Determination of coefficient of expansion of air

Determination of coefficient of expansion of air INTRODUCTION This experiment is based on investigating the coefficient of expansion of air using a simple laboratory set up; the stopper flask method, where pressure is constant throughout the experiment. The increase in volume of a gas is directly proportional its temperature increase and is expressed as a fractional changed in dimensions per unit temperature change. Air will easily expand when it is heated and contract when it is cooled. The aim of the experiment was to: * Determine the coefficient of expansion of air using a stoppered flask method. The flask was stoppered and a thick tube allowed interactions with the outside. The flask was heated in a beaker (with water) and then transferred immediately to cold water where the cold water was allowed to enter and air within the flask decreased. The initial and final volumes of air and water was calculated (directly or indirectly whichever appropriate) and the coefficient was calculated from these. The experiment in its design allowed the calculation of the coefficient of expansion of air to be 3.22 * 10-3 K-1. This was calculated at a temperature of 24oC and pressure of 1 atm, which gives a good approximation compared to the theoretical value of 3.37 * 10-3 at a temperature of 24 oC (297 K). THEORY Dooley (1919) indicates that gases are said to be perfectly elastic because they have no elastic limit and expand and contract alike under the action of heat. That is to say, every substance when in the gaseous state and not near its point of liquefaction has the same coefficient of expansion, this coefficient being 1/273 of its volume for each degree Centigrade. He further goes on to say that since a gas contracts 1/273 part of its volume when its temperature is lowered 1 ° C, such a rate of contraction would theoretically reduce its volume to zero at a temperature of 273 ° C. Since all gases reach their liquefying point before this low temperature is attained, however, no such contraction exists. At the same time, it may be said that if heat is considered as a motion of the molecules of a substance, that motion is to be considered as having ceased when the temperature has reached 273 ° C. This is the expansion coefficient of an ideal gas. GAY LUSSACS LAW Madan (2008: 81) indicates that the coefficient of expansion of a substance at any given temperature, t, is the small fraction of its volume by which one cubic centimeter of the substance will increase when heated from to. * Gases are affected by changes of temperature in the same general way as liquids and solids, expanding when heated and contracting when cooled. * For a given change in temperature, they change in volume to a far greater extent than either liquids or solids. * All gases, at temperatures considerably above their liquefying points, have practically the same coefficient of expansion. This was first observed by Gay Lussac and Charles, and is a very remarkable one, and a great contrast to what has been noticed in the case of solids and liquids, each of which has its own special coefficient of expansion, often differing widely from those of others. EXPANSION AGAINST CONSTANT PRESSURE Atkins (2006: p35) indicates that: By definition: At constant pressure: This indicates that the work done is actually the difference between the final and initial volumes multiplied a unit of pressure (which is constant). Once can say therefore that a gas expands (independent of pressure) but dependant on temperature as given by: METHOD Method as per hand out, however, a small beaker with water was used to heat the flask and atmospheric pressure was used instead of reading the barometric height (which was not available). MATERIALS/APPARATUS  · Conical Flask (100 mL)  · Rubber Stopper  · Metal Clip  · Short Glass Tube  · Heater  · Beakers (500 mL) 2  · Thick Walled Rubber Tube  · Thermometer (0 100oC)  · Electric Balance Weight of flask + fittings 136.4 + 0.1 g Weight of flask + fitting + water sucked in 168.6 + 0.1 g Weight of water sucked in 032.2 + 0.1 g Weight of flask + fittings + full water 279.8 + 0.1 g Weight of full water 143.4 + 0.1 g Temperature of boiling water 103.0 + 0.1 oC Temperature of cold water 024.0 + 0.1 oC Atmospheric Pressure 1.00 atm Volume of gas @ 103.0 oC 143.4 + 0.1 cm3 Volume of gas @ 24.0 oC 111.2 + 0.1 cm3 DISCUSSION The experiment investigated the coefficient of expansion of air. This value was found to be 3.22 * 10-3 experimentally. One would infer, at first glance, that the volume of air initially would have been the volume of the flask (100 mL), as the volume of a gas is the actual volume of the container. But why was the mass of the beaker found (filled with cold water)? Was it to give a better estimation of the volume of the air? By finding the volume using the