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The Stirling Engine: the Heat Engine

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The Stirling Engine: the Heat Engine Memorial University of Newfoundland Department of Physics and Physical Oceanography Physics 2053 Laboratory The Stirling Engine: The Heat Engine Under no circumstances should you attempt to operate the engine without supervision: it may be damaged if mishandled. Introduction Heat engines are generally described in terms of cyclic processes in which a gas absorbs heat QA at a high temperature, releases heat QB at a lower temperature, and performs an amount of work W . The efficiency of a heat engine is given by W η = ; QA however, even for an ideal (reversible) cycle in which there is no friction, efficiency is limited by the second law of thermodynamics. Q A p a T A Q A b T W A d Q TB B Q c B TB v Figure 1: The Carnot Cycle for an engine operating between two infinite heat baths. Carnot, in the 1820s, showed that the maximum theoretical efficiency available from a reversible heat engine depends only on the temperature change in the cycle. The Carnot 1 cycle is the reversible cycle which operates between two constant temperature baths. The pressure-volume diagram for the cycle is shown in Fig (1). Heat is absorbed and released as the gas is expanded or compressed along the isotherms a ! b and c ! d. During steps b ! c and d ! a, the gas is thermally isolated and changes temperature as it is expanded or compressed. The efficiency for this cycle is T η ≤ 1 − B TA where the equal sign applies only for a reversible (frictionless) cycle. The Carnot cycle is difficult to realize in practice and produces a relatively small amount of work per cycle. The Stirling cycle uses more than two thermal reservoirs but has the same maximum efficiency as the Carnot cycle and, for a given pair of temperatures and change in volume, produces more work per cycle. Robert Stirling (1790-1878) took out a patent for his engine in 1816. Unlike steam engines, it had no high pressure boiler and was thus somewhat safer. Its mechanical complexity limited the practical size and it was only used for small applications (e.g., farming) and only until the 1920s when the more powerful internal combustion engines became more popular. The Stirling engine continues to attract attention, periodically, as a more fuel efficient and potentially cleaner engine for some applications. Currently, the primary application of Stirling cycles is in refrigeration. The Stirling Cycle The pV diagram for an ideal Stirling cycle is shown in Fig (2). In our setup, two pistons move in the cylinder, shown schematically in Fig (3); the top region of the cylinder is heated by an electric heater and the lower walls of the cylinder are cooled by flowing water. The volume of air is changed by the movement of the lower piston. The upper piston moves the air from the heated region of the cylinder to the cooled region of the cylinder through a central hole in the piston which is filled with copper wool and is called the regenerator. When the air passes from the heated region, through the regenerator, to the cooled region, it releases heat to the copper wool and is cooled. When the air passes in the other direction, it retrieves this heat and is warmed. This shuttling of heat in and out of the regenerator is labeled QR in Figs 2 and 3. The regenerator can be thought of as a third, finite, thermal reservoir. The theoretical efficiency of a Stirling cycle operating between TA and TB is the same as for the Carnot cycle. The cycle is as follows: 2 p a Q A Q R b T Q R A d T Q B B c v Figure 2: The Stirling Cycle operating between the same temperature and volume limits as above. This cycle requires more than two thermal reservoirs. • [a] The volume is a minimum and most of the gas is in the heated part of the cylinder. The gas is at temperature TA. • [a ! b] The gas absorbs heat from the heater and expands at constant temperature. • [b] The gas is at its maximum volume and still at temperature TA. • [b ! c] The upper piston moves up forcing the gas through the regenerator and ex- tracting heat QR to leave the gas at temperature TB. • [c] The gas is still at its maximum volume, at temperature TB, and in contact with the cooled region of the cylinder. • [c ! d] The gas is compressed at constant temperature TB and releases heat QB to the cooling water. • [d] The gas is at its minimum volume and still at temperature TB. • [d ! a] The upper piston moves down and forces the gas through the regenerator where it reabsorbs heat QR and warms to TA. 3 QA a a b b QR d a b c QR d c d c QB Figure 3: Diagram to show the relative positions of the pistons during operation of the Stirling engine. Using the Pasco Interface Box 1. Check that the Rotary Motion Sensor is plugged into channel 1 (yellow) and channel 2 (black), and also that the differential pressure sensor is plugged into channel A. 2. Start the DataStudio program and click on Create Experiment. Select Rotary motion sensor and Pressure Sensor (Differential). 3. Click on the Rotary motion sensor icon to open the Sensor Properties window. Under the General tab, set the sample rate to 200 Hz; under Measurement, select Angular Position, measured in degrees (since we cannot measure volume directly). Repeat for 4 the pressure sensor, with pressure in kPa. 4. To create a graph of pressure versus volume: • Double-click on Graph (on the Displays menu). • Select Pressure as the data source. A set of axes will appear with pressure on the vertical axis and time on the horizontal axis. Click on the axis label `Time' and select Angular Position from the drop-down list. • Click Start to begin collecting data. Turn the engine slowly by hand and describe the correspondance between the position of the pistons and the resulting trace. Operation of the Stirling Engine as a Heat Engine Obtain your raw data as quickly as you can to prevent overheating of the con- necting wires due to high currents. 1. Start with a coil current of about 8 A. The engine is unlikely to start at lower currents. When the engine speed has stabilized, click on \Start" to obtain a new trace. At the same time determine the rate of rotation of the flywheel using the counter, and calculate the electrical power which is supplied to the heater coil. 2. Repeat the above steps, increasing the current by about ∼1 A each time. Do not let the coil current exceed 13 A. Turn off the Engine by switching off the heater current. Analysis 1. Save your pressure-volume data for each run using File - Export. 2. Import your raw data into a spreadsheet. You need pairs of (x; y) values corresponding to one complete loop only, as in Fig 4. Note that the \Angular Position" axis represents the volume change that occurs inside the cylinder so that the distance between maximum and minimum values on the horizontal axis of the graph corresponds to a volume change of 150 cm3. 3. The work done by the engine is obtained from the area of each loop. The area of a polygon with n vertices can be found from the Gauss-Green formula, n X (yi + yi+1) (xi − xi+1) i=1 2 5 140 120 100 80 60 Series1 Pressure (kPa) 40 20 0 -20 0 20 40 60 80 100 120 -20 angular position Figure 4: Typical output for one complete cycle from Stirling Engine experiment The curve needs to be a single loop that doesn't intersect itself. The loop must be closed so that the last x value is x1, and the last y value is y1. If necessary, add a copy of the first point to the end of the data list. 4. Calculate the area of the loop and the work done by the gas per cycle. Calculate also the power output and, by comparing with the electrical power input, the efficiency of the engine. 5. Summarize your results by plotting a graph of efficiency versus applied current, and discuss how well your results demonstrate the predictions of the Second Law. How much work is done in overcoming friction and other imperfections in the Engine? Reference: C. G. Deacon, R. Goulding, C. Haridass and B. de Young, Demonstration Experiments with a Stirling Engine, Physics Education 29, 180{183 (1994) 6.
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