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Graph for Avogadros Law What Laws have we learned were also direct relationships, in which their graphs were similar to Avogadros? Ideal Gas Law Example 1 (using moles) If the pressure by a gas at 30 o C in a volume of.05 L is 3.52 atm, how many moles of the gas is present? Ideal Gas Law Example 2 (finding grams) Avogadros Law allows us to write a gas law that is valid not only for any P, V, or T but also for any mass of any gas! Explanation Ideal gases do not have molecular volume and show no attraction between molecules at any distance Real gas molecules have volume and show attraction at short distances. Gas Laws Kinetic Theory A physical model that explains the properties of gases, liquids, and solids in terms of: (A) forces between particles of matter. Molecules in Motion A.the kinetic theory all matter is composed of small particles (atoms, ions, molecules) these small particles are in constant motion. Ideal Gases: Now that we know how gases behave when we manipulate P, V, and T, it’s time to start thinking about how to deal with things like moles and. There can be no doubt that before the time of Eratosthenes the ideas of the learned world on the subject of geography had assumed a more regular and systematic form. It appears indeed from repeated statements of Strabo that Eratosthenes made it the object of his special attention to a€?reform the map of the world,a€? as it had existed down to his time, and to reconstruct it upon more scientific principles. With regard to the fundamental idea of all geography - the position and figure of the earth - Eratosthenes adopted the views that were current among the astronomers of his day, which had been received almost without exception from the times of Aristotle (ca.
But Eratosthenes had the merit of making one valuable addition to the previously existing ideas upon this subject, by a more careful and successful measurement than had ever been previously attempted, of the magnitude of the earth, or circumference of the terrestrial globe.
The method pursued by Eratosthenes was theoretically sound, and was in fact identical in principle with that which has been adopted by astronomers in modern day. While still keeping to the geocentric views of the universe, Eratosthenes started from the assumption that the sun was so distant that for practical purposes one could consider its rays parallel anywhere on earth. The only theoretical error in this mode of calculation was in the assumption - which was inevitable in the days of Eratosthenes - that the earth was exactly spherical, instead of being as it really is, a slightly oblate spheroid, and that therefore a meridian great circle was equal to that of the equator. In the first place, it was assumed that Syene lay directly under the tropic, it being a well-known fact that at the summer solstice the sun could be seen from the bottom of a deep well, and that at the same time the gnomon cast no perceptible shadow.
It is remarkable that while the terrestrial measurement was thus grossly inaccurate, the observation of latitude as deduced from the gnomon at Alexandria was a very fair approximation to the truth: a fiftieth part of a great circle being equivalent to an arc of 7A°12a€™, thus exceeding by about 7a€™ only the true interval between Alexandria and Syene, while falling short of that between Alexandria and the real Tropic by about 30a€™ or half a degree.
It appears indeed almost certain that Eratosthenes himself was aware of the imperfection of his data, and regarded the result of his calculation only as an approximation to the truth. After all it must be admitted that the calculation of Eratosthenes, considering the disadvantages under which he labored, came surprisingly near the truth. Once the value of 252,000 stades was accepted, it was feasible also to work out the circumference of any parallel circle.
Having thus laid the foundation of what has been called in modern times a€?geodesya€? - the determination of the figure and dimensions of the earth, considered in its entirety, as a part of the system of the universe, Eratosthenes next proceeded to consider that portion of it which was in his time geographically known, or supposed to be inhabited. In his Geographica Eratosthenes discussed the best method of drawing a map of the inhabited area of the earth as known.
Therefore, as with earlier map construction, the length of the oikumene greatly exceeds the width, though by what proportion depends on how much of the northern, eastern and southern extremities were regarded as inhabited.
As approximations to sizes and shapes of parts of the world, Eratosthenes first divided the inhabited world by a line stretching from the Pillars of Hercules [Straits of Gibraltar] to the Taurus Mountains and beyond, then subdivided each of these two sections into a number of irregular shapes, or sphragides, which literally meant a€?an official seala€™ and later was extended to represent a plot of land numbered by a government surveyor, then by extrapolation to a numbered area on a map.
Eratosthenes undoubtedly conceived, in accordance with the prevalent belief in his day, that the Ocean was found immediately to the east of India, and that the Ganges flowed directly into it. From that point he supposed the coast to trend away towards the northwest, so as to surround the great unknown tracts of Scythia on the north, but sending in a deep inlet to the south, which formed the Caspian Sea.
His ideas of the geographical position and configuration of India were also in great measure erroneous.
