physics course exercisesLiceo Scientifico Giordano Bruno – Venezia-Mestre

where is the heat ?

in accordo con il

Ministero dell’Istruzione, Università, Ricercae sulla base delle

Politiche Linguistiche della Commissione Europea

percorso formativo a carattere tematico-linguistico-didattico-metodologico

scuola secondaria di secondo grado

teacherFrancesco Minosso

where is the heat?

Indice Modulo

Strategies – Before Prerequisites Linking to Previous Knowledge and Predicting con questionari basati su stimoli

relativi alle conoscenze pregresse e alle ipotesi riguardanti i contenuti da affrontare

Italian/English Glossary

Strategies – During

Video con scheda grafica Keywords riferite al video attraverso esercitazioni mirate Conceptual Map

Strategies - After

Esercizi: Multiple Choice Matching True or False Cloze Flow Chart Think and Discuss

Summary per abstract e/o esercizi orali o scritti basati su un questionario e per esercizi quali traduzione e/o dettato

Web References di approfondimento come input interattivi per test orali e scritti e per esercitazioni basate sul Problem Solving

Answer Sheets

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Strategies BeforePrerequisites

In order to understand the concepts and the ideas in the next unit, you will need some knowledge about heat and electric charge and some operations to measure the electrical work done when a charge flows through a circuit and heat is exchanged between a heater and some matter. The following scheme shows the unit prerequisites sequence: the titles of the learning units are circled in red, while the prerequisites are in the black boxes. The arrows show the time direction.

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Electriccharge Heat

Heat andelectriccharge

Where isthe heat?

How to measurean electric chargeflowing througha circuit with anammeter anda stopwatch

Electric currentAmmeter

How to measureabsorbed or

exchanged heat

Properties ofmatter involvingheat exchange

Heat capacity

Relationship betweenproduced heat and

electric charge:L = Q

VoltageVoltmeter

where is the heat?

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Strategies BeforeLinking to Previous Knowledge and Predicting

Answer on your exercise book and share the answers with your mates.

Electric charge

1. Which phenomena does electric charge involve?

2. Describe how to measure the electric charge on a little insulated conducting sphere: draw a sketch of the apparatus and write the operations and the calculations you should do.

3. Describe how to measure the electric charge flowing in a circuit: draw a sketch of the apparatus and write the operations and the calculations you should do.

4. Write some properties of the electric charge.

Heat

5. Which phenomena does heat absorption or exchange involve?

6. Describe how to measure the heat absorbed or exchanged by a certain substance in a thermometry experiment: draw a picture of the apparatus and write the operations and the calculations you should do.

7. Draw a sketch and explain how to use a device to measure when an object has absorbed one unit of heat.

8. Mention a few properties of matter involving heat exchange.

9. How could you do in order to measure the properties you have just listed?

Heat and electric charge

10. Experiment A. After electrically heating up an aluminium cylinder, you have measured the heat Q absorbed by the cylinder, varying the current I flowing through the heater for time t:you have found out that the electric charge and the heat are proportional. Write the formula resulting from the analysis of the collected data which expresses the relationship between the heat and the charge.

11. Experiment B. After electrically heating up an aluminium cylinder, you have measured the heat q absorbed by the cylinder when a unit charge has passed through the heater varying the number of flashlight cells: you have found out that the heat produced by a unit charge and the total voltage V applied are proportional. Write the formula resulting from the analysis of the collected data which expresses the relationship between the heat produced by a unit charge and the total voltage.

12. Using the formula of exercises no.10 and no.11, get the relationship between the heat produced by the heater and the electrical work done by the flashlight cells and express it with the electric current I, the voltage V and the working time t.

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13. Heat produced and work done are proportional and the numerical value of the proportionality constant depends on the unit used to measure heat, charge and voltage. To determine this value you can submerge a heater in the water and measure the temperature rise of the water. Here are the results of one run. Find the constant and use your words to write down what this constant represents. Remember to use the correct units.

