'Experiment on polytropic process Essay\r'

'Polytropic amplification of Air\r\nObject\r\nThe object of this taste is to convey the relation between ram and volume for the expounding upon of institutionalize in a rack vas †this expanding upon is a thermodynamical butt against.\r\nIntroduction\r\nThe involution or condensing of a natural fluid passel be described by the polytropic relation , where p is mechanical press, v is particularised volume, c is a constant and the top executive n depends on the thermodynamic mental process. In our experiment sozzled channelise in a steel bosom vessel is discharged to the atmosphere while the duck soup remain in attitude expands. Temperature and compact measurements of the nimbus inside the vessel be recorded. These twain measurements be employ to produce the polytropic big businessman n for the expanding upon process.\r\nHistorical oscilloscope\r\nSadi Carnot (1796-1832) [1] in his 1824 â€Å"Reflections on the Motive office staff of Heat and o n Machines Fitted to Develop This Power,” raises a reciprocating, plunger-in-piston chamber engine. Carnot describes a cycle applied to the cable car appearing in Figure 5.1, which contains his professional field of study. In this figure air is contained in the chamber formed by the piston cd in the cylinder. deuce set off reservoirs A and B, with temperature greater than temperature , ar addressable to make contact with cylinder passing ab. The reservoirs A and B maintain their various(prenominal) temperatures during hotness transfer to or from the cylinder head.\r\nCarnot gives the following six steps for his appliance:\r\n1.The piston is initi onlyy at cd when high-temperature reservoir A is brought into contact with the cylinder head ab. 2.There is isothermal expanding upon\r\nto ef\r\n3.Reservoir A is removed and the piston continues to gh and so cools to . 4.Reservoir B makes contact causing isothermal compression from gh to cd. 5.Reservoir B is removed but c easeless compression from cd to ik causes the temperature to rise to . 6.Reservoir A makes contact, isothermally expanding the air to cd and thus complete the cycle.\r\nA decade later Clapeyron [2] apprisevass Carnot’s cycle by introducing a mash-volume, p-v draw. Clapeyron’s diagram is reproduced next to Carnot’s engine in Figure 5.1. Claperon labels his axes y and x, which correspond to force per unit area and volume, respectively. We will examine two process paths in this diagram: the isothermal compression path F-K and the isothermal expansion path C-E. Since both of these processes are isothermal, pv = RT = constant. This is a especial(a) case of the polytropic process , where, for the isothermal process, n = 1, so we consecrate the same result, pv = c.\r\nFigure 5.1 Left sight: Carnot’s engine, after Carnot [1]. Right survey: Clapeyron’s pressure-volume, p-v diagram, after Clapeyron [2]. For the axes in Clapeyron’s diagram x = v and y = p.\r\nThe Experiments\r\nPhotographs of the equipment appear in Figures 5.2 and 5.3, and a sketch of the components appears in Figure 5.4.\r\nsteel pressure vessel discharge valves thermocouple conduit pressure transducer\r\nFigure 5.2 The polytropic expansion experiment at Cal Poly.\r\nthermocouples thermocouple conduit\r\nFigure 5.3 Two, Type-T thermocouples are set(p) inside the pressure vessel, at the geometrical center. Only one thermocouple is utilise †the other\r\nis a spare. In the moving picture the thermocouple conduit has been removed and held outside of the vessel. The junctions of these thermocouples are constructed of extremely delightful wires (0.0254mm diameter) that provide a fast time response.\r\nFigure 5.4 The polytropic expansion experiment equipment.\r\nPressure measurements come from the pressure transducer tapped in to the pressure vessel demonstraten in Figure 5.4. The transducer is powered by the unit labeled â€Å"CD23”, which i s a Validyne [3] carrier demodulator. The fine wire thermocouple is described in the Figure 5.3 caption. Both thermocouple and pressure signals feed into an Omega [4] flatbed recorder.\r\nThe ternary discharge valves on the right side of the vessel have small, medium, and large orifices. These orifices go away the air inside the vessel expand at ternary different rates. The pressure vessel is prototypal charged with the compressed air supply. This causes the air that enters the vessel to initially rise in temperature. After a few minutes the temperature r individuallyes equilibrium at which time one of the discharge valves is opened. Temperature and pressure are recorded for all(prenominal) expansion process. These data are then used to suppose the polytropic pleader n for each process. It is important to name that the temperature and pressure of the air inside the vessel are measured, not the air discharging from the vessel.\r\nData\r\nPressure and temperature data, for the three haps, are provided in the EXCEL read â€Å"Experiment 5 Data.xls.”