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air with helium. Because carbon dioxide is cheap, available in large quantities, and easily separated from helium, it was decided to displace the air with this gas. This method of inflation had previously been used on a test section of the hull with good results. An attempt was made to carry out the inflation in such a manner as to allow the carbon dioxide to displace the air with as little mixing of the gases as was possible. Since there are two chief causes of the mixing of these two gases-i. e., diffusion and turbulent flow of gas from the containers-it was necessary to determine the conditions of operation which would minimize the effect of these phenomena. As turbulence is mainly caused by rapid movement of the gas, an attempt was made to keep the velocity of the incoming carbon dioxide well within the region of quiet flow. Diffusion, on the other hand, depends upon a number of factors, among which are time, difference in density of the gasec, and the diffusing area. Taking all these factors into account, a rate of input of carbon dioxide of about 10,000 cubic feet per hour way tried, found satisfactory, and maintained throughout the inflation. Stratification of the carbon dioxide and air was quite complete. This was partially visible to the naked eye. During the inflation the interior of the ship was illuminated. Through the peep holes one could observe the moirture condensing out of the air and lying as a blanket of fog on the layer of cold carbon dioxide in the lower part of the ship. -1s the carbon dioxide rose higher and higher in the hull, the layer of fog preceded it. Results of the gas analysis also verified the completeness of stratification as shown by Figure 4, which gives the percentage of carbon dioxide a t various levels in the hull plotted against time during the inflation. The lower sampling tubes almost immediately indicated 100 per cent carbon dioxide. The rise in percentage of carbon dioxide was rapid, once appreciable quantities of the gas appeared in any tube. About 33,000 cubic feet of carbon dioxide were lobt in purging, which is extremely low. During the helium inflation stratification was not nearly so complete. This was due chiefly to the great difference in density betv-een helium and carbon dioxide. The input could
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not be kept within the region of quiet flow without considerable diffusion. While the volume was small and the area exposed to diffusion was not great, stratificationwas fairly complete, as shown by Figure 4. When appreciable quantities of helium had displaced the carbon dioxide, trouble began. Some of the causes of the rapid rise of helium in the exhaust before the scrubbing was started were as follows: The diffusing area, which was about 6000 square feet, had been at its maximum for some time; the gas came into contact with the tops of the inflated ballonets, causing a surging motion; the rate of input of helium had been increased. However, it is doubtful if diffusion between carbon dioxide and helium could have been prevented. The insertion of a drier or refrigerator between the scrubber and the hull would be a decided improvement. Spacing the sampling tubes symmetrically above and below the equator of the ship would give a more accurate check of the progress of inflation. The rate of input of helium was about 10.000 rubic feet per hour. Conclusions
The results show that the method employed i b relatively simple and efficient for inflating this type of ship. One hundred per cent ballonet could not be employed in a ship of this size. In a large ship, where 100 per cent ballonet may be used, the usual method of inflation can be carried out. Final conclusions concerning the diffusion of helium from this ship have not been reached, as it has been under study for too short a time. However, approximately 100 cubic feet of helium are added every 24 hours to replace leakage froin the hull. The purity of the gas in the ship has not decreased due to inward leakage of air. This fact is a decided advantage over the fabric ship, which allows appreciable inward leakage of air with a corresponding loss of lift. Literature Cited ( 1 ) Fritsche, J l e c h . E n g , 61, 905 (1920), gives complete description of
design, construction, and erection of the Z M C - 2 .
A Derivation of Duhring’s Rule’ A. McLaren White G E O R G IS~C H O O L
OF
TIXHKOLOGY, ATLANT.4, GA.
CRIKG the last few years the necessity for obtaining a simple yet accurate method of relating vapor pressures and temperatures has led to the rediscovery of Duhring’s rule. This relation has given valuable results when applied to solutions of salts in water ( I ) , to solutions of organic liquids (4), and to pure liquids. Duhring’s rule has been regarded as entirely empirical, though from its wide applicability and validity it would seem that it should have some thermodynamic basis. It is the object of this paper to point out how Drihring’s rule niay be reconciled with thermodynamics. Inasmuch as the Duhring relation inrolres vapor pressures and temperatures, it seems logical to believe that it must be connected with the Clausius-Clapeyron equation. This equation in its approximate form may be stated as
D
d In p/dT = AH/RT2
(1)
where p is the vapor pressure, T the absolute temperature, and AH the heat of vaporization. The vapor is here as1
Received November 29, 1929.
sumed to be a perfect gas, and the volume of the liquid negligible compared with that of the vapor. If the heat of vaporization is assumed to be constant over a small range of teniperature, this equation may be integrated, obtaining l n p = -AH/RT C (2) This equation proves experimentally to yield a straight line over small ranges of temperature. Now for t x o different substances, a and b, let the vapor pressures be equal at absolute temperatures, T , and Tb. Substituting in Equation 2 and equating the result
