Lab 1: Expansion of gases - kantiolten.ch · Lab 1: Expansion of gases ... isovolumetric,...

KS Olten Physics Lab: Heat Engines and Electromagnetism 3rd Gym

Lab 1: Expansion of gases

Learning Aims

• Experimental work:

– Investigate the increase in volume of an enclosed amount of air if the temperature israised and the pressure remains constant.

• Physics:

– You know Charles’ law.

Theory

• Basic facts about gas laws

– How do volume and temperature depend on each other if the pressure remains con-stant?

Procedure

V0 = 34.5cm3 of air are enclosed in a test tube. The increased temperature of the air betweentest tube and measuring pipette is negligible. Therefore it is possible to read the increase of thevolume (and only of this volume) V0 from the change of the water level in the pipette. In orderto read the measurement, the mobile tube has to be moved until the water level in both tubes isthe same. Then the pressure inside the test tube is the same as the atmospheric pressure outsideso that the increase in volume at constant pressure can be measured. Procedure:

• switch on the stirring device

• read and record temperature

• level the water level, read from the scale and record

• switch on heater, set the rotary knob to 250°C

• every 2 minutes: read and record temperature and water level

• stop measurements at about 75°C switch off heater and stirring device

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Evaluation

Use TI-nspire; the instructions are in the appendix

• enter the values into two lists for ’temperature’ and ’volume’

• calculate the regression line

• additionally, determine the intersection ϑ0 of the regression line with the x-axis

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Labs 2 – 4: Heat Engines

Station 1: Thermodynamic Cycles

Learning Aims

• Experimental work

– You can make and record measurements using an electronic data recording system

– Using the corresponding software, you can evaluate measurements as graphs or astables

• Physics:

– You know Boyle’s law and know what the p-V -diagram of an isothermal processlooks like

– You can interpret the p-V -diagramme of a thermodynamic cycle and describe thecorresponding processes

– you know how the internal energy of a gas changes when thermodynamic processeshappen and you can apply the 1st law of thermodynamics

Theory

• Processes of the ideal gas: isovolumetric, isothermal, isobaric, adiabatic

• 1st law of thermodynamics

– ∆U = W +Q (U : internal energy, Q: heat, W : mechanical work)

– If the energy in the system increases, the sign is positive, if it decreases, the sign isnegative.

Procedure

140 ml air are enclosed in an Erlenmeyer flask by a movable piston. Two sensors measure thepressure and temperature of the water in which the piston is completely immersed. Changes involume can be read from the scale of the syringe.

Experiment 1: isothermal process

• Make sure that both sensors are connected to the LabQuest interface. Start the interfaceand program LoggerPro on the laptop.

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• Set the menu «Versuch - Datenerfassung» from «zeitgesteuert» to «Ereignisse mit Tasta-tureingabe». Enter Volume as column title and ml as measuring unit.

• Push the piston completely into the syringe and start the measurement with the greenarrow.

• Click on «Beibehalten» and enter the initial volume.

• Repeat the last step several times, increasing the volume by 2-3 ml every time. Concludethe measurement after the last step (20 ml).

• Save the results and enter them into an excel sheet by copy-paste.

Experiment 2: thermodynamischer Kreisprozess

• Open a new document and set the data recording to «Ereignisse mit Tastatureingabe» asbefore.

• Set the piston of the syringe back to 0 and start the data recording by clicking on «Beibe-halten» again and entering the initial volume.

• Pour hot water into the prepared beaker and carefully put the piston with the completeequipment into the second beaker.

• When temperature and pressure remain stable, record the measured value using «Beibe-halten».

• Carry out the isothermal process as in the first experiment as fast as possible. The tempe-rature should change by a few degrees at most.

• Now cool the piston back down to air temperature (using a different beaker) and recorddata auf when pressure and temperature do not change any more.

• Now carry out an isothermal compression step by step until you reach the initial volumeand record the measurement values until you are back to the initial conditions. Then stopthe measurement and save the results.

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Evaluation

• Experiment 1: Using your data, confirm Boyle’s Law.