Mass of water in the calorimeter 100 gChange of temperature 7.0°C

Electric current 2.15 ATime of run 120 s

Voltage across the heater 11.3 V

The heat generated in the calorimeter is:

The electric charge passing through the heater is:

The electrical work done is:

The constant is:

The meaning of the constant is:

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Strategies BeforeItalian / English Glossary

22.25°C Twenty-two point two-five degreesAmpere (A) Ampere (A)Amperometro AmmeterApplicare (essere applicato): il voltaggio viene applicato

To apply (to be applied): voltage is applied

Aprire (spegnere, scollegare) il circuito To turn the circuit offAsse del motore Motor shaftAumento di temperatura Temperature rise / increaseAvvolgimento di filo di rame isolato Coils of insulated copper wire / windingBatteria di due pile 2-cells batteryBatteria di pile, pila BatteryCalcolare To calculateCalore HeatCalore mancante Lacking heatcaloria (cal) calorie (cal)Capacità termica Heat capacityCarica elettrica Electric charge / chargeCavi elettrici WiresChiudere / far funzionare / accendere il circuito

To turn the circuit on

Cinghia di gomma Rubber beltCinghia di trasmissione Belt driveCollegamenti ConnectionsCollegare in parallelo To connect in parallelConfrontare To compareContenitore ContainerControllare, verificare (sperimentalmente) To checkCorrente / tensione media Average current / average voltageCorrente elettrica Electric currentCronometro Stopwatch, chronometerDifferenza di potenziale Potential differenceDifferenza percentuale Percentage differenceEssere uguale a To equalFilo di nylon Nylon threadFondo scala Full scale rangeFormula FormulaFunzionare To run / to workFunzionare a vuoto, girare in folle To run in neutralGirare To rotateGrado centigrado Degree (Celsius)In condizioni (operative) diverse Under different (operating) conditions

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Intervallo di tempo Time / time intervalIsolare termicamente To insulateJoule (J) Joule (J)Kilogrammo KiloLavoro elettrico Electrical work /workLo scopo (obiettivo) dell'esperimento è The experiment aims atMassa MassMateriali MaterialsMeasurement unit Unità di misuraMisurare To measureMisurare la durata di qualcosa To time somethingMolletta da bucato Clothes pegMotore elettrico Electrical motorMotore elettrico in folle Electrical motor in neutralMultimetro digitale Digital multimeter / multimeterPolistirolo StyrofoamPotential difference Differenza di potenzialePredisporre l'apparato sperimentale To arrange the apparatusProcedura / protocollo di lavoro / schema di lavoro

Procedure

Procedura di elaborazione (dei dati) (data) Managing procedureProcedura per la raccolta dei dati Data collecting procedurePuleggia PulleyQuaderno di laboratorio Lab notebookQuantità AmountRaccogliere i dati To collect dataRapporto (numerico) RatioResistenza ResistorRiproducibilità (di un esperimento) ReproducibilityRiscaldatore HeaterRisolvere (un problema) To solve (a problem)Scatola di materiale isolante Insulating boxSchema SketchSecondo (s) Second (s)Sollevare To liftSpiegare / rendere conto To explainStrumentazione Equipment / instrumentsSvolgere i calcoli To carry out (the calculations)Tabella TableTanica JerrycanTemperatura TemperatureTemperatura ambiente Room temperatureTemperatura iniziale Initial temperatureTermometro ThermometerUguaglianza EquationUn quarto di divisione A quarter of the scaleUn set di 4 batterie di quattro pile A set of 4 batteries with four flashlight

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Volt (V) Volt (V)Voltaggio VoltageVoltmetro Voltmeter

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Strategies During Keywords

1) Circle which of the following keywords are associated with the relationship between heat and work in an electrical motor (project of the work)

To measure – heat produced – voltmeter – electrical work – electrical motor –degree –three steps – parallel connected – pulley – electrical motor in neutral – heat capacity

2) Circle which of the following keywords are associated with equipment and materials used to study the relationship between heat and work

Electrical motor – insulating box – voltage - chronometer – thermometer – heat capacity – tables – 4-cells batteries – connected in series – data – wires – heater – belt drive

3) Circle which of the following keywords are associated with the heat capacity measurement

Axis – rubber belt – heater – copper wires – to lift – project – equals – electric connections – mechanical connection – nylon thread – water – stable current – joule per degree

4) Circle which of the following keywords are associated with the motor working in different situations

Temperature decrease – pulley – windings – insulating box –sketch – circuit – styrofoam – lab notebook – heater – tables – L < Q – time –motor kit – initial temperature – final temperature – wooden support – average current – average voltage – clothes peg – percentage difference – electric wires – lacking heat – container

The following exercise refers to the planning of the experiment shown in the video Where is the heat?: discuss your choice with your mates and your teacher.

