The Relationship Betwixt Capacity of Gas and the Temperature - Report Example

Running head: Gas Laws Student’s name Student Number Institution Course: FY014 Experiment: Gas Laws Date of Experiment Date of Submission Abstract This report describes an experimental analysis of the relationship between temperature, pressure and volume of ideal gases usually known as Gas laws. To determine their relationship, these observable parameters; temperature, pressure and volume were used for the two experiments where at one instant pressure was kept constant while in another instant temperature was kept constant. From the results, graphs will be plotted and compared with the empirical results. Verification of the Gas laws was therefore the main aim of the experiment. The report describes the setup of the experiment; the results recorded, discussed and analyzed. Moreover, errors were analyzed and discussed. Contents 1.0 Introduction 4 2.0 Theory 5 3.0 Materials and Method 8 3.1 Part I 8 3.1.1 Apparatus 8 3.1.2 Procedure 8 3.1.3 Results and Calculations 9 3.1.4 Discussion 10 3.2 part II 11 3.2.1 Apparatus 11 3.2.2 Procedure 11 3.2.3 Results and Calculations 11 3.2.4 Discussion 13 3.3 Conclusion 14 4.0 Sources of Errors 14 5.0 References 15 1.0 Introduction Gas laws are an investigation of the behavior of various gases when subjected to different conditions. Experimentally, the laws linking all these properties of ideal gases are determined by keeping one factor constant in turn in relation to the other two factors to be investigated (Pople, 1987 P.134). For example, a change in temperature may result to changes in either its volume or pressure or both. The investigative activity uses the analysis of experimental results of volume, temperature and pressure. It is possible to estimate the properties of ideal gases theoretically through the application of gas laws. From theoretical discussions, there is a direct relationship between volume and temperature, and pressure and volume of an ideal gas. However, this relationship is only applicable to a certain limit of temperature called the absolute zero. Study of the properties of ideal gases borrows heavily from particulate nature of matter and the kinetic theory of gases. Particulate nature of matter and kinetic theory of gases postulates that matter is made up of small particles and that for gases; these particles are in constant random motion. Gases behave in this manner basically because the interactions between particles or molecules are weaker (Serway, p.641). Since the particles are in constant random motion, they collide with each other and the walls of the container. The result of this particle to particle and particle to container collisions is the increase in pressure. Temperature change is known to affect the speed of movement of particles within the container. Increase in temperature speeds up the movement of these particles and therefore the number of collisions also increases. Temperature therefore affects pressure. In the same way, a small volume will experience more collisions per unit area. Therefore, a small volume will experience a high pressure. Therefore, volume affects the pressure of an ideal gas. It is from this relationship that Gas laws were formulated. This experiment offers an opportunity for the establishment of relationships between the properties of ideal gases and verification of Gas laws. The main aims of the experiment were: To verify Boyle’s law To verify Charles’s law To familiarize with ideal gas property changes under different conditions and equipment used in the experiment 2.0 Theory Gas laws are simply the relationships between properties of ideal gases. Gas laws can be used to predict how various gases behave when they are subjected to different conditions. An important consideration for these laws is that they only apply to ideal or perfect gases. An ideal or perfect gas can be described as that gas that can be thought to adhere to kinetic molecular theory (Myers, 2006 P.113). A gas at an ideal state can be represented mathematically as; Where; is the gas pressure in NM-2 is the gas volume in M3 is the gas mole number in mol is the universal molar gas constant equal to 8.31 JK-1mol-1 is the gas temperature in Kelvin Gas laws have the limits under which they apply. Low temperature and high pressure gases are not ideal gases. Therefore, gas laws do not apply for gases under such conditions. In reality, no gas obeys these laws absolutely. However, they do provide fairly accurate information on the behavior of gases at normal conditions (Muncaster, 1993 P.250). The three gas laws are; Charles’s law, Boyle’s law and Pressure law. The focus of the experiment was Charles’s and Boyle’s laws. Robert Boyle came up with Boyle’s law after using a J-shaped piece of glass tubing whose one end was sealed. With this glass tubing, he was able to establish how the pressure and volume of air trapped inside the sealed end related. In order to establish the relationship, he varied the pressure while measuring the corresponding volume of each reading. He termed the relationship as Boyle’s law. Boyle’s law stated that; At a fixed mass and constant temperature, there exists an inverse proportionality between