• Experiment 2: Copy the p-V -Diagramm into a Word Document and label the four stepsof the thermodynamic cycle. Enter the names of the four processes in a table and addinformation on whether the values ∆U , Q and W are positive, negative or 0.Explain the significance of the surface below the isothermal lines in the diagram.

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Station 2: Diesel Engine and Turbo Charger

Learning aims

• You understand the functional principle of a 4-stroke diesel engine and of a turbo charger.

2A. The Diesel Engine (4-stroke version)

The diesel engine was invented by Rudolph Diesel in1893. Unlike an Otto engine (running onpetrol and to this day the most frequently used engine), a Diesel engine does not require anignition plug because the diesel-air mixture is pyrophoric, once it has been compressed in thecylinder.Like most engines, diesel engines consist of one or more cylinders (4 or 6 in most cars andlorries), in which a piston moves up and down periodically and is connected to the drivingshaft. The latter turns the car’s wheels.

The cylinders work in 4-stroke mode. Let’s look at an individual cylinder:A cylinder basically consists of a cylinder housing and a piston inside, which moves up anddown and in thus turns the driving shaft. The piston must be well lubricated in order to keep thefriction forces with the cylinder wall minimal. In a 4-stroke engine (the most frequent model!),the piston inside the cylinder works with the strokes Intake–Compression–Work–Exhaust (sofor a complete thermodynamic cycle the piston moves up twice and down twice).During the intake stroke, fresh air and fuel are mixed in dispersed form. In a diesel engine,this injection happens at the moment when the piston is at the upper dead centre, i.e. whenthe cylinder volume is smallest. Because of the strongly compressed air, the mixture is so hot(ca. 800°C), that it ignites by itself, unlike in a petrol engine, which uses an ignition plug. Theexplosion makes pressure and temperature (at practically identical volume) rise strongly so thatthey press the piston down with large force (of course pressure and temperature then fall againafter this phase). When the piston reaches the exhaust phase and shoots back up, the exhaustvalve opens and the used mixture is transported from the cylinder into waste gas duct. In thenext Phase (the Piston is up and has expelled all exhaust gases), the intake valve opens and theexhaust valve closes. The piston goes down and thus creates an underpressure which attractsfresh air and again generates a fuel-air-mixture. Note that the piston gains kinetic energy onlyduring the working stroke and then uses it to carry out the next three strokes!

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Exercise

Reconsider the 4 strokes using our model. You can achieve a complete thermodynamic cycle ifyou move the piston down, up again, down again and up again. This is how you can recognizethe strokes. Allocate them and make a sketch (or take photos). Now label the most importantelements!

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2B. The Turbo Charger

The turbo charger (also called turbo or exhaust turbo charger), (patented in 1905) was inventedby the Swiss engineer Alfred Büchi. The turbo charger is considered one of the most importantinventions of the 120th century!The turbo charger is an additional element of a combustion engine. It uses a part of the energyof the exhaust gas flow to achieve the increase in power and efficiency of the engine. A turbocharger makes it possible to achieve the same power with a smaller engine (Down-Sizing).

Structure: All turbo chargers are similarly constructed. Usually, the turbine and the compressorare two identical paddle wheels enclosed by a housing:

Exercise

The following briefly summarizes the mode of operation. You should enter in the text in thegraph below. Consider also our model of a real turbo charger.

Using an exhaust turbo charger, engine power should be increased. This can be achieved bycondensing the incoming air (ca. 18°C). Thanks to the higher density, a larger amount of airand therefore a larger amount of oxygen can enter the cylinder’s combustion chamber at everyintake stroke of the cylinder. The higher oxygen supply enables a better combustion and theengine power is increased.The exhaust of an engine (ca. 700°C) has heat and kinetic energy. These energies are used todrive the exhaust gas turbine of the turbo charger. The exhaust gas loses some of its energy in

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this process. It cools down to ca. 650°C. The exhaust gas turbine drives the compressor, whichturns at up to 200‘000 U/min! The compressor compresses the incoming air, which is heated toca. 120°C and so loses density. In the charge-air cooler, it is cooled down again to ca. 60°Cwhich raises the density. This density it is higher than the atmospheric pressure by ca. 0.8 bar(ca. 1 bar). This air is fed into the cylinder during the intake stroke. It is denser and thereforehas a higher oxygen concentration than fresh air which would be introduced into the cylinderwithout a turbo charger. The second difference is that the cylinder even receives kinetic energyduring the intake stroke since there is overpressure.