5) Circle which of the following sentences are associated with the relationship between heat and work in an electrical motor (project of the work)

Working in different ways – coils of insulated copper wires – missing heat – the batteries are connected in parallel – you have to record the temperature – the electrical work depends on the time – the temperature rises and drops – the motor

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runs freely – you need the mass of the container – draw the circuit – plan some formulas – the motor lifts and drops a container – first you have to measure the heat capacity of the motor

The following exercise refers to the part one of the video Where is the heat?: discuss your choice with your mates and your teacher.

6) Circle which of the following sentences are associated with setting and using equipment and materials to study the relationship between heat and work

Use the ammeter to measure the current flowing in the circuit – Calculate the temperature rise during the time the motor is connected to the batteries– the voltmeter is connected in parallel – measure the electric energy with ammeter and voltmeter – use electric wires for connecting the motor to the supply – use the stopwatch to record the time interval when the current flows through the motor – the motor behaves like an electric heater – Read the full scale range of the thermometer – use the same units for L and Q – arrange a styrofoam box to insulate the thermometer

The following exercise refers to the part one of the video Where is the heat?: discuss your choice with your mates and your teacher.

7) Circle which of the following sentences are associated with the heat capacity measurement

The motor shaft is fixed – the motor behaves like a heater – record the temperature every 10 seconds – electrical work and heat are equal – work and heat are measured separately - record the maximum temperature – the motor is connected to a pulley – connections are made with electric wires – voltmeter has a full scale range of 20 V – you have to calculate the missing heat

The following exercise refers to the part two of the video Where is the heat?: discuss your choice with your mates and your teacher.

8) Circle which of the following sentences are associated with measurement about a motor in neutral

The motor is like a heater – record the voltage every 10 seconds – electrical work and heat are equals – work and heat are measured separately – use the clothes peg with the rubber belt – the full scale range of the ammeter is 10 A – record the time of the temperature rising – record the time the circuit is turned on – use a nylon thread to connect the pulley to the motor – the total time for the temperature rise is more than 1 minute

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where is the heat?

The following exercise refers to the part three of the video Where is the heat?: discuss your choice with your mates and your teacher.

9) Circle which of the following sentencers are associated with measurement about a motor lifting an object

The mass of the container is not necessary – voltmeter in connected in series – the temperature rise needs more time than the batteries work – electrical work equals heat produced – connect the batteries in parallel– the temperature drops – use a peg to prevent turning – use the chronometer to time the circuit

The following exercises refer to the part four of the video Where is the heat?: discuss your choice with your mates and your teacher.

10) Circle which of the following phrases are associated with measurement about a motor lifting and dropping an object

The ratio between work and heat is less than 1 – the ammeter is connected in series – the multimeters full scale range are 10 A – total timing of the circuit is less than 1 minute – there is lack of heat – use the nylon thread to connect the container and the pulley – motor is put into a styrofoam box – disconnect the pulley before the container drops

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Strategies During Conceptual Maps

Copy on your lab notebook the conceptual maps and complete them using the following words. Discuss the meaning with your mates or teacher.

CONCEPTS: the axis; general; its temperature; heat; a battery; potential difference; L = Q; an electrical motor; a particular situation; the heat Q = kΔT

LINKING PHRASES: powered by; has to be verified; producing; flowing through; working for; can run; produced in; hence; warms up because; can lift; behaves like

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Strategies After 15

where is the heat?

Multiple Choice

1) When the heat is measured in joules and the electric charge in amperesecond, the heat per unit chargea. is numerically equal to the unit used to express the potential difference of a

batteryb. is numerically equal to the factor 4.2 J/cal needed to convert calories into joules c. is numerically equal to the voltage across the batteriesd. depends on the amount of charge which has been flowing through the circuit

2) An electric immersion heater can operate from a 12 V automobile battery. It draws an current of 10 A. How long will it take to heat cal? (It is the heat needed to bring to boil enough water to make a cup of tea.)a. About 45 sb. Less than 10 sc. Less than 5 mind. About 13 min

