Physics Engineering PC 1431 Experiment P2 Heat Engine. Section B: Brief Theory (condensed from Serway & Jewett)

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1 Pysics Engineering PC 1431 Experiment P2 Heat Engine Section A: Introduction Te invention of steam engine played a very significant role in te Industrial Revolution from te late 1700s to early 1800s. Te steam engine is an example of a eat engine wic converts termal energy into useful mecanical energy. Te First and Second Laws of Termodynamics, wic you will study (or ad just studied) in te later part of tis module, came about troug te effort to understand te nature of termal energy and to improve te efficiency of eat engines. In tis experiment, you will ave a cance to study ow a very simple eat engine works. Section B: Brief Teory (condensed from Serway & Jewett) A eat engine is a device tat takes in energy by eat and operating, in a cyclic process, expels a fraction of tat energy by means of work. For instance, in a typical process by wic power plant produces electricity, coal or some oter fuel is burned and te igtemperature gases produced are used to convert liquid water to steam. Tis steam is directed at te blades of a turbine, setting it into rotation. Te mecanical energy associated wit tis rotation is used to drive an electric generator. Te eat engine carries some working substance troug te process during wic (1) te working substance absorbs energy by eat from a ig-temperature energy reservoir, (2) work is done by te engine, and (3) energy is expelled by eat to a lower-temperature reservoir. It is useful to represent tis scematically as in Figure 2.1. Te engine absorbs a quantity of energy from te ot reservoir. Te engine does work W and ten give a quantity of energy c to e cold reservoir. Because te working substance goes troug a cycle, its initial and final internal energies are equal, and so te work done by te eat engine is equal to te net energy transferred to it. Terefore W net = Figure 2.1 c Te work done by a gas in any termodynamic process can be sown to be te area under te curve of a P-V diagram. Terefore if te working substance is a gas, te net work done in a cyclic process is te area enclosed by te curve representing te process on a P-V diagram. Tis is sown for an arbitrary cyclic process in Figure 2.2. Figure 2.2. Work done by a gas in a cycle.

2 Te efficiency e of a eat engine is defined as te ratio of te net work done by te engine to te energy input at te iger temperature during one cycle. Tus it is easy to see tat W e = net = c = 1 c. Section C: A Possible Scenario Your working group as been approaced by te Newton Apple Company about testing a eat engine tat lifts apples tat vary in mass from 50 g to 200 g from a processing conveyer belt to te packing conveyer belt tat is a few cm iger. Te engine you are to experiment wit is a real termal engine tat can be taken troug a four-stage expansion and compression cycle and tat can do useful mecanical work by lifting small masses from one eigt to anoter. In tis experiment we would like you to verify experimentally tat te useful mecanical work in lifting a mass, m, troug a vertical distance, y, is equal to te net termodynamic work done during a cycle as determined by finding te enclosed area on a P-V diagram. Essentially, you are comparing useful mecanical m a gy work (as in Figure 2.3a) wit te accounting of work in an engine cycle as a function of pressure and volume canges given by te expression (as in Figure 2.3b): W net = pdv Figure 2.3a Figure 2.3b

3 Section D: Apparatus (Te Incredible Mass Lifter Engine) Te eat engine consists of a ollow cylinder wit a grapite piston tat can move along te axis of te cylinder wit very little friction. Te piston as a platform attaced to it for lifting masses. A sort lengt of flexible tubing attaces te cylinder to an air camber (consisting of a small can sealed wit a rubber stopper tat can be placed alternatively in te cold and ot reservoirs). A diagram tis mass lifter is sown in Figure 2.4. Figure 2.4: Setup for te eat engine If te temperature of te air trapped inside te cylinder, ose and can is increased, ten its volume will increase, causing te platform to rise. Tus, you can increase te volume of te trapped air by moving te can from te cold to te ot reservoir. Ten wen te apple as been raised a distance y, it can be removed from te platform. Te platform sould ten rise a bit more as te pressure on te cylinder of te gas decreases a bit. Finally, te volume of te gas will decrease wen te air camber is returned to te cold reservoir. Tis causes te piston to descend to its original position once again. Te various stages of te mass lifter cycle are sown in Figure 2.5 and approximately represented troug te P-V diagram in Figure 2.3b. Figure 2.5. Simplified diagram of te eat engine at different stages of its cycle