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Station 3: Refrigerator

3A. Functional Principle

Learning Aims

• You know how a refrigerator/a heat pump works.

Theory

• the boiling point of a liquid depends on surrounding pressure

– When a liquid is heated to boiling point ϑs, steam bubbles are generated in theliquid, which rise to the surface. For these bubbles tob e generated, the pressure inthe steam bubble (steam pressure pD) must be at least as high as the surroundingpressure (air pressure pL).

• Specific steam heat

– Evaporating a liquid of the mass Masse m, requires the heat Q = mLv. Lv is thespecific steam heat of the liquid.

– When this gaseous substance of the mass m condenses again, the same heat Q = mLvis released into the environment.

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Functional Principle of a Compressor Fridge

A refrigerator transports heat from a cold reservoir (refrigerator, T1) to a warm reservoir (kit-chen, T2). This is only possible if work W is done.In the pipe system of a fridge, there is some cooling agent, which has a boiling point of about−40°Cat normal pressure. The cooling agent is moved in a closed circuit.

1) Evaporating (inside the fridge)The cooling agent reaches the refrigerator in liquid form at p1 ≈ .1 bar. Since the tem-perature of the refrigerator T1 is higher than −40°C, the cooling agent evaporates. Therequired steam heat Q1 is extracted from the fridge.

2) CompressThe gaseous cooling agent is compressed by an electric compressor, which increases thepressure of the cooling agent to p2 ≈ 8 bar. This raises the condensation temperature ofthe cooling agent to room temperature.

3) Condensating (outside the fridge)In the cooling web of the condensator (evaporator), the gaseous cooling agent (which isunder high pressure) condenses at room temperature T2. During this process, it releasesthe heat of condensation Q2 to the environment.

4) ExpandingAn expansion valve reduces the pressure of the liquid cooling agent. Back to p1 ≈ 1 barso that boiling temperature is back to −30°C. This liquid cooling agent is now directedinto the refrigerator and the process starts over again from the beginning.

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Exercise

1) Consider the dismounted circuit of the refrigerator. Turn it a and find out where the foursteps of the thermodynamic cycle take place. Where are the evaporator, the compressor,the condensator, the cooling web and the expansion valve?

2) Isobutane C4H10 contributes very little to the greenhouse effect auf and is therefore usedas a cooling agent with the identifier R600a in refrigerators and air conditioners. Thefollowing diagram shows the vapour pressure of isobutane as a function of temperature.(Watch out: Logarithmic scale for Pressure).

i) Calculate the boiling temperature of isobutane at normal pressure.

ii) To which value must the pressure be raised (using the compressor) so that the refri-gerator works also at 40°C?

iii) The cooling power of a refrigerator is 200 W. How much isobutane condenses persecond? The specific steam heat of the isobutane is 366.7 J/g.

3) What is the difference between a refrigerator and a heat pump?

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3B. Determining the coefficient of performance of a heat pump / coolingunit

Learning Aims


– You can question an experiment and identify sources of error– You can make suggestions for improving an experiment

• Physics:

– You can determine the coefficient of performance of a heat pump / cooling unit andknow its range of values.

Theory

• A heat pump / cooling unit transports heat from acold reservoir (temperature T1) to a warm reservoir(temperature T2). This is only possible if work Wis added and also transformed into heat.Consider that Q2 = Q1 +W .

• the coefficient of performance ε is a measuring degree for the quality of heat pumps /cooling units.

Heat pump (HP) Cooling unit (CU)The coefficient of performance is the ratioof the heat Q2 that is fed into the warmreservoir (apartment) and the investedwork W .

εHP =Q2

W

The coefficient of performance is the ratioof the heat Q1 that is extracted from thecold Reservoir (fridge) and the investedwork W .

εCU =Q1

W

Material

Model of a heat pump / cooling unit, two beakers with 700 g water each, two thermometers, twostirring staffs, stop watch, power meter

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Procedure

• Measure the initial temperature of the warm and of the cold reservoir.