3) A battery supplies 10 V to a heater. The current through the heater is 0.3 A and charge flows through the heater for 60 s. Calculate the heat produced in the heater.a. 0.174 calb. 180 Jc. 756 cald. You need the temperature rise

4) You can calculate the heat capacity of the electrical motor becausea. the motor behaves like a heaterb. It is small enoughc. You can neglect heat dispersiond. It is fixed to a pulley

5) In the experiment of the motor lifting a massa. applied voltage is much smaller than the voltage applied when the axis is

stoppedb. electrical work is more than the needed work when the motor runs in neutralc. heat produced in the motor is less than the work done when the axis is stoppedd. heat produced when the motor lifts a mass is more than the needed work

6) The missing heat is explained by saying thata. the missing heat was transferred to the jerrycan by means of the rubber beltb. the motor is not thermally insulated in a proper wayc. frictions slow down the lifting of the jerrycan by rising its temperatured. some work done by batteries was used to lift the object

7) The missing heat is recovered when the object drops to the ground again. The fact in explained by saying thata. frictions slow down the weight and heat the motorb. the weight, dropping down to the ground, exerts some work to the motorc. the belt transfers to the motor the heat absorbed by the weight during its liftingd. you should consider also the heat capacity of the lifted weight

8) In order to do these experiments you used 4 cells batteries connected in parallel. If you had used only 1 cells battery, voltage and current would be

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Voltage Currenta. equal equalb. equal greaterc. greater greaterd. greater greater

9) Under the same experimental conditions which of the sentences is/are correct?I – When the motor lifts an object, electrical work is greater than the motor works in neutral for the same timeII – When the motor lifts an object, electrical work is quite different as the motor lifts and drops an objectIII – When the object is risen some heat lacks, when the object comes back to the ground the missing heat is recovered

a. I onlyb. II onlyc. I and III onlyd. II and III only

10) A given amount of work can either lift a mass or heat up an object, and we can trade one change for the othera. by means the conservation energy principleb. by heating up the motor lifting the mass againc. by letting a falling mass produce heatd. disconnecting the mass before it falls down again

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Strategies After Matching

Match the words on the left with the correct definition on the right:

1) Voltmeter a) (final temperature) - (initial temperature)

2) Potential difference b) is connected in series

3) Ammeter c) wheel connected to the motor by a rubber belt

4) Current d) heat necessary to rise the temperature of an object of 1° C

5) Electrical work e) is the unit for electric current

6) ampere f) is applied to the motor

7) Heat capacity g) is connected in parallel

8) (charge) x (voltage) x (time) h) equals (heat capacity) x (temperature increase)

9) Heat i) is a power supply

10) Battery j) equals electrical work

11) Motor shaft k) the mean of some current values measured during one of the experiments

12) Pulley l) flows through the motor

13) Temperature increase m) is done by batteries

14) Average current n) rotating axis of the electrical motor

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Strategies After True or False

State if the following sentences are true (T) or false (F).

1) The batteries are connected in parallel to make sure that the voltage and current keep constant during a run

T F

2) A given amount of heat can be used either to lift an object without heating it or to heat an object without moving it

T F

3) In order to verify the relationship L=Q, you have to measure L and Q separately

T F

4) The motor reaches the maximum temperature at the time you turn the circuit off

T F

5) When the motor runs freely all the work is converted into heat T F6) When the motor runs, but its axis is stopped, all the work is

converted into heat T F

7) The heat capacity of the motor equals (specific heat of the motor) x (mass of the motor)

T F

8) In order to study the relationship L=Q you have to proceed in three steps

T F

9) If you stop the motor shaft with a peg, there is not any charge flowing through the coils inside the motor

T F

10) If you stop the motor axis with a peg, the batteries do not do any work

T F

11) You can measure the heat capacity of the motor because, if you stop the motor shaft, L=Q

T F

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Strategies After Cloze

Complete the text.

“In the motor ……………….. [1] electrical work can be used either to lift an object without changing ……………….. [2], or to raise the temperature of a motor without changing ……………….. [3]. Furthermore, we can trade the rise in position of an object for a rise in temperature of the motor. For this reason the same word is used to describe ……………….. [4]: in both cases we say that ……………….. [5] of the object increases. When a body is lifted, its ……………….. [6] increases. When the ……………….. [7] of a body rises, its thermal energy increases. The ……………….. [8] in thermal energy is equal to the ……………….. [9] added to the body. It makes no difference whether the heat flowed in ……………….. [10] or was generated in the body by an ……………….. [11]. We shall ……………….. [12] the changes of both kinds of energy in the same units, mostly in ……………….. [13].”

