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- 1. Tai-Wei (Andy) Lee<br />16 March 2009<br />IB Physics HL1 p.2<br />Mr. Eales<br />Pressure vs. Temperature Lab<br />Introduction<br />When a plugged flask which has a fixed quantity of air is placed in a water bath and the entire system is heated with a hot plate, temperature rises and pressure varies. By adding temperature, we add average linear kinetic energy per particle (Eales; class lecture). Pressure is defined as the force per unit area applied to an object in a direction perpendicular to the surface [1]. The bumping of a gas molecule into a wall and bouncing off into another direction is what causes pressure [2]. <br />It is predicted that pressure will have a direct relationship with temperature because an increase in temperature causes particles to possess a greater amount of kinetic/moving energy. More frequent collisions occur between particles which in turn increases pressure. Moreover, according to Gay-Lussac’s Law, when the volume is kept constant, the absolute pressure of a given amount of any gas varies directly with the thermodynamic temperature (Hecht).<br />[3]In simple words, if a gas's temperature increases then so does its pressure, if the mass and volume of the gas are held constant. The law can then be expressed mathematically as:<br />or<br />or using simple algebra,<br /> P=kT<br />where:<br />P is the pressure of the gas.<br />T is the temperature of the gas (measured in Kelvin).<br />k is a constant.<br />[3]In addition, Gay-Lussac’s law assumes ideal gases. Ideal gas is a Kinetic theory where there are no internal molecular forces (no bond form), kinetic energy is conserved during collisions, particles are point masses (no volume), collisions take no time and Newton’s Laws are applicable.<br />From this lab, the x intercept of the Pressure vs. Temperature (p-T) graphs is the absolute zero, which is a universal zero of temperature or the limit of low temperature for all gasses as the pressure falls to zero and the gas liquefies (Hecht). The absolute zero temperature is at 0 K or approximately-273.15°C. Therefore, the x-intercept of the Temperature vs. Pressure graph that will be collected is predicted to be equal to the absolute zero value or -273.15°C.<br />In this lab, the relationship between temperature and pressure and the absolute zero temperature will be investigated by heating up the flask inside a water bath on a hot plate (varying temperature) with a fixed quantity of air.<br />Design<br />Research Question: <br />How does temperature of a fixed quantity of air affect pressure?<br />Variables - <br />Independent variable: Temperature (units: Celsius)<br />Dependent variable: Pressure (units: Kilopascals)<br />Controlled variable: Quantity of air<br />32670753275330The independent variable was the temperature of the system. The dependent variable was the pressure inside the flask. The controlled variable was the quantity of air inside the flask. The independent variable was measured by a temperature probe by sticking the temperature probe through the stopper into the flask to record to the change in temperature inside the flask. The temperature probe then recorded the variation of temperature between 13.2±0.06 to 83.6±0.06 Celsius which consisted of 106 data points; data collection settings were set to collect one data point per every 30 seconds. Only one trial of adding temperature is done, though a wide range of data points were obtained from the one trial. The temperature was varied by turning on the hot plate to add temperature to the entire system. The temperature probe was ensured not to touch the bottom of the flask in order to be collecting the temperature of the air inside, not the inside surface of the flask. The dependent variable was measured also by sticking the pressure probe through the stopper into the flask to record the change in pressure inside the flask. The pressure probe then recorded the variation of pressure between 98.1±0.01 to 138.2±0.01 Kilopascals which consisted of 106 data points; data collection settings were set to collect one data point per every 30 seconds. The controlled variable, quantity of air, was controlled by tightly pushing in the stopper into the neck of the flask to ensure that air quantity was kept as a constant and to prevent any leakage of air. <br />Figure 1: Setup of the lab. The neck of the flask was jammed with a stopper and the temperature probe and the pressure probe were strongly stuck into the stopper. The flask was submerged into the water as deep as possible<br />Data Collection and Processing<br />Sample Calculation of instrumental uncertainties of pressure and temperature probes<br />Pressure probe Uncertainty calculated by using Standard DeviationPressure (kPa)97.1626571697.1626571697.1626571697.1626571697.1626571697.1626571697.1626571697.1626571697.1626571697.16265716Pressure