• Let the model the feat pump run for 10 minutes. Measure the invested electrical power.

• Touch the tubes of the heat pump: Where are they warm, where cold?

• Turn the heat pump off, stir until the temperatures of the warm reservoir and the coldreservoir are both stable and record the two final temperatures.

Evaluation

• Calculate the invested work W , the heat Q1 that is withdrawn from the cold reservoir andthe heat that is fed into the warm reservoir Q2.

– Q1 and Q2 are determined with the specific heat capacity. Q = cm∆T

– W is determined with power of the pump Q = P∆t.

• Calculate the coefficients of performance of the model if it is made to work as a heatpump εHP and as a cooling unit εCU.

• Why is the equation Q2 = Q1 +W not correct for our model?

• Which range of values can the coefficient of performance εHP take per definition?

• Why does it not make sense to run this model as a real heat pump (i.e. to heat water withthis model)?

• How should the model be improved to be an efficient heat pump?

Exercise

The public baths in Olten uses a heat pump for its pool heating. This pump extracts heat fromthe Aare and feeds this heat into the pool. Data:

• Total electricity: 69 kW

• Water in the river Aare: 100 m3

h

• Cooling of Aare water: 3 K

1) Determine the coefficient of performance of the heat pump. [4.6]

2) The heat pump works 1300 h every season. How much heating oil is saved per season?(The lower heating value of heating oil is 42.6 MJ/kg, its density is 860 kg

m3 .) [570 hl]

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Station 4: Stirling Engine

4A. Principle

Learning Aims

• You understand how a stirling engine works and can explain its functioning with the gaslaws.

Theory

Around 1816, the Scottish cleric ROBERT STIRLING invented and built a cyclic heat engine withair as its working medium. Stirling engines have a permanently heated part T1 and a permanentlycooled part T2. Using a displacer piston, the air is pushed backwards and forwards between thetwo heat reservoirs and so has alternately the temperature T1 and then the temperature T2. Thedisplacer piston of the Stirling engine is mechanically coupled with the working piston in such away that the displacement of the working gas happens at the right moment. The Stirling processhas four steps:

1) Isothermal expansion at a temperature T1The working gas with the initial volume V1 and the initial pressure p1 expands in thecylinder at the constant temperature T1 to the volume V2 at the pressure p2. In doing so,the working piston is pushed to the lower position, doing the work W1. The displacingpiston starts to move downwards when the working piston has almost reached the deadcentre. In this way, the hot working gas is moved into the cold part of the cylinder.

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2) Isovolumetric coolingIn this phase, the working gas is cooled down to the temperature T2 at the constant volumeV2 (pressure: p3). This process requires a release of heat to the reservoir T2.

3) Isothermal compression at the temperature T2The working piston is pushed upwards by the movement of the flywheel and thereforecompresses the working gas at T2 to the initial volume V1 (pressure: p4). This requires anexternal work W3 done to the system. The reservoir T2 prevents the gas from heating up.

4) Isovolumetric heatingWhen the working piston is in its upper dead centre, the displacing piston moves downagain and moves the cold working gas back into the hot part of the cylinder. The gasis heated up at the constant volume V1 to its initial temperature T1. In this process, thepressure rises from p4 to p1.

Exercises

1) Draw the p-V-diagram of a sterling engine.

2) Sketch the position of the two pistons at the beginning of every step.

3) Various configurations of a Stirling engine are possible. Below, you find four graphs thathave been jumbled. Label the components of the new Stirling engine in the image aboveright and put the picture in the correct order.

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Station 4: Stirling Engine – Application

Learning Aims


– You record a p-V-diagram of a Stirling cycle auf and calculate the gained work aswell as the efficiency of the engine.

• Physics:

– You understand how a Stirling engine works and can explain its functioning withthe gas laws.

Theory

• The universal gas law and its application in the Stirling engine

• The thermodynamic processes used in the Stirling engine

Material

• Stirling engine with current source

• Cassy-System

• Laptop

Procedure

1) At this station, the working diagram (p-V-Diagram) of the Stirling engine is to be registe-red

2) Before starting the engine, the cooling water must be switched on and the current sourcemust be set to max. 15 A.

