scholarly journals Gaseous combustion at high pressures.—Part XIII. The molecular heats of nitrogen, steam, and carbon dioxide at high temperatures

The only information available concerning the internal energy of gases at temperatures higher than 2000° C. or so is that provided by the results of explosion experiments in which the energy liberated during the combustion serves to raise the products and any other gases that may be present in the medium to some definite maximum temperature. By varying the proportions of the reacting gases, or by adding suitable quantities of some diluent gas, this temperature may be varied between comparatively wide limits. In a previous paper of this series the method of calculating the mean maximum temperature attained during a gaseous explosion in a closed vessel was discussed, and those calculated from our experiments for theoretical CO-air and H 2 -air explosions at initial pressures of between 3 atmospheres and 175 atmospheres were given. At Prof. Bone's request I have recently reviewed and analysed the mass of data accumulated during these researches, together with others resulting from the supplementary experiments described herein, with a view to seeing how far it is possible to deduce, not only a quantitative estimate of the energy distribution at the moment of maximum pressure in typical explosions at high pressures, but also the mean heat capacities of the various explosion products over a temperature range from 15° C. up to various definite points between 2600° and 3000° C. The results of this investigation are described in the present paper.

The power of an internal combustion engine is greatest when operating with a “rich” mixture, that is to say, with a mixture which contains more fuel than is necessary for complete combustion. Similarly, it is found that if mixtures of carbon monoxide and air in varying proportions are exploded in a closed bomb at constant initial temperature and pressure, the explosion pressure is greatest when the ratio CO/O 2 is greater than 2. These phenomena are known to be connected with the dissociation of carbon dioxide at high temperatures, for if there were no dissociation we should expect the explosion pressure to be greatest when CO/O 2 = 2. No attention appears, however, to have been paid to the position of the maximum. It can be shown in the following way that there is a very simple relation between the composition of the mixture giving maximum pressure on explosion, and the dissociation of carbon dioxide at the maximum explosion temperature. Let the initial composition be represented by the expression 2 (1 + a ) CO + O 2 + b N 2 (Total mols = 3 + 2 a + b ), and let P i , T i represent the initial pressure and temperature; P e the maximum pressure observed after explosion, and T e the corresponding maximum temperature.


In the previous paper of the series* on the explosion of isothermic hydrogen-air and carbon monoxide-air mixtures in the theoretical proportions for complete combustion, at an initial pressure of 50 atmosphere it was shown- (1) that whereas in the case of hydrogen-air mixtures, the maximum pressure was always attained in about 0·005 second after the commencement of combustion, and the cooling set in almost immediately thereafter, in the case of the corresponding carbon monoxide-air mixtures, the time similarly taken for the attainment of maximum pressure was about forty times longer (namely, between 0·18 and 0·24 second), and cooling was delayed for quite an appreciable interval, showing that heat energy was still being liberated long after the maximum temperature had been reached; and (2) that the replacement, even in very small properties, of carbon monoxide bu its equivalent of hydrogen in the mixture 2CO+O 2 +4N 2 had an altogether disproportionately large influence in accelerating the rise of pressure on explosion; indeed, it seemed as though the hydrogen had imposed its own character upon the whole course of the Carbon monoxide combustion, even to the extract of suppressing the aforesaid marked evolution of heat after the attainment of maximum pressure.


1998 ◽  
Vol 11 (1) ◽  
pp. 565-565
Author(s):  
G. Cayrel de Strobel ◽  
R. Cayrel ◽  
Y. Lebreton