Physical Science II, Prentice–Hall Inc., New Jersey, 1972, cap. 17, pag. 94

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Strategies After – Flow Chart

How did Stefano manage the experiment with the motor in neutral?

Complete the flow chart using the experimental steps listed below

1. He turned the circuit on starting the motor and the pulley

2. He measured the final temperature

3. He connected the ammeter in series to the motor

4. He started the stopwatch5. He measured the initial

temperature of the motor6. He calculated the percentage

difference between work and heat

7. He waited for the temperature to reach its maximum

8. He connected the 4-cells batteries in parallel

9. He waited 60 s then turned the circuit off making the motor stop

10. He calculated the average current and voltage

11. He measured voltage and current

12. He calculated the heat produced in the motor

13. He calculated the electrical work

14. He connected the voltmeter in parallel to the motor

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Strategies After Think and Discuss

The following activity can be performed in a written or oral form. The teacher will choose the modality, depending on the ability (writing or speaking) that needs to be developed, or the student can choose what he/she prefers. It could be possible to transform the exercise into a game among the students.

1) Write a report of your lab work based on your lab notebook. You have to write the aims of the project work you have carried out, the problem you studied and the phases and steps of the top-down analysis. Present data and results. Do not forget answering the problem.

2) Organize an oral speech about your project work as you had to present it to a science conference. Make some slides to illustrate your speech.

3) Write an article for a scientific review about the project work. You have to write an abstract, an introduction connecting the present research to previous works of yours or to literacy, focusing the aim of the work. Then write about the way the work was developed. Say how data were collected. Provide a conclusion that resumes the ideas and the produced answers.

4) Draw a poster of your project work like the ones used by research groups to highlight in a concise and schematic way the results of your project work.

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Strategies AfterSummary

The project work developed in this unit is based on some fundamental concepts: the definition of electric charge and heat and the equivalence between heat and work. Heat and work were defined in an operative way by means of instruments and procedures to measure them. The equivalence between heat and work was carried out by measuring the heat absorbed by an aluminium cylinder heated by a resistor when the current and the cells number vary.The experiments about the electrical motor carried out in the project work aim at understanding what happens if some amount of electrical work is used to run a motor under different conditions.First of all, you have to determine the heat capacity of the motor because it will be used, in other experiments, as a calorimeter to measure the heat developed inside it in various situations. You can measure it because, when the motor shaft is stopped, the copper insulated coils of the motor through which the current runs behave like a heater, so the relation L = Q is valid.In the following experiments the work done by the batteries to run the motor and the heat developed are measured independently and compared.In the first situation, the motor running in neutral, you found out that the heat produced equals the electrical work, but, if you use the motor to lift a mass, the heat generated is less than the electrical work. The mass slowly resuming its previous position generates the missing heat within the motor.Reasoning about the experimental results you found that the electrical work can be used either to lift an object without varying its temperature or to vary the temperature of the motor without moving it from its position. Therefore, you can trade an increase in the motor temperature with an increase in the height of an object. In both cases you can say that the energy of the object has risen. When an object is lifted you can say that its gravitational potential energy is increased, whereas when its temperature rises you can say that its thermal energy is increased.The increase in the thermal energy of a body equals the heat absorbed by the body either if the heat has entered the body from outside, such as when the water boils on the stove, or has been generated inside the body itself by an electric current such as in the motor.The idea that lifting an object and raising its temperature are two equivalent ideas is a generalization based on the experiments carried out on the motor. Such an idea is confirmed if analogous results are obtained in similar experiments. In the problem solving section some data, collected by students in the same way with the same equipment and procedures, are presented. Data analysis confirms the general ideas expressed up to now in spite of the fact that the data are still a little bit spread for the experimental errors in the measurements due to the approximations or to the not always perfect heat recovering due to poor insulation.You can reduce the measurements errors by designing the equipment better and using better instruments, but they cannot be entirely removed. In one sense, no matter how our measurements are good, you have to make guesses when you extrapolate your results in absence of heat losses towards the environment, or regardless of uncertainties due to approximations and to instrumental sensitivity in measuring temperature, current and so on.Experiments like these were carried out by James Joule (1818-1889). His measurements were not better than yours, but he equally understood that the

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electrical work could produce heat in a motor directly, for example making it run feely, or indirectly making it lift an object and dropping it slowly.

