Download Lab 1: Expansion of gases

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 is
raised 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 constant?
Procedure
V0 = 34.5 cm3 of air are enclosed in a test tube. The increased temperature of the air between
test tube and measuring pipette is negligible. Therefore it is possible to read the increase of the
volume (and only of this volume) V0 from the change of the water level in the pipette. In order
to read the measurement, the mobile tube has to be moved until the water level in both tubes is
the same. Then the pressure inside the test tube is the same as the atmospheric pressure outside
so 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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Physics Lab: Heat Engines and Electromagnetism
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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 as
tables
• Physics:
– You know Boyle’s law and know what the p-V -diagram of an isothermal process
looks like
– You can interpret the p-V -diagramme of a thermodynamic cycle and describe the
corresponding processes
– you know how the internal energy of a gas changes when thermodynamic processes
happen 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 is
negative.
Procedure
140 ml air are enclosed in an Erlenmeyer flask by a movable piston. Two sensors measure the
pressure and temperature of the water in which the piston is completely immersed. Changes in
volume 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 interface
and program LoggerPro on the laptop.
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Physics Lab: Heat Engines and Electromagnetism
3rd Gym
• Set the menu «Versuch - Datenerfassung» from «zeitgesteuert» to «Ereignisse mit Tastatureingabe». Enter Volume as column title and ml as measuring unit.
• Push the piston completely into the syringe and start the measurement with the green
arrow.
• Click on «Beibehalten» and enter the initial volume.
• Repeat the last step several times, increasing the volume by 2-3 ml every time. Conclude
the 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» as
before.
• Set the piston of the syringe back to 0 and start the data recording by clicking on «Beibehalten» again and entering the initial volume.
• Pour hot water into the prepared beaker and carefully put the piston with the complete
equipment into the second beaker.
• When temperature and pressure remain stable, record the measured value using «Beibehalten».
• Carry out the isothermal process as in the first experiment as fast as possible. The temperature should change by a few degrees at most.
• Now cool the piston back down to air temperature (using a different beaker) and record
data auf when pressure and temperature do not change any more.
• Now carry out an isothermal compression step by step until you reach the initial volume
and record the measurement values until you are back to the initial conditions. Then stop
the measurement and save the results.
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Physics Lab: Heat Engines and Electromagnetism
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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 steps
of the thermodynamic cycle. Enter the names of the four processes in a table and add
information 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 on
petrol and to this day the most frequently used engine), a Diesel engine does not require an
ignition plug because the diesel-air mixture is pyrophoric, once it has been compressed in the
cylinder.
Like most engines, diesel engines consist of one or more cylinders (4 or 6 in most cars and
lorries), in which a piston moves up and down periodically and is connected to the driving
shaft. 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 and
down and in thus turns the driving shaft. The piston must be well lubricated in order to keep the
friction 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 (so
for 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. when
the 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. The
explosion makes pressure and temperature (at practically identical volume) rise strongly so that
they press the piston down with large force (of course pressure and temperature then fall again
after this phase). When the piston reaches the exhaust phase and shoots back up, the exhaust
valve opens and the used mixture is transported from the cylinder into waste gas duct. In the
next Phase (the Piston is up and has expelled all exhaust gases), the intake valve opens and the
exhaust valve closes. The piston goes down and thus creates an underpressure which attracts
fresh air and again generates a fuel-air-mixture. Note that the piston gains kinetic energy only
during the working stroke and then uses it to carry out the next three strokes!
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Physics Lab: Heat Engines and Electromagnetism
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Exercise
Reconsider the 4 strokes using our model. You can achieve a complete thermodynamic cycle if
you move the piston down, up again, down again and up again. This is how you can recognize
the strokes. Allocate them and make a sketch (or take photos). Now label the most important
elements!
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2B. The Turbo Charger
The turbo charger (also called turbo or exhaust turbo charger), (patented in 1905) was invented
by the Swiss engineer Alfred Büchi. The turbo charger is considered one of the most important
inventions of the 120th century!
