydrogen Calorimetry,” where the apparatus then used is illustrated. Continuing the use of the same method, but with some modification of the apparatus, the investigation has been extended to a large number of inorganic and organic bodies. In this later series of experiments, the measurements of the specific heats of materials by the liquid hydrogen calorimeter were made over a range of temperature from boiling nitrogen to boiling hydrogen, a fall of temperature of some 57° Abs.


1891 ◽  
Vol 48 (292-295) ◽  
pp. 440-441 ◽  

In this first notice the specific heats, at constant volumes, of air, carbon dioxide, and hydrogen are treated over pressures ranging from 7 to 25 atmospheres. The range of temperature is not sensibly varied. It is found that the specific heats of these gases are not constant, but are variable with the density. In the case of air the departure from constancy is small and positive; that is, the specific heat increases with increase of the density. The experiments afford directly the mean value 0·1721 for the specific heat of air at the absolute density of 0·0205, corresponding to the pressure of 19·51 atmospheres. A formula based on the variation of the specific heat with density observed in the experiments ascribes the value 0·1715 for the specific heat at the pressure of one atmosphere.


1927 ◽  
Vol 23 (8) ◽  
pp. 890-900 ◽  
Author(s):  
W. H. McCrea

SummaryTwo alternative forms of the CO2 molecule have been suggested by various authors who have discussed the band spectrum data. The specific heat curves based on these models are considered here. It is found that neither is quite satisfactory over the whole range of temperature and we discuss the difficulties for the low temperature and high temperature portions separately. In order to get agreement for low temperatures we find it necessary to introduce a further hypothesis about the molecular model which also seems to explain one or two outstanding difficulties in interpreting the fine structure of the bands. This assumption does not make any difference at higher temperatures where we show the error in one of the curves to be of the order we should expect to be accounted for by a centrifugal stretching of the molecule.


1894 ◽  
Vol 55 (331-335) ◽  
pp. 390-391 ◽  

In the former experiments on this gas, recorded in the first part of this research, the highest absolute density at which the specific heat was determined was 0·0378. In the present observations the determinations of specific heat have been carried to densities at which the substance was partly in the liquid state at the lower limit of temperature of the experiments. Observations dealing with true specific heat, uncomplicated by the presence of thermal effects due to the presence of liquid, are limited by the density 0·1444. At this density the mean specific heat over the range, 12° C. to 100° C., is 0·2035.


1894 ◽  
Vol 55 (331-335) ◽  
pp. 392-393

In order to investigate the question of the variation of the specific heat of carbon dioxide with temperature, a steam calorimeter was constructed having double walls of thin brass, between which the vapour of a liquid boiling under atmospheric pressure could be circulated. The vessels used in the experiments were hung in the closed inner chamber. Into this chamber steam could be admitted after the temperature had become stationary and the same as that of the jacketting vapour. In this way the initial temperature could be varied.


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