1) Answer the following questions. The questions could be answered in a written or oral form, depending on the teacher’s objectives.

a) Compare the thermal energy rise of 50 g of water heated from 25 °C to 75 °C with the thermal energy decrease in the water when it cools again to 25 °C

b) A hot piece of copper (mass 15 g, specific heat 0.39 Jg-1°C-1, temperature 98 °C) is submerged in a calorimeter containing cold water (mass 50 g, specific heat 4.2 Jg-1°C-1, temperature 25 °C). The equilibrium temperature is 27 °C. Compare the thermal energy variation of the copper with the thermal energy variation of the water. Make the same with the temperature variation.

c) The shafts of two electrical motors are connected together with a rubber belt. A flashlight bulb is connected to the terminals of one of them. When a battery is connected to the terminals of the other motor, the motors run and the bulb lights up. How would you expect the electrical work done by the battery is with respect to the heat produced in the motor to which the bulb is connected?

d) A motor is used to lift a mass 1.5 m and the temperature varies of ΔT. What is the temperature variation you expect if you lift the mass twice? And what if you lift the mass 3 m once?

e) A motor is used to lift an object whose mass is m to a height h and the missing heat is Q. If you use the same motor to lift an object whose mass m’ is less than m to the same height h, how much heat will be missing: more, less o equal? And if the object m was lifted to a greater height h’?

f) Supply a motor with a variable number of cells. Make it run in neutral and measure the current I flowing in the circuit versus the voltage V at the motor terminals. Draw a graph where the x-axis is the voltage and the y-axis is the current and say if the motor which runs in neutral obeys Ohm’s law. Make the same for the motor when the motor shaft is stopped: does the motor obey Ohm’s law?

2) Write a short abstract of the summary (max 150 words) highlighting the main points.

Web References

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Students are invited to visit the websites listed below to widen their knowledge. Some historical readings about the principle of energy conservation are suggested. Reading, filing and summing up the historical memories written by the scientists who founded the concept of energy and overcame the concept of the caloric such as Rumford, Joule, Mayer and Helmoltz is an enriching and rewarding experience.The essays are not easy, because they were written in a time when the concepts of energy and the heat theory were not well understood yet. The students should be aware that the experiment described in these historical papers paved the way to modern thermodynamics. It is up to the teacher to decide on what passages to focus the reflections of the students.The most interesting activities based on historical memories are summarizing, presenting and class discussion to show how the well known concepts of heat, energy, work and energy transformation were introduced and understood in a way sometimes quite different from the approach of the modern physics handbooks.

1. An introductory article about the mechanical equivalent of heat, which was a issue in history of science to understand the energy conservation principlehttp://en.wikipedia.org/wiki/Mechanical_equivalent_of_heat

2. An inquiry concerning the source of heat which is excited by friction, by Benjamin Count of Rumford, Phil. Trans. R. Soc. Lond. 1798, 88, 80-92. This essay suggests the equivalence between heat and mechanical work and was a starting point for some of the experiments carried out by Joule. The first experiment described should be sufficient to understand how Rumford carried out his inquiry and its importance in solving the question about caloric.http://rstl.royalsocietypublishing.org/content/88/80.full.pdf+html

3. On the Caloric Effects of Magneto-Electricity, and on the Mechanical Value of Heat, by J. P. Joule, Philosophical Magazine, 1843, Series 3 23: 263–276, 347–356, 435–443. Joule describes and explains some experiments that are a little bit similar to those carried out on the electrical motor in the video. It is a very important essay on which one of the first statements of the principle of energy conservation is based.http://books.google.it/books?id=uFAwAAAAIAAJ&printsec=frontcover&hl=it#v=onepage&q&f=false

4. On the mechanical equivalent of heat, by J. P. Joule, Philosophical Transactions of the Royal Society of London, 1850, vol. 140, Part 1, pages 61–82. Joule describes his famous equipment and the way he used it to measure the mechanical equivalent of heat j = 4.2 J/cal. What is very interesting is the description of the apparatus and the care employed to carry out measurements and take into account anything that might affect the results. The initial review about the principle of energy conservation is also interesting for the definitive overtaking of the caloric theoryhttp://rstl.royalsocietypublishing.org/content/140/61.full.pdf+html

