UBC Phys 420 Oct.14 (2008) Hiroko Nakahara Stirling Engine

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UBC Phys 420 Oct.14 (2008) Hiroko NakaharaStirling EngineOutline :1. Introduction2. Engine and heat source3. Why study Stirling engines?3-0. What is a Stirling engine?3-1. Heat and Temperature3-2. Work and PV-diagrams3-3. Heat engines3-4. Thermal efficiency4. Demonstration of Stirling engine5. SummaryReference dex.phpUniversity Physics 10th edition, Addison Wisely, Young & Freedman

1. Introduction Cars are very useful and a keytransportation tool for people in Canada.Have you ever opened the hood of your carand wondered what was going on in there?Gasoline cars have heat engines (usuallyjust called an engine).

2. Engines and Heat Sources Heat engine (engine) a device that converts thermal energy (heat) to mechanicalmotionTwo types of heat engines–Internal heat sourceUses combustion of fuel inside a confined volumeEx. Gasoline engine–External heat sourceUses an external heat sources (Gasoline, solar energy, decaying plant matter etc)Ex. Steam engine, Stirling engineInternal heat sourceInternal combustionExternal heat sourceExhaustvalveSchematic of Stirling engine

3. Why Study Stirling Engines? The Stirling engine uses an external heat source Gas inside the Stirling engine does not leave the engine Environmentally friendly alternative engineUsing a Stirling engine as an example of a heat engine we can learn the following:0. What is a Stirling engine?1. Heat and Temperature2. Work and PV-DiagramsTemperatureThermalefficiencyHeat3. Heat engines4. Thermal efficiencyHeatenginesWorkPV-Diagrams

3-0. What is a Stirling Engine?6 components1. Containers2. Piston --- tightly sealed3. Displacer --- large piston, loose4. Crank shaft5. Fly wheel6. External heat sourceModel Stirling engine

3-0. What is a Stirling Engine?1. The air at the bottom heats up,creating pressure on the smallpower piston, which moves upand rotates the wheel.2. The rotating wheel moves thebig displacer down3. The air cools down at the top,reducing the pressure andallowing the power piston tomove down.4. This motion of the powerpiston moves the displacerupwards and the air at thebottom is heated again.The key principles of a Stirling engine:a fixed amount of a gas is sealed inside the engine

3-1. Heat and TemperatureIf you take a canof coke from thefridge and leaveit in the ldCokeHotCoffeeEnergyQ HeatTCold coke --- Because energy is transferredfrom environment to Cold CokeEnergyQ HeatIf you make a cupof hot coffee andleave it in thekitchen,THot coffee --- Because energy is transferredfrom Hot coffee to environmentTemperature Indicator of how much energy matter has, [K]cold --- less energyhot --- more energyHeat Energy that is transferred between a system (coke or coffee) andits environment (kitchen) because of the temperature difference, [J]

3-2. WorkWorkForce FWork done by piston in cylinderPressure PDistance traveled lCrosssectionalArea ATraveled distance lDefinition : WorkW F lUnit :1 J 1N mCaution : Don't confuse W (work)with w (weight).W F l PA l P VFP AA l VForce acting on pistonCross sectional area ofpistonChange in volume afterpiston moves by lWork done in VW P V V V2 - V1V1V2

3-2. Work and PV-diagramW P VW P VConstantPressure V V2 - V1VariedPressure V V2 - V1V1V2In a PV-diagram, work is area under the curve.V1More work--- Larger areaLess work --- Smaller areaV2

3-2. Work in PV-diagramsPP1abP2 dcThis PV-diagram represents the system goingthrough a thermodynamic cycle (Ex. A pistonmoves from a to b, pressure decreases fromb to c. Then the piston moves from c to d andpressure increases from d to a. This processrepeats for a complete cycle) Which part ofthe diagram corresponds to work, W ?VV1P1a bV2b cc dd a P2V1V1V2W P V P1 (V2 - V1) W 0W 0V2W P V P2 (V1 - V2)W 0W 0WNET 0In PV-diagramsWork is area inside closed path

3-3. Heat engineHotSource THTHQQinColdTCHeat engineHeat flows from “Hot” to “Cold”when the two systems at differenttemperature are placed in contact.WQoutSink TCHeat engine extracts work from the heat flow from “Hot” to “Cold”.RequiresSource at THSink at TC

3-4. Thermal EfficiencySource THQinHeat engineW1. Source at TH adds Qin to heat engine2. Heat engine does work W by using Qin.Not all of Qin is used to work.The left over heat is Qout.3. Qout is dumped into sink at TCQoutQin – W QoutW Qin – QoutSink TCHeat enginerepeatsthis cycleQin Heat flow from sourceto heat engineQout Heat flow from engineto sinkW work done by heat engineEfficiency for ideal engineQoutQin – QoutOutputWQQ QQ 1 InputQinQinQQQinQIdeal heat engine returns to its initial state (TH) perfectly at the end of each cycleTCQWout W QQQinTHEfficiencyfor ideal engineTC 1 TH

4. Demonstration of Stirling EngineWhen you place the Stirling engine ontop of a cup of hot water, we are the following?(Assume that the engine is ideal.)(a) the PV-diagram(b) How much work does the engine do per cycle?(c) What is the power P of the engine?(d) What is the efficiency of the engine?

3-0. What is a Stirling Engine?1. The air at the bottom heats up,creating pressure on the smallpower piston, which moves upand rotates the wheel.2. The rotating wheel moves thebig displacer down3. The air cools down at the top,reducing the pressure andallowing the power piston tomove down.4. This motion of the powerpiston moves the displacerupwards and the air at thebottom is heated again.The key principles of a Stirling engine:a fixed amount of a gas is sealed inside the engine

4. Demonstration of Stirling Engine102.2102.0Pressure 544.644.7344.844.9(b) Closed area in PV-diagram. (Unit is J)1. The area inside the loop was dividedinto small rectangles2. Area of each rectangles werecalculated3. All area of each rectangles wereadded to obtain the area inside theloop.Work 0.46 mJVolume (cm )(c) The power of the engine is W done per cycle divided by the time length ofeach cycle. (Unit is W)1 HP (horse power) 745.7 WW [[J]J]P W f (0.46 mJ)(7.5 Hz) 3.4 mW 4.6 10-6 HPt [s][s]Pcar 120 HP(d) Substitute the two temperature TC and THTC 24 273 [[K]K] 1 1 0.193 19%TH 95 273 [[K]K]19 %

6. SummaryFrom envronmentally friendly Stirling engine, we learned:(1) Process of Stirling engine (How it works)(2) Temperature is an indicator of how much energy matter has.Heat is Energy transferred from one body to another body due to a temperaturedifference(3) Work is product of force on a body and the distance traveled by that body.Ex. Work of piston in cylinder --- W P V(4) Work in a PV-diagram is represented by area under curve/line and area in the closedpath.(5) Heat engine is a device that convertsheat to mechanical work as it repeatsas a cycle(6) Efficiency for ideal engine is given byTC 1 TH TemperatureHeat enginesIs illustratedbyuseHeatFor energy to do WorkIs calculated inIs illustratedby ThermalefficiencyPV-Diagrams

Stirling Engine 1.Introduction 2.Engine and heat source 3.Why study Stirling engines? 3-0. What is a Stirling engine? 3-1. Heat and Temperature 3-2. . If you make a cup of hot coffee and leave it in the kitchen, 3-2. Work Distance traveled