Experiment on polytropic process Essay

Polytropic refinement of AirObjectThe object of this experiment is to find the relation amid imperativeness and volume for the expanding upon of appearance in a obligate watercraft this expansion is a thermodynamic process.IntroductionThe expansion or compression of a screw up can be described by the polytropic relation , where p is pressure, v is specific volume, c is a continuous and the index finger n depends on the thermodynamic process. In our experiment two-dimensional rail line in a stigma pressure vessel is carry through to the atmosphere while the product line remaining in perspective expands. Temperature and pressure measurements of the air within the vessel are recorded. These two measurements are used to bring up the polytropic exponent n for the expansion process.Historical backgroundSadi Carnot (1796-1832) 1 in his 1824 Reflections on the Motive force out of love and on Machines Fitted to Develop This Power, realizes a reciprocating, piston-in-pisto n chamber engine. Carnot describes a roulette wheel applied to the machine appearing in guess 5.1, which contains his pilot film skeleton. In this figure air is contained in the chamber formed by the piston cd in the cylinder. Two heat reservoirs A and B, with temperature greater than temperature , are available to make trace with cylinder head ab. The reservoirs A and B maintain their respective temperatures during heat transfer to or from the cylinder head.Carnot gives the following six steps for his machine1.The piston is initially at cd when high-temperature reservoir A is brought into contact with the cylinder head ab. 2.There is equal expansionto ef3.Reservoir A is take away 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 unvarying compression from cd to ik causes the temperature to heave to . 6.Reservoir A makes contact, isothermally expanding the air to cd and a nd so completing the cycle.A decade later Clapeyron 2 analyzed Carnots cycle by introducing a pressure-volume, p-v diagram. Clapeyrons diagram is reproduced next to Carnots engine in run across 5.1. Claperon labels his axes y and x, which correspond to pressure and volume, respectively. We go forth examine two process caterpillar treads 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 = perpetual. This is a modified case of the polytropic process , where, for the isothermal process, n = 1, so we have the equivalent result, pv = c.Figure 5.1 Left sketch Carnots engine, after Carnot 1. Right sketch Clapeyrons pressure-volume, p-v diagram, after Clapeyron 2. For the axes in Clapeyrons diagram x = v and y = p.The ExperimentsPhotographs of the equipment appear in Figures 5.2 and 5.3, and a sketch of the components appears in Figure 5.4.steel pressure vessel discharge valves thermocouple junction junction conduit pressure transducerFigure 5.2 The polytropic expansion experiment at Cal Poly.thermocouples thermocouple conduitFigure 5.3 Two, Type-T thermocouples are locate inside the pressure vessel, at the geometric center. Only one thermocouple is used the otheris a spare. In the photo the thermocouple conduit has been removed and held outside of the vessel. The junctions of these thermocouples are constructed of extremely fine wires (0.0254mm diameter) that provide a straightaway time response.Figure 5.4 The polytropic expansion experiment equipment. squash measurements come from the pressure transducer tapped in to the pressure vessel shown in Figure 5.4. The transducer is major strengthed by the unit labeled CD23, which is a Validyne 3 carrier demodulator. The fine wire thermocouple is described in the Figure 5.3 caption. Both thermocouple and pressure signals operate into an Omega 4 flatbed recorder.The trey discharge valves on the right side of the vessel have small, medium, and large orifices. These orifices allow the air inside the vessel expand at three different rates. The pressure vessel is setoff 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 severallyes equilibrium at which time one of the discharge valves is opened. Temperature and pressure are recorded for each(prenominal) expansion process. These info are then used to compute the polytropic exponent n for each process. It is important to note that the temperature and pressure of the air inside the vessel are measured, not the air discharging from the vessel.DataPressure and temperature data, for the three runs, are provided in the EXCEL file Experiment 5 Data.xls. abstractIn many cases the process path