density of water, it was found to be 143.2 cm3 which is a large difference compared to the 100 mL of the flask. Then one realized that the flask was filled to the top close to the stopper itself, and therefore assuming that the volume of air was 100mL would have been a grave mistake and calculating the volume by density was the best and accurate method to use. The experiment relies on the fact that the volume of a substance, in this case, air, is dependent on the temperature of the system. The flask (opened) was heated in boiling water, this was indirect heating of the flask, it allowed the inside of the flask to be dry and consequently allowed the air to be dry. In addition, by heating the flask in boiling water, the temperature of the air inside the flask increased as well (according to the zeroth law of thermodynamics), indicating that there will be some form of thermal equilibrium. At this point, the initial volume and temperature of the air will be obtained. The tube was closed with a clip and placed in the water at a lower temperature. The question that arises at this point is why was the clip closed? A logical assumption is that to disallow further interaction between the atmospheric air (at a lower temperature) and the flasks air (at a higher temperature), also one can say that because of the temperature gradient, their will want to escape and in so doing create a thermal equilibrium between the two. The water was allowed to enter, to replace the air and thus the volume of air decreased. This method was unique in its design that it used a backward approach. Rather than obtaining the expansion of air from a lower to a higher temperature, it measured the contraction of the air from a higher to a lower temperature. In the end, the initial and final volumes and temperatures of the air being considered were obtained, and thus the coefficient was able to be calculated. SIGNIFICANCE OF EXPANSION COEFFICIENT The value ascertained experimentally was 3.22 * 10-3. This can be termed a fractional change as it is very small (0.001th of a value 3.22). It can be inferred that this fractional change affects the volume of the sample when a rise in temperature occurs. It means therefore, that for every change in temperature from to to (t+1)o, the volume of air in one cm3 of air will increase by 3.22 * 10-3 at 1 atm (experimental condition). A small value of ÃŽÂ ±, indicated by Atkins (2006) implies that it responds weakly to changes in temperature i.e. the air responds weakly to changes in temperature which is important in life itself, as air responding strongly to temperature changes would be hazardous to our health, and may even result in cardiac arrests with sudden decreases in temperature (during winter time in north America and Europe among other places) and where there are heat surges. COMPARING EXPERIMENTAL AND THEORETICAL EXPANSION COEFFICIENT The theoretical value of the expansion coefficient should be, since. The deviation is (3.37 * 10-3- 3.22 * 10-3) = 1.5 * 10-2. This deviation represented almost 4.66% of the theoretical value! What can account for this deviation? It all leads to experimental errors, since pressure is constant. Obviously, by looking at the formula, the process of obtaining the final and initial volumes and temperatures will have an effect on the expansion coefficient. The volume of water sucked in may not have been at maximum due to hindrances in the tubing attached to the flask, or the water was not allowed to go in as fast as it should. Also, one can consider that the density of water used to calculate the volume of air after the water had been sucked in may have been different and hence affected the calculated the volume). All of these can contribute uncertainties to the coefficient of expansion and can be used to explain the difference observed. SOURCES OF ERRORS * The difference between the experimental and established values is therefore attributed to factors such as temperature, volume, and the accuracy at which these values were obtained as described above. * The density of water probably affected the results when it was used to calculate the final volume of air and initial volumes of air. * Within the limits of experimental error, the value ascertained was close to the theoretical value with only about 5% deviation. * The volumes and temperatures had uncertainties of + n, where n represented the volume and temperature. The final result of the coefficient had an uncertainty of 0.41%. LIMITATIONS * The method did not allow the calculations of the volumes and temperatures directly but indirectly. A direct method, if possible, would have contributed to a more accurate value of the coefficient of expansion. * The experiments were not repeated to ascertain different values of the volumes and temperatures. Averaging the values would have allowed a more accurate