5. Remarks on the Forces of Inorganic Nature, by J. R. Mayer, Annalen der Chemie und Pharmacie, 1842,vol. 43, page 233 as translated by G. C. Foster, Phil. Mag. [4] 24, 371–377 (1862). This famous paper contains one of the first definition of the principle of energy conservation. Starting from formal considerations about chemical and mechanical equations and then reasoning about the meaning of some words and concepts he could state the principle of energy conservation by arguing philosophicallyhttp://books.google.it/books?id=UmwwAAAAIAAJ&pg=PA371&redir_esc=y#v=onepage&q&f=false

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6. On the Conservation of Force, by H. von Helmoltz. Introduction to a Series of Lectures Delivered at Karlsruhe in the Winter of 1862–1863. Translated by Edmund Atkinson. The author explains energy and its conservation law describing many situations in which many transformations occur. Starting from simple mechanical devices well known at the time, he defines different kinds of energies operatively extending the principle of energy conservation to phenomena involving heat. The caloric theory is also taken into consideration and Joule’s experiments are examined. At the end he explains the heat theory in the way we generally intend it.http://www.bartleby.com/30/125.html

In this amusing site you can find Variations of the 1st Law of Thermodynamics, a lot of different ways to state the first principle of thermodynamics.http://www.humanthermodynamics.com/1st-Law-Variations.html#anchor_112

Conservation of Energy, by R. P. Feynman, in The Feynman lectures on Physics, chap. 4, Addison-Wesley 1963. Also translated and published in R. P. Feynman Six Easy Pieces, Perseus Books, 1995. A masterpiece!

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13

Activities Based on Problem SolvingExperimental results obtained with a motor under different work situations are interesting, but it is better to found an experimental result on studying its reproducibility by repeating the experiments many times in the same manner with the same apparatus in order to improve the statistics and value the measurement uncertainties. A research similar to yours was conducted by two groups with six motors and kits like those of the movie. The experiments were carried out in the same way and the results are in the charts below. In the first chart data are collected to measure the heat capacity of the motor. The second contains data about the motor in neutral, the third data about the motor lifting an object, the last data about the motor lifting and dropping the mass.

Heat capacity of an electrical motor

Team Voltage Current Time Initial T.

Final T.

V A s °C °CG01 2.01 0.69 60 24.2 25.6G02 2.24 0.73 90 24.6 27.3G03 2.47 0.72 90 24.4 26.9G04 2.41 0.68 60 23.9 25.6G05 2.04 0.79 120 25.4 28.7G06 2.43 0.65 90 22.6 24.8G07 2.13 0.68 60 24.4 25.8G08 2.29 0.69 60 24.0 25.6G09 2.47 0.77 60 24.4 26.6G10 2.20 0.79 60 18.8 20.7

Motor in neutral

Team Voltage Current Time Initial T.

Final T.

V A s °C °CG01 5.16 0.24 75 22.6 24.3G02 4.40 0.29 90 23.0 25.2G03 4.75 0.29 60 23.9 25.2G04 4.85 0.20 120 24.0 26.0G05 5.07 0.26 60 23.8 25.3G06 5.49 0.19 50 25.9 26.9G07 5.03 0.21 60 26.5 27.5G08 5.28 0.24 72 26.6 28.2G09 5.65 0.19 60 27.2 28.6G10 5.70 0.24 72 24.0 26.0G11 2.86 0.22 60 28.2 29.0G12 5.50 0.25 60 24.0 25.1

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where is the heat?

The motor lifts an object

Team Voltage Current Time Initial T.

Final T.

V A s °C °CG01 4.48 0.52 30 24.8 25.8G02 4.03 0.43 40 24.8 25.8G03 4.90 0.51 30 20.4 21.1G04 3.74 0.32 45 25.5 26.2G05 4.96 0.47 30 21.5 22.3G06 3.97 0.51 45 22.2 23.3G07 4.76 0.59 25 26.8 27.4G08 4.80 0.54 25 25.8 26.4G09 5.48 0.50 22 24.9 25.7G10 5.20 0.57 29 27.0 27.8G11 4.49 0.53 26 25.4 26.3G12 5.12 0.42 20 26.6 27.2

The motor lifts and drops an object

Team Voltage Current Time Initial T.