for a gas expanding or contracting follows the relationship(5.1)The polytropic exponent n can theoretically identify from . However, Wark 5 reports that the relati on is especially useful when . For the following simple processes the n set areisobaric process (constant pressure)n = 0isothermal process (constant temperature)n = 1isentropic process (constant entropy)n = k ( k=1.4 for air) isochoric process (constant volume)n = In our experiment the steel pressure vessel is initially charged with compressed air of spile . Next, the vessel is discharged and the remaining air aggregated is . This final mass was part of the initial mass and occupied part of the volume of the vessel at the initial state. Thus expanded within the vessel with a corresponding change in temperature and pressure. Therefore mass can be considered a closed system with a moving system boundary and the following form of the first police force of thermodynamics applies(5.2)If the system undergoes an adiabatic expansion , and if the work at the moving system boundary is reversible. Furthermore, if we consider the air to be an ideal gas with constant specific heat. With the se considerations the first law reduces to(5.3)Using the ideal gas assumption and differentiating this equation gives(5.4)Substituting comparability 5.4 into 5.3 and using the relationships and givesSeparating variables and integrating this equation, , yields(5.5)which is a special case of the polytropic relationship abandoned by compare 5.1, with n = k.It is important to note that in the festering of Equation 5.5 the expansion of inside the pressure vessel was assumed to be reversible and adiabatic, i.e. an isentropic expansion. In our experiment the adiabatic assumption is hi-fi during initial discharge. However, the reversible assumption is clearly not applicable because the air expands irreversibly from high pressure to low pressure. Therefore we anticipate our data to yield .Two approaches are used to determined the polytropic exponent n from the data1. 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 curve fit using TRENDLINE will disclose n.2. Equation 5.6 (subsequently developed) may be used with only two states to determine n.Here is the outline 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(5.6)The temperatures and pressures in Equation 5.6 are all arrogant and the subscripts 1 and 2 represent the initial and final states.Required1. Pressure and temperature data are provided for all three runs in Experiment 5 Data.xls. Use the ideal gas law, pv = RT, to compute v corresponding to each p. Use SI units m3/kg for v and Pa for p.2. Plot p versus v and find nFor each run, on a bust graph, plot p on the ordinate (vertical) axis versus v on the abscissa (horizontal) axis. Use linear scales. tick the polytropic exponent n for each run using a TRENDLINE power curve fit. 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.3. subtract Equation 5.6.4. Find n for each run using Equation 5.6, where states 1 and 2 represent the beginning and ending states, respectively.5. In a single table show all of the n values.6. Discuss the pith of your n values, that is, how does your n value compare with n values for other, cognize processes?Nomenclaturec constant, N mspecific heat constant pressure, kJ/kg Kspecific heat constant volume, kJ/kg Kk specific heat ratio, dimensionlessn polytropic exponent, dimensionlessp absolute pressure, Pa or psiaQ heat transfer, kJR gas constant, kJ/kg K (Rair = 0.287 kJ/kgK)T temperature, C or KU internal energy, kJv specific volume, m3/kgV volume m3W work, kJSubscripts1,2 thermodynamic statesReferences1. Carnot, S., Rflexions sur la puissance motive du feu et sur les machines propres dvelopper cette puissance, genus Paris, 1824. Reprints in Paris 1878, 1912, 1953. English translat ion by R. H. Thurston, Reflections on the Motive Power of Heat and on Machines Fitted to Develop This Power, ASME, New York, 1943.2. Clapeyron, E., Memoir on the Motive Power of Heat, Journal de lcole Polytechnic, Vol. 14, 1834 translation in E. Mendoza (Ed.) Reflections on the motive Power of Fire and Other Papers, Dover, New York, 1960.3. Validyne Engineering Sales Corp., 8626 Wilbur Avenue, Northridge, CA. 91324 http//www.validyne.com/4. zee Engineering, INC., One Omega Drive, Stamford, Connecticut 06907-0047 http//www.omega.com/5. Wark, K. Jr. & D.E. Richards, Thermodynamics, 6th Ed, WCB McGraw-Hill, Boston, 1999. 2005 by Ronald S. Mullisen visible Experiments in Thermodynamics Experiment 5