The turbo charger is an additional element of a combustion engine. It uses a part of the energy
of the exhaust gas flow to achieve the increase in power and efficiency of the engine. A turbo
charger 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 compressor
are two identical paddle wheels enclosed by a housing:
Exercise
The following briefly summarizes the mode of operation. You should enter in the text in the
graph below. Consider also our model of a real turbo charger.
Using an exhaust turbo charger, engine power should be increased. This can be achieved by
condensing the incoming air (ca. 18°C). Thanks to the higher density, a larger amount of air
and therefore a larger amount of oxygen can enter the cylinder’s combustion chamber at every
intake stroke of the cylinder. The higher oxygen supply enables a better combustion and the
engine power is increased.
The exhaust of an engine (ca. 700°C) has heat and kinetic energy. These energies are used to
drive the exhaust gas turbine of the turbo charger. The exhaust gas loses some of its energy in
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Physics Lab: Heat Engines and Electromagnetism
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this process. It cools down to ca. 650°C. The exhaust gas turbine drives the compressor, which
turns at up to 200‘000 U/min! The compressor compresses the incoming air, which is heated to
ca. 120°C and so loses density. In the charge-air cooler, it is cooled down again to ca. 60°C
which 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 therefore
has a higher oxygen concentration than fresh air which would be introduced into the cylinder
without a turbo charger. The second difference is that the cylinder even receives kinetic energy
during 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 the
liquid, which rise to the surface. For these bubbles tob e generated, the pressure in
the steam bubble (steam pressure pD ) must be at least as high as the surrounding
pressure (air pressure pL ).
• Specific steam heat
– Evaporating a liquid of the mass Masse m, requires the heat Q = mLv . Lv is the
specific steam heat of the liquid.
– When this gaseous substance of the mass m condenses again, the same heat Q = mLv
is 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 (kitchen, 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 temperature of the refrigerator T1 is higher than −40°C, the cooling agent evaporates. The
required steam heat Q1 is extracted from the fridge.
2) Compress
The gaseous cooling agent is compressed by an electric compressor, which increases the
pressure of the cooling agent to p2 ≈ 8 bar. This raises the condensation temperature of
the cooling agent to room temperature.
3) Condensating (outside the fridge)
In the cooling web of the condensator (evaporator), the gaseous cooling agent (which is
under high pressure) condenses at room temperature T2 . During this process, it releases
the heat of condensation Q2 to the environment.
4) Expanding
An expansion valve reduces the pressure of the liquid cooling agent. Back to p1 ≈ 1 bar
so that boiling temperature is back to −30°C. This liquid cooling agent is now directed
into 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 four
steps of the thermodynamic cycle take place. Where are the evaporator, the compressor,
the condensator, the cooling web and the expansion valve?
2) Isobutane C4 H10 contributes very little to the greenhouse effect auf and is therefore used
as a cooling agent with the identifier R600a in refrigerators and air conditioners. The
following 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 refrigerator works also at 40°C?
iii) The cooling power of a refrigerator is 200 W. How much isobutane condenses per
second? 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 / cooling
unit
Learning Aims
• Experimental work
– 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 and
know its range of values.
Theory
• A heat pump / cooling unit transports heat from a
cold reservoir (temperature T1 ) to a warm reservoir
(temperature T2 ). This is only possible if work W
is 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)
The coefficient of performance is the ratio
of the heat Q2 that is fed into the warm
reservoir (apartment) and the invested
work W .
Q2
εHP =
W
Cooling unit (CU)
The coefficient of performance is the ratio
of the heat Q1 that is extracted from the
cold Reservoir (fridge) and the invested
work W .
