Thermodynamics lab report - This report is meant to be written for a reader who does not have in-depth knowledge of the subject so all working must be included/ all equations must be stated and explained. please do not just put the equation without explaining what the equation is used for
Instructions:1. Please watch the experiment video
2. Please read the experiment file3. Please read the Task sheet + layout file
4. Please read the marking rubric5. Please go back and read the experiment file and answer the exercise questions (this will later be used in the report OR it can be attached to the appendix)
6. Start the report7. Please do no leave out anything - Both the criteria sheet and task sheet say to CLEARLY label all graphs/tables and define the variable used on the axes and tables8. Only use credible sources9. All calculations need to have full working shown10. please meet word count - I have labelled how many words are required for each section.11. Please answer all exercise questions on the sterling experiment file and follow each step/requirement. Do not leave any of them out12. Any questions please ask my email is open 24.713. Please double-check everything has been answered according to requirements- I have listed everything in detailed both here and on the task sheet and the criteria sheet and the experiment explains everything as well.
Stirling Engine Video .mp4 __MACOSX/._Stirling Engine Video .mp4 Stirling Engine-Data.xlsx Sheet1 1EXPERIMENT 1: Work by the engine 2Temperature (Cold Reservoir) degrees CelciusErrorTemperature (Hot Reservoir) degrees CelciusErrorArea hPa cm3 3250.297.30.142190 4250.298.40.135710 5250.2100.20.156780 6250.295.80.152750 7250.294.80.159560 8250.296.70.147890 9250.297.40.132310 10250.298.10.147710 11250.299.90.145210 12250.2102.50.148670 13250.21100.130640 14250.2119.50.134510 15250.21200.143480 16250.21250.150550 17250.2124.50.140070 18 19EXPERIMENT 2: Voltage Comparison 20 216 VOLTS, Tc = 298.15K, Th = 304.55K8 VOLTS, Tc = 298.15K, Th = 308.65K10 VOLTS, Tc = 298.15K, Th=318.05K12 VOLTS, Tc = 298.15K, Th = 327.05K 22Time initialTime finalPeriodTime initialTime finalPeriodTime initialTime finalPeriodTime initialTime finalPeriod 230.140.520.380.160.480.320.020.230.210.180.40.22 240.520.890.370.480.810.330.230.430.20.40.630.23 250.891.30.410.811.150.340.430.650.220.630.850.22 261.031.680.651.151.480.330.650.860.210.851.090.24 271.682.060.381.481.820.340.861.070.211.091.30.21 282.062.460.41.822.150.331.071.290.221.31.540.24 292.462.860.42.152.510.361.291.510.221.541.780.24 302.863.260.42.512.860.351.511.730.221.7820.22 313.263.670.412.863.20.341.731.930.222.240.24 323.674.080.413.23.550.351.932.150.222.242.460.22 334.084.50.423.553.890.342.152.370.222.462.710.25 344.54.920.423.894.250.362.372.590.222.712.930.22 __MACOSX/._Stirling Engine-Data.xlsx Screen Shot 2020-06-18 at 11.24.54 pm.png __MACOSX/._Screen Shot 2020-06-18 at 11.24.54 pm.png Experiment - StirlingEngine read first.pdf The University of Queensland PHYS2020 – Thermodynamics PHYS2020 – Thermodynamics Laboratory – Stirling Engine (extended experiment) Revision: April 13, 2018 Warning: • Don’t touch the upper half of the heat-exchange cylinder (behind the metal grille) – it gets very hot! • The engine needs to be running while the heater is turned on, otherwise it will not dissipate enough heat. Turn the flywheel to start the engine once the element is glowing, and if the engine stops, turn off the heater. • Avoid running the Stirling engine for too long at high speeds/voltages. Preparation Before you turn up to the laboratory to start this experiment, please complete each of the following: • Read through the relevant sections of the text [1]: – pp 122–127 Heat Engines – pp 133-134 Stirling Engine • Work through the theory in Section 2 of these notes. • Attempt the exercises in Section 2.3. If you have queries arising from them, please ask one of the teaching staff at the laboratory session. 1 Introduction The Stirling engine was first developed in the early 19th century as a safer alternative to steam engines. Despite having an efficiency that in principle can approach the ideal Carnot limit, it was largely superseded by the rise of high-power internal combustion engines. However, in the drive for energy efficiency, Stirling engines have become of recent interest, as a way to generate electricity from industrial and domestic waste heat [2]. In this experiment, the pressure and piston displacement of a Stirling engine are recorded so that you can construct the pV diagram at different operating temperatures. From these diagrams you can calculate the actual efficiencies of the Stirling engine and compare to those of the ideal Carnot cycle operating between the same temperatures. You will can also investigate the output power and torque as a function of temperature. 2 Theory 2.1 Stirling Cycle The ideal Stirling cycle, illustrated in Fig. 1(a), consists of a combination of isochoric (constant volume) and isothermal expansions and contractions of its working substance, usually a gas such as air [1]. Note that if you replaced the isochoric segments with adiabats, you would achieve the familiar Carnot cycle. The apparatus in this experiment implements the Stirling cycle by means of two pistons within one cylinder. The lower part of the cylinder is sealed with the working piston, which allows the gas to expand and contract, and thereby to do mechanical work on the flywheel to which the piston is connected. The displacing piston moves an inner glass chamber up and down in order to push the gas into thermal contact alternately with hot and cold reservoirs. This inner chamber has the topology of a doughnut, with the air moving through copper wool in the centre of the ‘doughnut’ as the displacing piston moves up and down. In the set-up here, the heat is provided by a heating element at the top of the cylinder rather than through an external reservoir. Contact with the cold reservoir is provided by the cooling water circulating around the lower half of the cylinder. 