uncertainty is ±0.01 kPa<br />Table 1: To calculate instrumental uncertainty, we set LoggerPro to collect data for a short period of time, in this case, 6 seconds, where there will be no major change in pressure. Then the data that was collected in that short period of time was copied and pasted into Microsoft Excel and calculated its uncertainty by clicking on a empty box, then type ‘=STDEV’, which stands for standard deviation into the f(x) bar and then highlighted the figures/data that we want to calculate then click ok. In this table, only 10 figures are shown as an example because showing all 63 figures would be meaningless and boring to see. <br />Temperature probe Uncertainty calculated by using Standard DeviationTemperature (°C)12.2724371212.1367692312.0689352912.0689352912.1367692312.2046031712.2046031712.1367692312.2046031712.20460317Temperature uncertainty is ±0.07 °C<br />Table 2: The same process outlined in Table 1 is also done to temperature (this table) to calculate uncertainty.<br />Figure 2: Pressure-Temperature graph which takes into account every data point. However, the curvy end where pressure continues to increase but temperature remains the same doesn’t make sense. Nonetheless, our graph shape is pretty much linear which matches with what theory predicts.<br />Figure 3: Second Pressure-Temperature graph. However, this time the data points on the curvy ends on the end of the line were not considered because it doesn’t really make sense. On this graph, only the uncertainty of temperature is shown because it is the larger uncertainty of the two. In addition, because the uncertainty is so small in comparison to the data and the slope is not significant, another graph with high-low fit will not be shown.<br /> <br />≈ -182⁰C<br />Figure 4: Pressure-Temperature graph showing the x intercept which theoretically supposed to be the absolute zero at-273.15°C. However, our result turned out to be approximately <br />-182°C which is far from the expected value for absolute zero.<br />Conclusion <br />As said in the introduction, this lab deals with a direct/linear relationship so we assume the equation:<br />y = mx+b<br />and apply figures received from Figure 3 and the uncertainty which was calculated in sample calculations which would then give the relationship between pressure and temperature<br />P=0.504kPa°C T±0.07°C+93.67 kPa<br />where<br /> P is pressure (kPa)<br />The slope, 0.504 is the rate of change of pressure to temperature (kPa°C) or the k constant which was stated in the introduction.<br />93.67, the y intercept in this experiment is a only a constant which has little to no significance<br />In addition, the x intercept which theoretically supposed to be the absolute zero, was found in this experiment to be approximately-182°C. <br />Evaluation<br />In this lab, there were some weaknesses in data collection. A systematic error may have occurred due to old and faulty equipments. For example, the temperature probes were quite old and didn’t quite measure temperature as precisely as we hoped. Other groups using similar equipments also acquired similar results, which supports the idea that the equipments were defective. For another example, the stopper that we placed as tightly as we could into the neck of the flask, were particularly old and had a yellowish look. Therefore, it could have contributed a leakage to the entire system that leads to inaccurate data collection. However, other groups from other classes have also done the same experiment and received the same flawed data, it is possible that the equipments are not defective but that there is an unknown factor that hadn’t been taken in account in which none of us have realized yet. These systematic errors caused by defective equipment can be improved by buying new equipment. Though the unknown factor that might hinder us from acquiring accurate data can only be found by doing further experiments.<br />A weakness of the lab setup was that the flask was not entirely submerged into the water bath because the beaker that was filled with water and ice was not large enough to submerge the entire flask. Therefore, the temperature distribution will not be equal for the flask, only the part in the water bath will be added temperature. As a result, the temperature inside the flask will not be equal which leads to flawed data. A solution to this problem is to simply buy new beakers that are larger than the ones the school already has. <br />The results received in this lab are valid only if the same or similar equipment are used and the experiment is conducted under same environment/circumstances using the same independent, dependent and controlled variables. Nonetheless, it is encouraged that different equipments are used to further test for different results.<br />

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