Physical geography, in the modern sense of the term, was still quite in its infancy in the days of Eratosthenes, and it cannot be said that he did much to impart to it a scientific character. Eratosthenes also adopted, and apparently developed at considerable length, an idea first suggested by the physical philosopher Strabo, that the Mediterranean and the Euxine [Black] Seas had originally no outlet, and stood in consequence at a much higher level, but that they had burst the barriers that confined them, and thus given rise to the Straits of the Bosphorus, the Hellespont and that of the columns. This map of the known world was a very striking achievement and may be considered to be the first really scientific Greek map. Enable every woman who can work to take her place on the labour front, under the principle of equal pay for equal work. What is Avogadros Law Avogadros Principle – equal volumes of gases at the same temperature and pressure contain equal numbers of particles. P t = the total pressure P 1 = Partial Pressure of gas 1, P 2 = Partial Pressure of gas 2, etc.
What is Avogadro’s Law Avogadro’s Principle – equal volumes of gases at the same temperature and pressure contain equal numbers of particles.
VARIABLES THAT DESCRIBE A GAS Compressibility: a measure of how much the volume of matter decreases under pressure. 13.1 The Gas Laws The gas laws apply to ideal gases, which are described by the kinetic theory in the following five statements. Kinetic Theory of Gases ? Gases exert pressure because their particles frequently collide with the walls of their. 2 Properties of Gases Expand to completely fill their container Take the Shape of their container Low Density –much less than solid.

More symmetrical than accurate, its partitions were the forerunners of parallels and meridians after DicA¦archus (#111).
And it is certain also that these had been embodied in the form of maps, which, however imperfect, were unquestionably very superior to anything that had preceded them. It is this enlarged and philosophical view of the subject that constitutes his special merit, and entitles him to be justly called as the a€?parent of scientific geographya€?.
Once the idea of a spherical earth was accepted, and that it was a perfect sphere, the measurement of this body was a logical step, even to Greek scholars who were more given to philosophical speculation than to quantification and experimentation. The method pursued by Eratosthenes is fully stated and explained by the astronomer Cleomedes, in his work on the Circular Motion of the Heavenly Bodies. He observed that the rays of the sun, at midday, at the time of the summer solstice, fell directly over Syene [modern-day Aswan] and that the vertical rod of the sun dial (gnomon or style) would not cast a shadow (predicated on the assumption that Syene was situated exactly under the Tropic of Cancer). But, though these facts were perfectly correct as matters of rough observation, such as could be made by general travelers, they were far from having the precise accuracy requisite as the basis of scientific calculations. Hence, as mentioned above, he felt himself at liberty to add 2,000 stades to the 250,000 obtained by his process, in order to have a number that would be readily divisible into sixty parts, or into degrees of 360 to a great circle. His measurement of 250,000 stades (the immediate result of his calculation) would be equivalent to 25,000 geographical miles, while the actual circumference of the earth at the equator falls very little short of 25,000 English miles. Thus Eratosthenes calculated that the parallel at Rhodes, 36A°N., was under 200,000 stades in circumference. And here it must be observed that the relation between the habitable world, which was alone regarded as coming within the scope of the geographer (properly so called), and the terrestrial globe itself, was, in the days of Eratosthenes, and even long afterwards, a very different one from that which we now conceive as subsisting between them.
The first task of the geographer therefore, according to the notions then prevailing, was to determine the limits and dimensions of the map of the world, which was to form the subject of his special investigations. India he suggested drawing as a rhomboid; Ariana [the eastern part of the Persian Empire] would be illustrated as approximating a parallelogram. Just to the north of the Ganges the great mountain chain of Imaus, which he regarded as the continuation of the Indian Caucasus and the Taurus, descended (according to his ideas) to the shores of the Eastern Ocean; and he appears to have given the name of Tarnarus to the headland which formed the termination of this great range.
Of the northern shores of Asia or Europe he had really no more knowledge than Herodotus (#109), but, unlike that historian, he assumed the fact that both continents were bounded by the Ocean on the north; a fact which is undoubtedly true, but in a sense so widely different from that supposed by Eratosthenes that a can hardly be held as justifying his theory. As mentioned above, he conceived it to be of a rhomboidal form, which may be regarded as a rough approximation to the truth, and he even knew that the two sides, which enclosed the southern extremity, were longer than the other two. In treating the mountain chains of Asia as one continuous range, to which he applied the name of Taurus, he may be regarded as having made a first attempt, however crude, at that systematic description of mountain ranges to which we now give the name of orography. In proof of this theory he alleged the presence of marine shells far inland in Libya, especially near the temple of Jupiter Ammon, and on the road leading to it, as well as the deposits and springs of salt that were also found in the Libyan deserts.
Although the dimensions are not known exactly, as it was presented to the Egyptian court a may be assumed to have been fairly large.