3) After a brief heating phase (ca. 1 min.), the engine can be switched on at the fly wheel.As soon as it is turning, the current in the heating coil auf 12 A must be reduced.

4) To register the working diagram, stop the engine again. The position of the measuringwheel must be in such a way that the upper dead centre of the working piston shows avolume of ca. 50 cm3.

5) The measurement of diagram is started with key F9. During a fixed period of time, mea-surements are being registered and displayed.

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Evaluation

The inner diameter of the working piston is 60 mm. Together with the displacement of the pistonthis gives the change in volume ∆V .

1) To calculate the net work of the engine, integrate over the surface. Click into the diagramwith a right mouse click and click the menu «integrieren». Now click on the starting pointand retrace a tour, keeping the mouse key pressed. The area is shown in status line.

2) The mechanical power of the engine is calculated using the rotary frequency f :

Pmech = W · f

3) Using the values of voltage U and current I, the done electric power can be calculated:

Pel = U · I

This determines, finally, the efficiency η .

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Lab 5: Direct Current 1

Learning Aims


– Know where and how voltage and current can be determined / measured in a simplecircuit. Know why it is necessary to tap the voltage in a parallel way and the currentserially.

• Physics:

– Know the concepts ”voltage” and ”electric current” and their physical meanings.

Theory

• Basic facts about direct current

– What is the difference between direct and alternating current?

– What is the difference between the technical direction of current and the physicalone?

– What are current-voltage characteristics and what do they look like for a wire or alight bulb?

Procedure

1) current-voltage characteristics of a constantan wire

• It is to be investigated how the voltage V on a wire and the current I that flowsthrough the wire at this voltage correlate. Use at least 10 different voltage measure-ments. Please note that the voltage should be no higher than ca. 10 V. Your teacherwill show what could happen otherwise.

• Record the current-voltage characteristics of the wire in a neat voltage-electric cur-rent graph (current y-axis, voltage x-axis).

• What is the wire’s resistance? Is it constant? These and other questions and calcula-tions should be found in the report. Remember the definition of resistance:

R =VI

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2) current-voltage characteristics of a light bulb Now investigate the same questions fora light bulb. Please note: the voltage should not exceed the working range of the lightbulb (e.g. 6 V).In addition, note differences between light bulb and wire:

• At which points do the two current-voltage characteristics diverge?

• How can these differences be explained?

• What is the physical explanation?

• Does this mean that the formula for calculating resistance (R = V/I) is wrong?

Evaluation

For the evaluation, proceed as follows: Discuss the set questions in the given order and presentyour results in a scientifically correct report.

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Lab 6: Direct Current 2

Learning Aims


– Measure the resistance in a circuit. The following variables are of interest: the volta-ge over the resistor, the current through the resistor, the resultant resistance (whichmay also be measured directly with the Ohm meter).

• Physics:

– Know the dependence of a wire’s resistance (cf. also Lab 1.) on its geometrical andphysical characteristics and be able to calculate a wire’s resistance using tables

– Know the term of direct and indirect proportionality of a quantity and be able to findit mathematically and experimentally

Theory

• The Resistance formula describes the dependence of the resistance R on length, cross-section and material of the wire.

Material

1) Wires of various sizes and materials

2) Power supply, tension pullers for the wires, alligator clips for tapping various lengths ofwire

3) Ampère and volt meters

Procedure

1) In this lab session, the main aim is to verify the resistance formula. Use wires made ofvarious materials and with varying lengths and cross-sections.

2) Consider how the physical variables contained in the resistance formula can be varied andmeasured.

3) Verify the formula by changing one variable and keeping the others constant. How shouldresistance then change according to the formula?

4) The wires do not need to be cut, it is sufficient to clamp them at the required length.

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Evaluation

1) The report should first of all discuss the resistance formula in more detail. Which physicalunits does it contain and what do they stand for? Which of them are geometrical, whichdescribe materials?

2) Describe the experimental procedure: How are the variables in the formula changed? Howdoes this affect the resistance formula? Can these answers be confirmed experimentally?