its pressure and temperature of a gas (Pople, 1987 P. 136). It can be represented as; A mathematical expression of this law is; Where is the pressure of the gas is the volume of the gas is the proportionality constant Boyle’s law can be used to relate pressure and volume of a gas at constant temperature initially and finally. It can be represented mathematically as; Jacques Charles on the other hand established the relationship between temperature and volume of a gas. The relationship was termed as Charles’s law. From the experiments conducted, doubling the temperature of a gas results to a corresponding doubling of its volume. Charles’s law states that; For a fixed mass of a gas at constant pressure, the volume is directly proportional to the temperature measured in Kelvins (Pople, 1987 P. 136). Mathematically, this relationship can be represented as; where is the volume of the gas is the temperature of the gas is the proportionality constant Importantly, absolute temperature ought to be used when applying this law. On increasing the temperature of a gas, the particles acquire more kinetic energy. As a result, more particle to particle and particle to wall collisions occur. Increase in pressure will result from increased collisions among these particles and the walls of the container. 3.0 Materials and Method 3.1 Part I 3.1.1 Apparatus Adjustable cylindrical tube 3.1.2 Procedure 1. Before the start of the experiment, familiarization with the cylindrical tube was very important. 2. The release valve was opened to set the pressure to atmospheric, O on the gauge (1 BAR absolute). At the same time, the connecting rod was pulled out to the 50ml volume position, as seen when the first (red) calibration mark on the connecting rod was viewed. 3. The release valve was then closed and the connecting rod was pulled out till the second calibration, 100ml was brought into view and the meter reading was then recorded. N/B; the experiment had to be performed quickly due to leakages being experienced. 4. The process was carried on until the 150ml, 200ml and 250ml marks were reached. At each volume both pressure and temperature were recorded. 5. The experiment was repeated five times. From the results, the average value of pressure for each volume was calculated. 6. With the help of values of p, the actual pressure in pounds per square inch and also in Pascals at each volume was calculated. 7. The results were compared with Boyle’s Law was compared and a graph was drawn. 3.1.3 Results and Calculations 1 2 3 4 5 Average pressure 100ml 0.8 0.7 0.7 0.8 0.75 0.75 150ml 0.6 0.6 0.65 0.66 0.6 0.622 200ml 0.4 0.45 0.45 0.4 0.4 0.42 250ml 0.3 0.3 0.35 0.3 0.3 0.31 Volume of gas (ml) Average pressure (Bar) Actual Absolute Pressure (Bar) Actual pressure in Pounds per square inch (psi) Actual pressure in Pascals (pa) 100 0.75 1.75 25.375 175000 150 0.622 1.622 23.519 162200 200 0.42 1.42 20.590 142000 250 0.31 1.31 18.995 131000 3.1.4 Discussion From these experimental values, it is clear that as the volume rises, pressure decreases. This is an indication of the presence of an inverse relationship between the two properties of ideal gases. The gradient of the graph can be determined as; The negative gradient indicates presence of an inverse relationship between the variables. 3.2 part II 3.2.1 Apparatus Adjustable cylindrical tube 3.2.2 Procedure 1. Before the experiment began, familiarization was done 2. The silicon tube was adjusted from the nozzle on the end of the apparatus to reset pressure to ambient. 3. The silicon tube from the nozzle on the end of the apparatus was then reconnected. The pressure gauge was a water manometer whose one millimeter difference between the levels of water was. 4. The temperature and its corresponding pressure were recorded. 5. The heating element was turned on and, temperature and pressure were recorded after every 10 seconds 6. A graph of temperature against pressure was plotted using the results obtained. 3.2.3 Results and Calculations Pressure Temperature (0 Celsius) Temperature (Kelvin) 52.3 24 297 53 24 297 53.5 24 297 54 24 297 54.8 26 299 55.5 26 299 56 27 300 57 28 301 57.7 29 302 58.5 29 302 60 30 303 63 31 304 64.5 32 305 65 35 308 65.7 37 310 66.1 37 310 67 37 310 3.2.4 Discussion The graph plotted has a positive gradient to indicate a direct relationship between temperature and pressure. It is a proof of pressure law which states that under constant volume, the pressure of a gas with a certain mass will increase for every degree Celsius rise in temperature by a constant fraction of 1/273 in its pressure. 3.3 Conclusion The results of the two experiments were able to proof Boyle’s law and Pressure law. In both of them, gas laws have been determined through a relationship between two properties of ideal gases. 4.0 Sources of Errors Leakage of pressure from the pipe 5.0 References Jewett, S. Physics for Scientists and Engineers (6 th ed). California: Thomson Brooks. 2004. Print. Muncaster, R. A-Level Physics (ed 4) Cheltenham: Nelson Thornes, 1993. Print. Myers, R. L. The Basics of Physics. Westport, CT: Greenwood Publishing Group, 2006. Print. Pople, S. Explaining Physics Gcse. (ed 2) Oxford: Oxford University Press, 1987. Print. Read More