Q1
εCU =
W
Material
Model of a heat pump / cooling unit, two beakers with 700 g water each, two thermometers, two
stirring 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 cold
reservoir 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 and
the 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 heat
pump 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 with
this 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 from
the Aare and feeds this heat into the pool. Data:
• Total electricity: 69 kW
3
• Water in the river Aare: 100 mh
• 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?
kg
(The lower heating value of heating oil is 42.6 MJ/kg, its density is 860 m
[570 hl]
3 .)
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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 gas
laws.
Theory
Around 1816, the Scottish cleric ROBERT S TIRLING invented and built a cyclic heat engine with
air as its working medium. Stirling engines have a permanently heated part T1 and a permanently
cooled part T2 . Using a displacer piston, the air is pushed backwards and forwards between the
two heat reservoirs and so has alternately the temperature T1 and then the temperature T2 . The
displacer piston of the Stirling engine is mechanically coupled with the working piston in such a
way that the displacement of the working gas happens at the right moment. The Stirling process
has four steps:
1) Isothermal expansion at a temperature T1
The working gas with the initial volume V1 and the initial pressure p1 expands in the
cylinder 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 displacing
piston starts to move downwards when the working piston has almost reached the dead
centre. In this way, the hot working gas is moved into the cold part of the cylinder.
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2) Isovolumetric cooling
In this phase, the working gas is cooled down to the temperature T2 at the constant volume
V2 (pressure: p3 ). This process requires a release of heat to the reservoir T2 .
3) Isothermal compression at the temperature T2
The working piston is pushed upwards by the movement of the flywheel and therefore
compresses the working gas at T2 to the initial volume V1 (pressure: p4 ). This requires an
external work W3 done to the system. The reservoir T2 prevents the gas from heating up.
4) Isovolumetric heating
When the working piston is in its upper dead centre, the displacing piston moves down
again and moves the cold working gas back into the hot part of the cylinder. The gas
is heated up at the constant volume V1 to its initial temperature T1 . In this process, the
pressure 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 that
have been jumbled. Label the components of the new Stirling engine in the image above
right and put the picture in the correct order.
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Station 4: Stirling Engine – Application
Learning Aims
• Experimental work
– You record a p-V-diagram of a Stirling cycle auf and calculate the gained work as
well as the efficiency of the engine.
• Physics:
– You understand how a Stirling engine works and can explain its functioning with
the 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 registered
2) Before starting the engine, the cooling water must be switched on and the current source
must 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 measuring
wheel must be in such a way that the upper dead centre of the working piston shows a
volume of ca. 50 cm3 .
5) The measurement of diagram is started with key F9. During a fixed period of time, measurements 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 piston
this gives the change in volume ∆V .
1) To calculate the net work of the engine, integrate over the surface. Click into the diagram
with a right mouse click and click the menu «integrieren». Now click on the starting point
and 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
• Experimental work:
– Know where and how voltage and current can be determined / measured in a simple
circuit. Know why it is necessary to tap the voltage in a parallel way and the current
serially.
• 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 physical
one?
– What are current-voltage characteristics and what do they look like for a wire or a
light 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 flows
through the wire at this voltage correlate. Use at least 10 different voltage measurements. Please note that the voltage should be no higher than ca. 10 V. Your teacher
will show what could happen otherwise.
• Record the current-voltage characteristics of the wire in a neat voltage-electric current graph (current y-axis, voltage x-axis).
• What is the wire’s resistance? Is it constant? These and other questions and calculations should be found in the report. Remember the definition of resistance:
R=
19
V
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Physics Lab: Heat Engines and Electromagnetism
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2) current-voltage characteristics of a light bulb Now investigate the same questions for
a light bulb. Please note: the voltage should not exceed the working range of the light
bulb (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 present
your results in a scientifically correct report.
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Lab 6: Direct Current 2
Learning Aims
• Experimental work:
– Measure the resistance in a circuit. The following variables are of interest: the voltage over the resistor, the current through the resistor, the resultant resistance (which
may also be measured directly with the Ohm meter).