4 Section E: Procedure Part I Before taking data on te pressure, air volume and te eigt of lift wit te eat engine, you sould set it up and run it troug a few cycles to get used to its operation. A good way to start is to fill one container wit room temperature water and anoter wit preeated water at about C. Te engine cycle is muc easier to describe if you begin wit te piston resting above te bottom of te cylinder. Tus we suggest you raise te piston a few cm before inserting te rubber stopper firmly in te can. Also, air does leak out of te cylinder slowly. If a large mass is being lifted, te leakage rate increases. Terefore, we suggest tat you limit te added mass to someting between 50 g and 200 g. Run troug te cycle (witout taking any data) as indicated below a few times. i) Transition a b: Add te mass to te platform; ii) Transition b c: Place te can in te ot reservoir; iii) Transition c d: Remove te mass from te platform; iv) Transition d a: Place te can in te cold reservoir. After observing a few engine cycles, describe wat appens during eac of tese transitions carefully in your report, indicating wic of tese are approximately adiabatic (were no eat enters or leaves te system) and wic are isobaric. You can observe te canges in te volume of te gas directly and you can predict ow te pressure exerted on te gas by te surroundings ougt to cange from point to point by using te definition of pressure as force per unit area. Part II Set up te low pressure and rotary motion sensors and start te DataStudio software as explained in Appendix A. Wit te ot and cold temperatures still at C and room temperature respectively, run troug te complete cycle as indicated above. Wit te piston about 2 cm above te bottom, close te system to outside air. Make sure tat te rubber stopper is firmly in place in te can. You will start te cycle at point a wit te can in te cold reservoir. Start te data collection on te computer at tis point. Proceed troug te rest of te cycle. You sould repeat te experiment several times to obtain te best results. Print te best plots for tree different masses, e.g., 50 g, 100 g and 150 g, on a single grap. Indicate also te temperatures of te ot and cold reservoir in your report. Part III We will next study ow te work done is affected by increasing te temperature of te ot reservoir to about C and decreasing te temperature of te cold reservoir to tat of melting ice. Please use caution wen andling te ot water. Stir to maintain a uniform temperature and do NOT eat until te water boils. Record te temperatures in your report.

5 Again, perform te cycle several times to obtain te best results. Repeat wit te same masses you ave used in Part II and print te best results. Section F: Calculations and discussion 1 Explain ow you can calculate te work done by te engine from te P-V diagram. State any approximations you will make. Similarly explain ow you will calculate te mecanical work done in raising te different masses troug different eigts in Parts II and III. 2 Tabulate your results for te six plots and compare te work done obtained from te P-V diagrams and te mecanical work done. 3 Discuss some possible reasons wy te two works done calculated above could be different. 4 Compare te work done at te different ot and cold reservoir temperatures, i.e., between Part II and Part III. State any conclusion you can draw from te results. Possible data tat you may need in your calculations and discussion. Piston diameter = (32.5 ± 0.1) mm Mass of piston & platform = (35.0 ± 0.1) g You may also request for oter measuring instruments from te lab officers if you want to determine any oter values. Appendix A : Science Worksop Connections & Software Interface Setup 1 Connect te tubing from te low pressure sensor gauge to te second pressure port of base apparatus and te low pressure sensor cable to Analog Cannel A of te Science Worksop Interface (as sown in Figure 2.6). 2 Devise a suitable metod to measure te position of te platform wit te Rotary Motion Sensor. For example you could loop a string over te large pulley wit one end tied to a 50-gram weigt resting on te platform and te oter end tied to a 5-gram weigt so tat te string is always taut and pulley rotates wen te platform moves. Connect te Rotary Motion Sensor cable to Digital Cannels 1 and 2. 3 Connect te Science Worksop interface to te computer, turn on te interface. Start DataStudio.

6 Digital Cannel 1 & 2 Analog Cannel A Figure 2.6: Te Science Worksop interface 4. Start experiment by double click te DataStudio icon. 5. Left click on te mouse at Analog Cannel A and select te Low Pressure Sensor. 6. Set te Low Pressure Sensor so tat it measures te Pressure, C A (kpa). Unceck Voltage, CA (V). Tis is te default setting. 7. Left click on te mouse at Digital Cannels 1 & 2 and select te Rotary Motion Sensor. 8. Set te Rotary Motion Sensor so tat te sample rate is 50 Hz (default); it measures Position, C 1 & 2 (m); it records 360 divisions per rotation (default); Linear calibration set to Large Pulley (groove) if you ad followed te instruction in step 2, or set according to wat you ave done. 9. In te program, select a grap display and set it to sow Pressure (kpa) on vertical axis and click on orizontal axis to replace Time to Position, C1&2 (m). (Strictly speaking, tis is not a P-V grap but a grap of pressure versus position. In your calculation, remember to convert position to volume.) 10. You are now ready to collect data.