After having studied in great detail the observational HR diagram (log Teff, Mbol) composed by 40 main sequence stars of the Hyades (Perryman et al.,1997, A&A., in press), we have tried to apply the same method to the observational main sequences of the three next nearest open clusters: Coma Berenices, the Pleiades, and Praesepe. This method consists in comparing the observational main sequence of the clusters with a grid of theoretical ZAMSs. The stars composing the observational main sequences had to have reliable absolute bolometric magnitudes, coming all from individual Hipparcos parallaxes, precise bolometric corrections, effective temperatures and metal abundances from high resolution detailed spectroscopic analyses. If we assume, following the work by Fernandez et al. (1996, A&A,311,127), that the mixing-lenth parameter is solar, the position of a theoretical ZAMS, in the (log Teff, Mbol) plane, computed with given input physics, only depends on two free parameters: the He content Y by mass, and the metallicity Z by mass. If effective temperature and metallicity of the constituting stars of the 4 clusters are previously known by means of detailed analyses, one can deduce their helium abundances by means of an appropriate grid of theoretical ZAMS’s. The comparison between the empirical (log Teff, Mbol) main sequence of the Hyades and the computed ZAMS corresponding to the observed metallicity Z of the Hyades (Z= 0.0240 ± 0.0085) gives a He abundance for the Hyades, Y= 0.26 ± 0.02. Our interpretation, concerning the observational position of the main sequence of the three nearest clusters after the Hyades, is still under way and appears to be greatly more difficult than for the Hyades. For the moment we can say that: ‒ The 15 dwarfs analysed in detailed in Coma have a solar metallicity: [Fe/H] = -0.05 ± 0.06. However, their observational main sequence fit better with the Hyades ZAMS. ‒ The mean metallicity of 13 Pleiades dwarfs analysed in detail is solar. A metal deficient and He normal ZAMS would fit better. But, a warning for absorption in the Pleiades has to be recalled. ‒ The upper main sequence of Praesepe, (the more distant cluster: 180 pc) composed by 11 stars, analysed in detail, is the one which has the best fit with the Hyades ZAMS. The deduced ‘turnoff age’ of the cluster is slightly higher than that of the Hyades: 0.8 Gyr instead of 0.63 Gyr.


2005 ◽  
Vol 36 (1) ◽  
pp. 31-39 ◽  
Author(s):  
Daniel Pasquini ◽  
Maria Teresa Borges Pimenta ◽  
Luiz Henrique Ferreira ◽  
Antonio Aprigio da Silva Curvelo

2014 ◽  
Vol 32 (1) ◽  
pp. 30-70 ◽  
Author(s):  
Xiaohong Chen ◽  
David T. Jacho-Chávez ◽  
Oliver Linton

We establish the consistency and asymptotic normality for a class of estimators that are linear combinations of a set of$\sqrt n$-consistent nonlinear estimators whose cardinality increases with sample size. The method can be compared with the usual approaches of combining the moment conditions (GMM) and combining the instruments (IV), and achieves similar objectives of aggregating the available information. One advantage of aggregating the estimators rather than the moment conditions is that it yields robustness to certain types of parameter heterogeneity in the sense that it delivers consistent estimates of the mean effect in that case. We discuss the question of optimal weighting of the estimators.


2015 ◽  
Vol 1092-1093 ◽  
pp. 498-503
Author(s):  
La Xiang ◽  
Yu Ding

Natural gas (NG) is one of the most promising alternative fuels of diesel and petrol because of its economics and environmental protection. Generally the NG engine share the similar structure profile with diesel or petrol engine but the combustion characteristics of NG is varied from the fuels, so the investigation of NG engine combustion process receive more attentions from the researchers. In this paper, a zero-dimensional model on the basis of Vibe function is built in the MATLAB/SIMULINK environment. The model provides the prediction of combustion process in natural gas engines, which has been verified by the experimental data in the NG test bed. Furthermore, the influence of NG composition on engine performance is investigated, in which the in-cylinder maximum pressure and temperature and mean indicated pressure are compared using different type NG. It is shown in the results that NG with higher composition of methane results in lower maximum temperature and mean indicated pressure as well as higher maximum pressure.