They all take up space and interact with other molecules (attraction, repultion) but most gases will behave like ideal gases at the right conditions of temp. Geographic information that was gathered by Alexander the Great and his successors was the primary source used by Eratosthenes, a scholar with vision large enough to put this information into a logical framework. The first use of world maps by the Greeks had been introduced at a very early period by Anaximander (ca.
The materials at his command were still very imperfect, and the means of scientific observation were wanting to a degree which we can, at the present-day, scarcely figure to ourselves; but the methods which he pursued were of a strictly scientific character, and his judgment was so sound that he proved in many instances to be better informed and more judicious in his inferences than geographers of two centuries later. He was not indeed the first who had attempted the solution of this problem, which would naturally engage the attention of astronomers and geometers, as soon as it was agreed that the earth was of a spherical form. Both the method and the accuracy of Eratosthenesa€™ well-known measurement of the earth have evoked the admiration of later workers, and his calculation is regarded as one of the greatest achievements of Greek science.
Syene is in fact situated in latitude 24A° 5a€™ 30a€?, or nearly 37 miles to the north of the Tropic. Ever since the discoveries of the great Portuguese and Spanish navigators in the 15th and 16th centuries opened out to us new continents, and extensions of those already known, far beyond anything that had previously been suspected or imagined, men have been accustomed to regard the a€?map of the worlda€? as comprising the whole surface of the globe, and including both the eastern and western hemispheres, while towards the north and south it is capable of indefinite extension, until it should reach the poles, and is in fact continually receiving fresh accessions. This question, which was taken up by Eratosthenes at the beginning of his second book, had already been considered by several previous writers, who had arrived at very different results. Rather than a rectangle, he thought of the oikumene as tapering off at each end of its length, like a chlamys [short Greek mantle]. In fact the conclusion of Eratosthenes was mainly based upon the erroneous belief that the Caspian communicated with the Ocean to the north in the same manner that the Persian Gulf did to the south; a view which was adopted by all geographers for a period of three centuries, on the authority of Patrocles.
Yet the erroneous idea of its communication with the Ocean to the north sufficiently shows how questionable the information possessed by the Greeks really was. But as he supposed the range of Imaus that bounded the country to the north to have its direction from west to east, while the Indus flowed from north to south, he was obliged to shift around the position of his rhomb, so as to bring the other two sides approximately parallel to the two thus assumed. He also arrived at a sound conclusion concerning the causes of the inundation of the Nile, a subject that must naturally have engaged the attention of a geographer resident in Egypt.
It must have been drawn as closely as possible to scale, and its influence on subsequent Greek and Roman cartography was tremendous.
With low temperatures (close it gass liquefication point), the molecules do not have enough energy to continue on their path to avoid the attraction. He regarded the earth as a sphere, placed in the center of the universe, around which the celestial sphere revolved every twenty-four hours: besides which, the sun and moon had independent motions of their own. Aristotle refers to the calculation of a€?mathematiciansa€? who had investigated the subject (without naming them) that the earth was 400,000 stades in circumference.

Secondly, Alexandria, instead of being exactly on the same meridian with Syene, lay in fact not less than three degrees of longitude to the west of it: an error of no trifling moment when the distance between the two was assumed as the basis of calculation.
Thus was established the basis of a fairly accurate system of coordinates for any sectional mapping of the Mediterranean based upon the Rhodes parallel. With the Greek geographers on the contrary, from Eratosthenes to Strabo, the known or habitable world was conceived as a definite and limited portion of the eartha€™s surface, situated wholly within the northern hemisphere, and comprised within about a third of the extent of that section.
On one point indeed they were all agreed, that the length of the habitable world, from west to east, greatly exceeded as breadth, from north to south. Moreover, Strabo tells us that to the above total of 74,000 stades Eratosthenes, using another mathematical ploy, added 2,000 at each end, to prevent the width being more than half the length. Hence he conceived the projecting angle of India to have a direction towards the southeast instead of the south, and even supposed it to advance farther towards the east than the mouth of the Ganges. On the other hand he stated a strange hypothesis: that the surplus waters of the Euphrates were carried by subterranean channels to Coele, Syria, and thence again underground so as to feed the streams which broke out near Rhinocorura and Mount Casius. Indeed, with Ptolemya€™s inaccurate alterations to the overall dimensions of the world and the oikumene, it can be said to have affected world maps right down to the Age of Discovery.