3) Confirm the formula numerically as well as graphically. Graphs are essential.

4) Discuss the final results. Has the resistance formula been verified? In the evaluation, dis-cuss possible sources of error and their influence.

5) Find the resistivity of constantan and compare it with the literature value: 4.9 · 10−7 Ωm(20°C).

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Lab 7: Direct current 3

Learning Aims


– Set up circuits with several resistors and measure their resistance.

– Understand the term “electric power” and measure such power in circuits, directlyand indirectly.

• Physics:

– Know Kirchhoff’s Laws and use them to calculate all measured voltages. Voltageand resistors in the circuit are given.

– Calulate the total resistance in a given circuit.

– Calculate the overall electric power and the partial electric power and understandtheir interdependence.

Theory

• The electric power P (in Watt) done by any resistor (may also be a household appliancelike an iron)

• Kirchhoff’s Laws

Material:

1) plug-in-board, power supply and multimeter

2) 4 resistors, you should measure first by yourself. Use the found values for the calcula-tions. Here you see the rounded values:

• 2 à 1000 Ω

• 1 à 470 Ω

• 1 à 100 Ω

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Procedure

1) Set up the following three circuits. The total resistance is to be determined experimentallyas well as calculated from all partial resistances. The voltage is 10 V every time.

i)

1kΩ 1kΩ 470Ω 100Ω

ii)

1kΩ

100Ω

470Ω

iii)

100Ω

470Ω1kΩ

1kΩ

2) Measure and calculate the total resistance of the circuit.

3) Measure and calculate the partial voltages, partial currents and power consumption in atleast one of the circuits 2) and 3), using Kirchhoff’s Laws as well as the total resistance.Compare the values.

Evaluation

1) Assemble all measurements and calculations using tables.

2) Compare the measured values to the calculated values. Relative and absolute deviationsshould also be noted here.

3) In conclusion, discuss the results.

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Lab 8: Electric Motors

Learning Aims


– Describe how a technical application of physics works, using physical laws.

• Physics:

– Understand how an electric motor works.

Theory (short)

• Basics: Magnetism

• The magnetic field of a long straight wire

Material

1) Power supply, coil N=500 (solenoid), test magnet, bar magnet, magnetic core

2) Plug-in-board, bar magnet, 2 pole pieces, connection plate, coil rotor, brush yoke, powersupply

Procedure

1) The magnetic field of a solenoid

• What could the magnetic field of a solenoid look like? Formulate a hypothesis basedon your knowledge about the magnetic field of a long straight wire.

• Connect the coil with 500 turns to the power supply (DC) and set the voltage to 5 V.Investigate the direction of the magnetic field around the coil using a test magnet.

• Approach the solenoid with the north or south pole of a bar magnet. What can beobserved?

• Raise the voltage briefly (!) to 10 V and repeat the experiment with the bar magnets.What is the effect?

• Introduce a magnetic core into the coil (at 5 V). How does this influence the strengthof the magnetic field outside the coil? Explain.

• Sketch the magnetic field of a coil (inside and outside the coil) and compare yoursketch to the magnetic field of a bar magnet. Which parameters does the strength ofa coil’s magnetic field depend on?

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2) DC electric motor with permanent-magnet stator field

• On the plug-in-board, construct a horseshoe magnet (1st stator) which is extendedat a right angle by a bar magnet with two pole shoes. Determine the direction of themagnetic field in the horseshoe magnet using the test magnet.

• Place the rotatable coil (2nd rotor) in middle of the horseshoe magnet.

• Put the brush yoke (3.2) on the connection plate and fix the brush springs in position2 so that they touch the inner (a) and outer (c) collector ring of the connection plate(3.1).

• Connect the coil to a DC power supply.

• Set the voltage to 6 V and start the motor.

– Why does the coil rotate?– Why does the coil do half a revolution at most?– What could be done to make it go on rotating?

• Fix the brush springs at position 1 so that they touch the commutator ring (b) of theconnection plate.

• Set the voltage to 6 V and start the motor by hand.

– Why does the coil continue to rotate?– Explain how the commutator ring works.