value of the temperatures and volumes and by extension the coefficient of expansion. ASSUMPTIONS * It was assumed that air was ideal in nature and followed the ideal gas equation. Introduction of van der waals coefficient would have proved to be more tedious in calculating the coefficient of expansion of air. * It was assumed that the volume of dry air in the flask was the volume of the water in cm3. As mentioned previously, the water was filled to the top of the flask (close to the stopper), and assuming 100mL would have been grossly inadequate contributing to more uncertainties and thus a more inaccurate value of the expansion coefficient. * It was assumed that rate at which the temperature and volume decreased when the flask was placed in the water allowed the expansion coefficient to be ascertained. This was very important, as it implied that the temperature affected the expansion and or contraction of air and water which ultimately enabled the calculation of the coefficient. CONCLUSION With reference to the aim, it can be concluded that the experiment in its design allowed the calculation of the coefficient of expansion of air to be 3.22 * 10-3 K-1. This was calculated at a temperature of 24oC and pressure of 1 atm. BIBLIOGRAPHY Anand, A and Negi, S. A Textbook of Physical Chemistry. USA: John Wiley Sons, 1985. Atkins, Peter and De Paula, Julio. 2006. Physical Chemistry 8th Edition. USA : W. H Freeman Company, 2006. Castellan and Gilbert. 1983. Physical Chemistry 3rd Edition. Massachusetts: Addison Wesley Publishing Company, 1983. Chirlian and L.E. Chemistry 103 Home Page. Department of Chemistry 103. [Online] [Cited: November 7, 2009.] http://www.brynmawr.edu/Acads/Chem/Chem103lc/chem103.html. Daley, Henry and OMalley, Robert. 1988. Problems in Chemistry 2nd Edition. USA: CRC, 1988. Dooley, William. Applied Science for Metal Workers. USA: Kessinger Publishing, LLC, 2008. Flowers and James. 2004. Cracking the MCAT with CD-ROM. USA: Princeton Review, 2004. Haven, Mary, Tetrault, Gregory A and Schenken, Jerald R. 1994. Laboratory Instrumentation 4th Edition. USA: Wiley, 1994. Kaufman, Myron. 2002. Principles of thermodynamics . USA: CRC, 2002. Lide, David. 1993. Handbook of Chemistry and Physics 74th Edition. USA: CRC, 1993. Madan, G.H. An Elementary Treatise on Heat. USA: Law Press, 2008. Mortimer, Roger. 2008. Physical Chemistry 3rd Edition. Canada: Elsevier Academic Press, 2008. Orme, T. A. An Introduction to the Science of Heat. USA: BiblioLife, 2008.

A New Product Concept

Every parent wants his child to develop good logical thinking skills and learn new things. That is why many parents employ different tutors or coaches for their children. Certainly, it is impossible to underestimate the contribution of books and developing games, but frequently children are getting bored of solving different problems or puzzles and throw such games away.Therefore, a new product concept is a new type of a developing game, which will offer a reward for solving one or another puzzle or problem.It is a new generation of heuristic games, which uses a powerful stimulation – a bonus (it can be some money, a chewing gum, a cinema ticket, and so on), which can not be reached in other way but solving a puzzle.A number of the first bonuses will be placed into the game box by the manufacturer, and after those prizes are won by the child, parents can place new bonuses of their own choice and make different exciting surprises for their kid. In addition, it will be possible to choose a type of bonus stimulation: giving a bonus for every single puzzle solved, or giving some bigger bonus for a number of problems solved, etc.The game will have an option of selecting a level of difficulty, so it can be used for children of different ages, starting from 5 and above. Undoubtedly, this game develops not only logical thinking, but also, persistence, determination, willpower and perseverance. The main advantage of this game is the opportunity to transform the process of learning into some real fun and entertainment, which will also be rewarded in the end.I suppose that this innovative developing game will receive a good demand and find its market easily. This product does not require any sophisticated technological process of manufacturing and can be produced from a polymer material, which is safe for children.It is possible to use different color designs and decoration. At the most modest estimate, it is possible to start manufacturing of such games within 6-7 month, and receive the first profits in 3-4 month after entering the market. This business idea does not require huge financial investments and other resources, besides it has important social implication.Bibliography:Dotson, L. (2000, February 1). Top 7 Ways to Get New Product Ideas. Top 7 Business. Ed. Christopher M. Knight.. Retrieved April 3, 2007, from .