Real gases do NOT behave like ideal gases at extremely high pressures and extremely low temperatures. 24, #115) to whom we are indebted for much of our knowledge of geography in antiquity, including the work of Eratosthenes whose relevant works, neither of which have survived, were On the Measurement of the Earth and Geographica, Cleomedes summarized the former, Strabo criticized the latter. The obliquity of the suna€™s course to that of the celestial sphere was of course well known; and hence the great circles of the equinoctial, and the ecliptic, or zodiacal circle, as well as the lesser circles, called the tropics, parallel with the equinoctial, were already familiar to the astronomers of Alexandria. But a much graver error than either of these two was that caused by the erroneous estimate of the actual distance between the two cities. Towards the north and south it was conceived that the excessive cold in the one case, and the intolerable heat in the other, rendered those regions uninhabitable, and even inaccessible to man.
Democritus, two centuries before Eratosthenes, had asserted that it was half as long again as it was broad, and this view was adopted by DicA¦archus (#111), though recent discoveries had in his day materially extended the knowledge of its eastern portions.
On the parallel of Rhodes, this total of 78,000 stades corresponds to about 140A° longitude, which is roughly the distance from Korea to the west coat of Spain. He appears in fact to have obtained, probably from the information collected by Patrocles, a correct general idea of the great projection of India in a southerly direction towards Cape Comorin, but was unable to reconcile this with his previously conceived notions as to its western and northern boundaries, and was thus constrained altogether to distort its position in order to make it agree with what he regarded as established conclusions. Nor can it be doubted that the discoveries resulting from the conquests of Alexander the Great (ca.
Future scholars, however, would have a higher opinion of Eratosthenes, regarding him, a€?as the parent of scientific geographya€? and at least a€?worthy of alphaa€? in that subject, particularly for his remarkable measurement of the circumference of the earth. Moreover it appears that these conceptions, originally applied to the celestial sphere, had been already transferred in theory to the terrestrial globe.
What mode of measurement had been resorted to, or how Eratosthenes arrived at his conclusion upon this point, we are wholly without information: but it may well be doubted whether he had recourse to anything like actual menstruation.
That there might be inhabitants of the southern hemisphere beyond the torrid zone, or that unknown lands might exist within the boundless and trackless ocean that was supposed to extend around two-thirds of the globe from west to east, was admitted to be theoretically possible, but was treated as mere matter of idle speculation, much as we might at the present day regard the question of the inhabitants on Mars.
The astronomer Eudoxus on the other hand maintained that the length was double the breadth; Eratosthenes went a step farther and determined the length to be more than double the breadth, a statement that continued to be received by subsequent geographers for more than three centuries as an established fact. It was doubtless from the same source that he had learned the name of the Coniaci, as the people inhabiting this southernmost point of India; a name that hence forward became generally received, with slight modifications, by ancient geographers.
Thus the idea of the globe of the earth, as it would present itself to the mind of Eratosthenes, or any of his more instructed contemporaries, did not differ materially from that of the modern geographer.
But as a mathematical ploy, in order to achieve a number divisible by 60 or 360, so as to correlate stades with his subdivisions or degrees, he emended this to 252,000 stades [a stade, stadion, stadia], originally the distance covered by a plough before turning, was 600 feet of whatever standard was used]. Indeed the difficulty which modern experience has shown to attend this apparently simple operation, where scientific accuracy is required, renders it highly improbable that it was even attempted; and the round number of 5,000 stades at once points to its being no more than a rough approximation.
The same thing was the case in ancient times, and it is highly probable that if you could now recover the map of the world as it was generally received in the time of the first Ptolemies, we should find it still retaining many of the erroneous views of Herodotus and HecatA¦us (#109 and #108). For all geographical purposes, at least as the term was understood in his day, the difference between the geocentric and the heliocentric theories of the universe would be unimportant. A conversion to modern units of measure finds Eratosthenesa€™ calculation to be somewhere between 45,007 km (27,967 miles) to 39,690 km (24,663 miles), as compared to actual equatorial circumference of 40,075 km (24,902 miles), there has always been some controversy over the equivalent modern length of a stade as used by Eratosthenes. But even considered as such, it exceeds the truth to a degree that one could hardly have expected, in a country so well known as Egypt, and in an age so civilized as that of the Ptolemies. Alexandria is in fact situated at a distance of about 530 geographical miles (5,300 stades) from Syene, as measured on the map along the nearest road but the direct distance between the two, or the arc of the great circle intercepts between the two points, which is what Eratosthenes intended to measure, amounts to only 453 miles or 4,530 stades. But we have no information as to the data on which these first crude attempts were based, or the mode by which he authors arrived at their results. Eratosthenes, therefore, in fixing the length of this arc at 5,000 stades, was 470 beyond the truth. The difference in latitude between Alexandria and Syene really amounts to only 7A° 5a€™, so that the direct distance between the two cities, supposing them to have been really situated on the same meridian (as Eratosthenes assumed them to be) would not have exceeded 425 miles or 4,250 stades, instead of 5,000.