There have not appeared recently any new determinations of the rate of change of the volume coefficient of expansion of condensable gases at pressures in the neighbourhood of a half to one metre. The work of Henning and Heuse and Heuse and Otto has been confined to a study of the permanent gases, their results leading to the conclusion that up to a pressure of 1 metre the rate of change of either the pressure or volume coefficient is a linear function of the pressure. Our knowledge of the behaviour of the condensable gases in this connection rests almost entirely on the very careful work of Chappuis, who in 1907 made a series of accurate determinations of the volume coefficient of expansion of carbon dioxide at a series of pressures from 1500 mm. to 500 mm. and over several temperature ranges. The investigation led to one unexpected conclusion which Chappuis left largely unexplained. On linear extrapolation to zero pressure of the graph of pressure against the mean coefficient of expansion over temperature intervals 0-20º, 0-40º, 0-100ºC., the limiting value of the coefficient rose from the normal value of 0.003661 for the 0-20º determinations to 0.003671 for those made over the range 0-100ºC. Chappuis concludes "that condensation on the reservoir surface plays a part in the irregularities but it is difficult to obtain a satisfactory explanation." As far back as 1853 Magnus demonstrated that the adsorption of sukphur dioxide on glass was sufficient to affect measurements of the expansion coefficient of gasses, and the importance of this error was recognized by Chappuis who in 1879 applied a correction to Regnault's measurements. Richards and Mark and Baly and Ramsay have pointed out the necessity for a knowledge of the amount of adsorption on the walls of the containing vessels when undertaking such determinations.


During the researches upon high-pressure explosions of carbonic oxide-air, hydrogen-air, etc., mixtures, which have been described in the previous papers of this series, a mass of data has been accumulated relating to the influence of density and temperature upon the internal energy of gases and the dissociation of steam and carbon dioxide. Some time ago, at Prof. Bone’s request, the author undertook a systematic survey of the data in question, and the present paper summarises some of the principal results thereof, which it is hoped will throw light upon problems interesting alike to chemists, physicists and internal-combustion engineers. The explosion method affords the only means known at present of determining the internal energies of gases at very high temperatures, and it has been used for this purpose for upwards of 50 years. Although by no means without difficulties, arising from uncertainties of some of the assumptions upon which it is based, yet, for want of a better, its results have been generally accepted as being at least provisionally valuable. Amongst the more recent investigations which have attracted attention in this connection should be mentioned those of Pier, Bjerrum, Siegel and Fenning, all of whom worked at low or medium pressures.


2006 ◽  
Vol 104 (4) ◽  
pp. 696-700 ◽  
Author(s):  
Yongquan Tang ◽  
Martin J. Turner ◽  
A Barry Baker

Background Physiologic dead space is usually estimated by the Bohr-Enghoff equation or the Fletcher method. Alveolar dead space is calculated as the difference between anatomical dead space estimated by the Fowler equal area method and physiologic dead space. This study introduces a graphical method that uses similar principles for measuring and displaying anatomical, physiologic, and alveolar dead spaces. Methods A new graphical equal area method for estimating physiologic dead space is derived. Physiologic dead spaces of 1,200 carbon dioxide expirograms obtained from 10 ventilated patients were calculated by the Bohr-Enghoff equation, the Fletcher area method, and the new graphical equal area method and were compared by Bland-Altman analysis. Dead space was varied by varying tidal volume, end-expiratory pressure, inspiratory-to-expiratory ratio, and inspiratory hold in each patient. Results The new graphical equal area method for calculating physiologic dead space is shown analytically to be identical to the Bohr-Enghoff calculation. The mean difference (limits of agreement) between the physiologic dead spaces calculated by the new equal area method and Bohr-Enghoff equation was -0.07 ml (-1.27 to 1.13 ml). The mean difference between new equal area method and the Fletcher area method was -0.09 ml (-1.52 to 1.34 ml). Conclusions The authors' equal area method for calculating, displaying, and visualizing physiologic dead space is easy to understand and yields the same results as the classic Bohr-Enghoff equation and Fletcher area method. All three dead spaces--physiologic, anatomical, and alveolar--together with their relations to expired volume, can be displayed conveniently on the x-axis of a carbon dioxide expirogram.


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