Evaluation

Answer the following question in a short text (50–100 words): ”How does a direct currentelectric motor work?”

• Remember to relate your text to the experiments carried out during the lab sessions.

• You may use sketches to illustrate your explanation.

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Lab 9: Lorentz force/Alternating current

Learning Aims


– Understand how the PicoScope works.

• Physics:

– Know about alternating current and how it is generated.

Theory

• Lorentz force: What happens when a conductor moves in a homogeneous magnetic field?

• Oscillation: Define “oscillation period” and “amplitude”

• Sinusoidal voltage:

Vrms =V0√

2

Material

Power supply, PicoScope, laptop, plug-in board, bar magnet, 2 pole shoes, wire coil with 2 x350 turns, plug-in board with three connector rings, brush yoke, belt transmission, multimeter

Procedure

1) Functionality of the PicoScope:The picoscope measures the voltage curve as a function of time and represents it in anx-y-graph. (x axis = time, y axis = voltage)

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• Connect channel A of the PicoScope to a DC power supply.

• Start the PicoScope 6 software (desktop) and set the following settings:1© Scale of the x axis: 1 s/div (seconds per division)2© Scale of the y axis: ± 20 V DC (direct current)3© Trigger: automatic A

• Start the measurement ( 4© green arrow), vary the voltage (max. 20 V) and observewhat happens.

2) Voltage curve of an AC power supply

• Connect channel A of the PicoScope to an AC power supply.

• Set the following software settings:1© Scale of the x axis: 10 ms/div2© Scale of the y xis: ± 20 V AC (alternating current)

• Set the voltage of an AC power supply to 10 V.

• Start the measurement ( 4© green arrow) and generate a freeze image of the voltagecurve ( 4© Stopsymbol)

• Determine the oscillation period T , the frequency f , and the amplitude V0 (peakvalue) of the voltage.

• Connect a multimeter to the power supply parallel to the PicoScope and read thevoltage.

• The multimeter measures the so-called r.m.s. (root-mean-square) value of the volta-ge Vrms . This is the voltage which needs to be generated by a DC power supply in

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order to generate the same average electric power as the AC power supply.Show that Vrms = 1√

2V0

3) Generating AC current with a generator

• Construct an AC generator on the plug-in board:– Use a horseshoe magnet which is extended (at a right angle) by a bar magnet

with two pole shoes.– Fix the driving belt to the coil and place the coil in the magnetic field.– Fix the brush yoke at position 2 so that the brush springs touch the inner and

outer collector ring of the plug-in board.

• Connect the coil to channel A of the PicoScope.• Set the following software settings:

1© Scale of the x axis: 50 ms/div2© Scale of the y axis: ± 2 V AC

• Turn the crank and record the voltage curve.• Save the voltage curve as a png-image for your report.• Vary the rotational speed and observe the effect.

Evaluation

• Explain the sine curve of the course of the induced voltage of an AC generator by con-sidering a single rectangular conductor loop which is being rotated in a homogeneousmagnetic field.

– Use Walter Fendt’s applet:http://www.walter-fendt.de/ph14e/generator.htm

• Determine the position of the conductor loop for the maximal and the minimal voltage aswell as for voltage 0 V.

• Determine the oscillation period T , the frequency f , and the amplitude V0 and the rms-value Vrms of the voltage produced by the generator. What quantities change and howmuch, if you change the speed of rotation?

• Why does the voltage which is generated in this experiment deviate from a perfect sinecurve?

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A Using the TI-nspire

A.1 Entering measured data

Enter the measured data as lists:

A.2 Creating diagrams

The measured data are recorded in lists (procedure see above). To display them, change into anew window by clicking ’ctrl-I’ and ’Add Data & Statistics’.

Then ’Click to add variables’ and select the correct variable.

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A.3 Establishing a regression line

Now put a straight line through the points in the graph – a so-called regression line. To do this:’Menu – Analyze – Regression – Show Linear (mx+b)’.

If necessary, adapt the axes using ’Menu – WindowZoom – WindowSettings’.

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Lab 1: Expansion of gases - kantiolten.ch · Lab 1: Expansion of gases ... isovolumetric,...

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