Advantages And Disadvantages Of Technology In Education

According to Albert Einstein’s wording, he never taught pupils; and only tried to provide the conditions in which they can learn. Now-a-days, in this enriching technological era, where a man is encircled with gadgets and techno-era usages in all the aspects of life, it is highly convincible to use the same in education system as well. Though, this advancement is inevitable, still there are many fall-outs that the teachers and the education providers should look forward to. I would like to extend my views regarding the problems that may arise during and due to the usage and overdependence of technology for teaching purposes and precisely in ESL context, especially when the students are unable to adapt the new technique of teaching. Also, I†¦show more content†¦However, it may be seen that both within and across countries, there is extreme unevenness in access to ICT. 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Livia Drusilla the 1st Empress of Rome

Livia (58 B.C. - A.D.29) was a long-lived, influential matriarchal figure in the early years of the Roman Principate. She was held up as an example of womanly virtue and simplicity. Her reputation has also been negative: she may have been a murderer and has been described as treacherous, avaricious, and power-hungry. She may have been instrumental in the banishment of Augustus daughter, Julia. Livia was the wife of the first Roman emperor, Augustus, mother of the second, Tiberius, and deified by her grandson, the Emperor Claudius. Livias Family and Marriages Livia Drusilla was the daughter of Marcus Livius Drusus Claudius (note the Claudian, the gens that had produced Appius Claudius the Blind and the colorful Clodius the Beautiful, among others) and Alfidia, daughter of M. Alfidius Lurco, in c. 61 B.C. In his book,  Anthony Barrett says Alfidia appears to have come from Fundi, in Latium, near Campania, and that Marcus Livius Drusus may have married her for her familys money. Livia Drusilla may have been an only child. Her father may also have adopted Marcus Livius Drusus Libo (consul in 15 B.C.). Livia married Tiberius Claudius Nero, her cousin when she was 15 or 16—around the time of the assassination of Julius Caesar in 44 B.C. Livia was already the mother of the future emperor, Tiberius Claudius Nero, and pregnant with Nero Claudius Drusus (January 14, 38 B.C. - 9 B.C.) when Octavian, who would be known to posterity as the Emperor Augustus Caesar, found he needed the political connections of Livias family. He arranged for Livia to be divorced and then married her after she gave birth to Drusus, on January 17, 38. Livias sons Drusus and Tiberius lived with their father until he died, in 33 B.C. They then lived with Livia and Augustus. Augustus Adopts Livias Son Octavian became the Emperor Augustus in 27 B.C. He honored Livia as his wife with statues and public displays; however, instead of naming her sons Drusus or Tiberius as his heirs, he acknowledged his grandchildren Gaius and Lucius, sons of Julia, his daughter by his previous marriage to Scribonia. By 4 A.D., Augustus grandsons had both died, so he had to look elsewhere for heirs. He wanted to name Germanicus, son of Livias son Drusus, as his successor, but Germanicus was too young. Since Tiberius was Livias favorite, Augustus eventually turned to him, with provision made for Tiberius to adopt Germanicus as his heir. Augustus died in 14 A.D. According to his will, Livia became a part of his family and was entitled to be called Julia Augusta from then on. Livia and  Her Descendants Julia Augusta exerted a strong influence on her son Tiberius. In A.D. 20, Julia Augusta interceded successfully with Tiberius on behalf of her friend Plancina, who was implicated in the poisoning of Germanicus. In A.D. 22 he minted coins showing his mother as the personification of Justice, Piety, and Health (Salus). Their relationship deteriorated and after the Emperor Tiberius left Rome, he would not even return for her funeral in 29 A.D., so Caligula stepped in. Livias grandson the Emperor Claudius had the Senate deify his grandmother in A.D. 41. Commemorating this event, Claudius minted a coin depicting Livia (Diva Augusta) on a throne holding a scepter. Source Larry Kreitzer  Apotheosis of the Roman Emperor  Larry Kreitzer  The Biblical Archaeologist, 1990Alice A. Deckman  Livia Augusta  The Classical Weekly, 1925.