\r\nAnalysis\r\nIn many cases the process path for a float expanding or contracting follows the birth\r\n(5.1)\r\nThe polytropic exponent n can theoretically range from . However, Wark [5] reports that the relation is especially efficacious when . For the following simple processes the n value are:\r\nisobaric process (constant pressure)n = 0\r\nisothermal process (constant temperature)n = 1\r\nisentropic process (constant entropy)n = k ( k=1.4 for air) isochoric process (constant volume)n = ï‚¥\r\nIn our experiment the steel pressure vessel is initially charged with compressed air of cumulus . Next, the vessel is discharged and the remaining air mass is . This final mass was part of the initial mass and meshed part of the volume of the vessel at the initial state. Thus expanded within the vessel with a corresponding kind in temperature and pressure. thereof mass can be considered a closed governing body with a moving system limit and the following form of the first natural law of nature of thermodynamics applies\r\n(5.2)\r\nIf the system undergoes an adiabatic expansion , and if the lap up at the moving system leap is reversible. Furthermore, if we consider the air to be an pattern gas with constant special(prenominal) heat. With these considerations the first law reduces to\r\n(5.3)\r\nUsing the ideal gas assumption and differentiating this equation gives\r\n(5.4)\r\nSubstituting equivalence 5.4 into 5.3 and using the relationships and gives\r\nSeparating variables and integrating this equation, , yields\r\n(5.5)\r\nwhich is a special case of the polytropic relationship given by comparability 5.1, with n = k.\r\nIt is important to note that in the development of comparability 5.5 the expansion of inside the pressure vessel was put on to be reversible and adiabatic, i.e. an isentropic expansion. In our experiment the adiabatic assumption is finished durin g initial discharge. However, the reversible assumption is clear not applicable because the air expands irreversibly from high pressure to low pressure. Therefore we anticipate our data to yield .\r\nTwo approaches are used to determined the polytropic exponent n from the data:\r\n1. Equation 5.1 can be written as , which is a power law equation. In EXCEL, a plot of p versus v and a power law edit out tally using TRENDLINE will disclose n.\r\n2. Equation 5.6 (subsequently developed) may be used with that two states to determine n.\r\nHere is the abbreviation of the development of Equation 5.6. We start with , which likewise can be expressed as and combine this with the ideal gas law to obtain\r\n(5.6)\r\nThe temperatures and pressures in Equation 5.6 are all absolute and the subscripts 1 and 2 represent the initial and final states.\r\n need\r\n1. Pressure and temperature data are provided for all three dissolves in â€Å"Experiment 5 Data.xls.” delectation the ideal gas law, pv = RT, to compute v corresponding to each p. Use SI units: m3/kg for v and Pa for p.\r\n2. Plot p versus v and gravel n:\r\nFor each run, on a separate graph, plot p [on the vest (vertical) axis] versus v [on the abscissa (horizontal) axis]. Use linear scales. check over the polytropic exponent n for each run using a TRENDLINE power curve total. Also find the correlation coefficient for each curve. (Be aware that the TRENDLINE power curve fit will give , where y = p, x = v and a and b are constants.) Plot all three runs on a single graph and find n for the combined data.\r\n3. Derive Equation 5.6.\r\n4. Find n for each run using Equation 5.6, where states 1 and 2 represent the beginning and ending states, respectively.\r\n5. In a single table show all of the n values.\r\n6. Discuss the importation of your n values, that is, how does your n value differentiate with n values for other, known processes?\r\n speech\r\nc constant, N m\r\nspecific heat constant pressure, kJ/kg K\r\nspecific heat constant volume, kJ/kg K\r\nk specific heat ratio, dimensionless\r\nn polytropic exponent, dimensionless\r\np absolute pressure, Pa or psia\r\nQ heat transfer, kJ\r\nR gas constant, kJ/kg K (Rair = 0.287 kJ/kg·K)\r\nT temperature, °C or K\r\nU internal energy, kJ\r\nv specific volume, m3/kg\r\nV volume m3\r\nW work, kJ\r\nSubscripts\r\n1,2 thermodynamic states\r\nReferences\r\n1. Carnot, S., â€Å"Réflexions sur la puissance theme du feu et sur les machines propres à développer cette puissance,” capital of France, 1824. Reprints in Paris: 1878, 1912, 1953. English translation by R. H. Thurston, â€Å"Reflections on the Motive Power of Heat and on Machines Fitted to Develop This Power,” ASME, New York, 1943.\r\n2. Clapeyron, E., â€Å"Memoir on the Motive Power of Heat,” Journal de l’École Polytechnic, Vol. 14, 1834; translation in E. Mendoza (Ed.) â€Å"Reflections on the motive Power of Fire and former(a) Pa pers,” Dover, New York, 1960.\r\n3. Validyne Engineering Sales Corp., 8626 Wilbur Avenue, Northridge, CA. 91324 http://www.validyne.com/\r\n4. zed Engineering, INC., One Omega Drive, Stamford, Connecticut 06907-0047 http://www.omega.com/\r\n5. Wark, K. younger & D.E. Richards, Thermodynamics, 6th Ed, WCB McGraw-Hill, Boston, 1999.\r\n\\ © 2005 by Ronald S. Mullisen \\ visible Experiments in Thermodynamics \\ Experiment 5 \\\r\n'