• Physics:
– Know the dependence of a wire’s resistance (cf. also Lab 1.) on its geometrical and
physical 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 find
it mathematically and experimentally
Theory
• The Resistance formula describes the dependence of the resistance R on length, crosssection 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 of
wire
3) Ampère and volt meters
Procedure
1) In this lab session, the main aim is to verify the resistance formula. Use wires made of
various materials and with varying lengths and cross-sections.
2) Consider how the physical variables contained in the resistance formula can be varied and
measured.
3) Verify the formula by changing one variable and keeping the others constant. How should
resistance 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 physical
units does it contain and what do they stand for? Which of them are geometrical, which
describe materials?
2) Describe the experimental procedure: How are the variables in the formula changed? How
does 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, discuss 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
• Experimental work:
– Set up circuits with several resistors and measure their resistance.
– Understand the term “electric power” and measure such power in circuits, directly
and indirectly.
• Physics:
– Know Kirchhoff’s Laws and use them to calculate all measured voltages. Voltage
and 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 understand
their interdependence.
Theory
• The electric power P (in Watt) done by any resistor (may also be a household appliance
like 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 calculations. 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 experimentally
as well as calculated from all partial resistances. The voltage is 10 V every time.
1kΩ
1kΩ
470Ω
100Ω
i)
1kΩ
470Ω
100Ω
ii)
1kΩ
100Ω
1kΩ
470Ω
iii)
2) Measure and calculate the total resistance of the circuit.
3) Measure and calculate the partial voltages, partial currents and power consumption in at
least 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 deviations
should also be noted here.
3) In conclusion, discuss the results.
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Lab 8: Electric Motors
Learning Aims
• Experimental work:
– 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, power
supply
Procedure
1) The magnetic field of a solenoid
• What could the magnetic field of a solenoid look like? Formulate a hypothesis based
on 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 be
observed?
• 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 strength
of the magnetic field outside the coil? Explain.
• Sketch the magnetic field of a coil (inside and outside the coil) and compare your
sketch to the magnetic field of a bar magnet. Which parameters does the strength of
a 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 extended
at a right angle by a bar magnet with two pole shoes. Determine the direction of the
magnetic 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 position
2 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 the
connection 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 current
electric 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
• Experimental work:
– 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:
V0
Vrms = √
2
Material
Power supply, PicoScope, laptop, plug-in board, bar magnet, 2 pole shoes, wire coil with 2 x
350 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 an
x-y-graph. (x axis = time, y axis = voltage)
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Physics Lab: Heat Engines and Electromagnetism
3rd Gym
• 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
4 green arrow), vary the voltage (max. 20 V) and observe
• Start the measurement (
what 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/div
2 Scale of the y xis: ± 20 V AC (alternating current)
• Set the voltage of an AC power supply to 10 V.
4 green arrow) and generate a freeze image of the voltage
• Start the measurement (
4 Stopsymbol)
curve (
• Determine the oscillation period T , the frequency f , and the amplitude V0 (peak
value) of the voltage.
• Connect a multimeter to the power supply parallel to the PicoScope and read the
voltage.
• The multimeter measures the so-called r.m.s. (root-mean-square) value of the voltage Vrms . This is the voltage which needs to be generated by a DC power supply in
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Physics Lab: Heat Engines and Electromagnetism
3rd Gym
order to generate the same average electric power as the AC power supply.
Show that Vrms = √12 V0
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/div
2 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 considering a single rectangular conductor loop which is being rotated in a homogeneous
magnetic 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 as
well as for voltage 0 V.
• Determine the oscillation period T , the frequency f , and the amplitude V0 and the rmsvalue Vrms of the voltage produced by the generator. What quantities change and how
much, if you change the speed of rotation?
• Why does the voltage which is generated in this experiment deviate from a perfect sine
curve?
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A.1
Physics Lab: Heat Engines and Electromagnetism
3rd Gym
Using the TI-nspire
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 a
new 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
Physics Lab: Heat Engines and Electromagnetism
3rd Gym
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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