Determination of coefficient of expansion of air

Determination of coefficient of elaborateness of nervous strainINTRODUCTIONThis experiment is based on investigating the coefficient of elaboration of air using a simple laboratory set up the stopper flaskfulfulful method, where pressure is constant throughout the experiment. The affix in garishness of a gas is directly proportional its temperature increase and is expressed as a fractional switch overd in dimensions per unit temperature change. Air will easily brandish when it is het up(p) and contract when it is cooled. The aim of the experiment was to* Determine the coefficient of intricacy of air using a stoppered flask method.The flask was stoppered and a cryptic tube allowed interactions with the outside. The flask was heated in a beaker (with water system) and then transferred immediately to cold water where the cold water was allowed to enter and air within the flask decreased. The initial and nett peoples of air and water was calculated (directly or indirectly whi chever appropriate) and the coefficient was calculated from these.The experiment in its normal 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 comp atomic number 18d to the theoretical value of 3.37 * 10-3 at a temperature of 24 oC (297 K). THEORYDooley (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 essence when in the gaseous state and not near its point of liquefaction has the alike coefficient of expansion, this coefficient being 1/273 of its majority 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 the ir liquefying point before this low temperature is attained, however, no such contraction exists. At the same m, 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 LAWMadan (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 aver special coefficient of expansion, often differing widely from those of others. EXPANSION AGAINST CONSTANT PRESSUREAtkins (2006 p35) indicates thatBy definitionAt constant pressureThis indicates that the work done is actually the residual between the final and initial volumes multiplied a unit of pressure (which is constant). Once piece of tail say therefore that a gas expands (independent of pressure) but dependent on temperature as given byMETHODMethod 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 con Glass Tube Heater Beakers (500 mL) 2 Thick Walled Rubber Tube Thermometer (0 100oC) Electric BalanceWeight of flask + adapted s136.4 + 0.1 gWeight of flask + fitting + water sucked in168.6 + 0.1 gWeight of water sucked in032.2 + 0.1 gWeight of flask + fittings + full water279.8 + 0.1 gWeight of full water143.4 + 0.1 gTemperature of boiling water103.0 + 0.1 oCTemperature of cold water024.0 + 0.1 oCAtmospheric Pressure1.00 atmVolume of gas 103.0 oC143.4 + 0.1 cm3Volume of gas 24.0 oC111.2 + 0.1 cm3DISCUSSIONThe 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 f illed 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 work out the volume by density was the best and completed 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 thermic 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(prenominal) 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 COEFFICIENTThe 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 , 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 COEFFICIENTThe 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 stand for almost 4.66% of the theoretical value What can account for this deviation? It all leads to ex perimental 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 value 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 mistaken 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 calcu lating 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.CONCLUSIONWith 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. BIBLIOGRAPHYAnand, A and Ne gi, S. A Textbook of Physical chemistry. USA John Wiley Sons, 1985.Atkins, Peter and De Paula, Julio. 2006. 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