1 The University of Queensland PHYS2020 – Thermodynamics (a) (b) Figure 1: pV diagram of the Stirling cycle. (a) Ideal cycle; (b) A representation of the actual cycle. All images taken from [3]. The stages of the Stirling cycle are: isothermal expansion As the gas is heated by the hot reservoir, it expands, pushing down the working piston. isochoric cooling With the working piston fully lowered, the displacing piston moves up to push the gas down into contact with the cold reservoir. The gas then cools at constant volume to a lower pressure. isothermal contraction The working piston is then raised, using energy stored in the flywheel, to compress the gas while it is in thermal contact with the cold reservoir. isochoric heating Finally, the displacing piston is lowered in order to push the gas to the hot reservoir end of the cylinder. The pressure of the gas increases as it absorbs heat, ready to begin another expansion stroke. In the real device, the pistons move continuously in a sinusoidal fashion (see Fig. 2) with the displacing piston a quarter of a cycle ahead of the working piston. This fact, together with the finite time that the gas is in contact with the reservoirs, means the actual cycle produces a much more ‘smooth’ pV diagram, as illustrated in Fig. 1(b). 2.2 Efficiency The actual efficiency of a heat engine is the ratio of the work produced (benefit) to the heat absorbed in order to achieve this work (cost) [1]: η ≡ W Qh = 1− Qc Qh , (1) where all quantities are taken to be positive. The Carnot efficiency gives the maximum possible efficiency for an ideal engine operating between the same two reservoirs. In an ideal engine, no new entropy is generated, thus Qh = Th∆S and Qc = Tc∆S, giving ηC ≡ 1− Tc Th . (2) 2 The University of Queensland PHYS2020 – Thermodynamics Figure 2: Actual position of the working piston (Ak) and the displacing piston (Vk) during a cycle. There are a number of reasons why the Stirling engine in this experiment falls short of the Carnot efficiency. In your report, you should discuss the main mechanisms that lead to inefficiencies, and use your experimental data to characterise them. It can be helpful to define an ‘internal efficiency’ ηi based on the actual amount of heat that the gas absorbs during a cycle, and an ‘internal Carnot efficiency’ ηiC , based on the highest and lowest temperatures the gas actually reaches during a cycle. In practical applications, it is often not efficiency that we are most concerned about, but the output power, which is the rate at which the engine does work Pw = W/∆t, where ∆t is the duration of one cycle. 2.3 Exercises Try to work through these exercises before the laboratory session. You should either incorporate your answers within the body of your report, or append them at the end. (a) Suppose that the air in the Stirling engine can be treated as an ideal gas and that the pressure and volume around each point of the cycle are known. Write down an expression that lets you evaluate the heat absorbed or released between any two points on the cycle. (b) What do you think the main causes of inefficiency will be in the engine? Describe how the different efficiencies defined above could be used to quantify their contributions to a less-than-perfect efficiency. You may want to refine this answer once you have seen the engine in operation. (c) Sensors on the Stirling engine record the relative pressure in hPa and the piston displacement in cm (so that you can work out the volume). What level of precision and sampling frequency would be reasonable for each of these quantities? Justify your answer. Again, you may want to refine your answer once you have seen the engine in operation. 3 Experiment 3.1 Equipment The displacement of the working piston and the relative pressure in the chamber are monitored by sensors connected to the desktop computer via the CASSY board. The data can be analysed and plotted using the installed CASSY software. The hot reservoir is maintained by heat generated by an electrical heating element, whose resistance is R = 0.65 ± 0.01Ω. You can apply different voltages to the element by the way you hook it up to the transformer. The useful range of voltages is from 6 V (below which the engine generally can’t provide enough torque to turn the flywheel) to 16 V (above which the engine goes a little too fast). The relevant dimensions of the engine are: 3 The University of Queensland PHYS2020 – Thermodynamics • internal diameter of cylinder: 60 mm • minimum gas volume: approx 200 cm3 • maximum gas volume: approx 350 cm3 • diameter of flywheel: 25 cm • mass of flywheel: 4.25 kg • moment of inertia of flywheel: 0.043 kg m2 3.2 Guided Exploration Work through the following exercises during the first session for this experiment, noting down answers, observations and queries in your logbook. Getting started • Turn on the CASSY board, and open up the CASSY software on the desktop. The software should recognise the board and bring up a dialogue box, on which you can click the A and B inputs in order to activate them (in the upper and middle boxes on the right-hand side of the schematic). Before you close the dialogue box, click also on ‘Show Measuring Parameters’ to open up the settings panel on the right. • In the settings panel, you will see a number of options for the output of the rotary motion sensor. Probably the most useful will be the path (in cm). By manually rotating the flywheel, check that the measured path values lie within the specified range, and adjust the range if it does not. For later reference, you may want to note the path readings when the working piston is fully up and fully down. • In the settings panel, you can set the measurement interval (i.e. sampling rate) for each sensor, and choose whether the measurement runs are to be terminated manually or automatically