Final T.

V A s °C °CG01 4.75 0.50 36 22.8 24.3G02 4.77 0.51 35 22.3 23.6G03 4.57 0.58 35 20.6 22.4G04 4.69 0.50 25 24.3 25.3G05 5.35 0.45 23 26.4 27.4G06 4.88 0.58 23 24.6 26.0G07 4.94 0.52 20 25.0 26.0G08 4.96 0.53 25 26.0 27.2G09 5.00 0.50 29 25.0 26.4G10 5.44 0.50 25 24.6 25.7G11 5.31 0.49 23 27.0 28.1G12 5.44 0.50 20 24.0 25.0

Problem no.1 – data pocessing: heat capacity of the motorsProcess the data in the first chart, you may use a spreadsheet or share the job with your mates. In particular:

• evaluate the uncertainty of direct measurement of current and voltage know-ing that data sheets of instrumentation show that, for a full scale range of 20 V, data are affected by an uncertainty of ±(0.5% + 1) and, for a full scale range of 10 A by an uncertainty of ±(2% + 5)

• use the data to determine the average heat capacity of the motors• has the running time of the motor any influence on the obtained results? • determine the experimental uncertainty of the mean heat capacity or the root

mean square of the average• compare the goodness of your statistical result with that of a single datum of

heat capacity (for example that found using the data given in the movie)

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where is the heat?

Problem no.2 – equivalence between work and heat: analysis of repeated experimentsProcess the data of the charts about the three experiments about a motor working under different conditions, you may use a spreadsheet or share the job with your mates. In particular:

• calculate the electrical work L done by the batteries, the heat Q generated in-side the motor and the ratio L/Q using the measured heat capacity

• draw a graph of the heat Q versus the work L and draw the line Q = L (use The same units for both axes)

• what could have happened to team G11 doing the experiment with the motor in neutral? Are the obtained results different from the others?

• do the results depend on the working time of the motor?• discuss charts and graph prepared comparing these results with those ob-

tained in the movie with your mates .

Problem no.3 – work done to run the motorThe data of the current in the experiment with the motor in neutral are less than the data in the other experiments.

• Explain this fact connecting the data and the experimental observations. • If you let the motor run freely for a time equal to the time spent by the motor

lifting the mass, how do the data modify in the work-heat graph?

Problem no.4 – verify the theoriesFour lab teams have done some experiments with the same equipment so that the running time would be more or less the same in each experiment.

• Process the data like before and verify that the results are consistent with those found previously (eventually put them in the graph with the others)

• Can you say that the motor heats up less when it lifts a mass than when it works freely?

• What is the meaning of the sentence “the heat is missing when the motor lifts an object”?

In order to answer, observe the values of the voltage and current under the different situations and the electrical work done by the batteries. Write your observations in a concise way showing the situation and explaining your conclusions. Compare your job with your mates and organize your finds in one shared text.

Motor in neutral

Team Voltage Current Time Initial T.

Final T.

V A s °C °CG01 5.11 0.36 42 20.0 21.4G02 4.89 0.26 51 20.4 21.6G03 5.10 0.33 50 20.2 21.7G04 4.98 0.22 33 21.0 21.6

The motor lifts an object

Team Voltage Current Time Initial T.

Final T.

V A s °C °CG01 5.12 0.97 45 22.0 25.0

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where is the heat?

G02 4.82 0.90 53 20.0 23.1G03 5.03 0.88 53 22.7 25.6G04 4.94 1.09 36 20.0 22.5

The motor lifts and drops an object

Team Voltage Current Time Initial T.

Final T.

V A s °C °CG01 5.08 0.96 48 21.6 25.5G02 4.79 0.88 51 22.6 26.0G03 5.05 0.85 55 21.4 25.2G04 4.91 1.03 39 20.6 24.1

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where is the heat?

Answer Sheets

Keywords:

1) To measure – heat produced – electrical work – electrical motor – three steps – electrical motor in neutral – heat capacity

2) Electrical motor – insulating box – chronometer – thermometer – 4-cells batteries – wires – belt drive

3) Axis – heater – copper wires – equals – electric connections – stable current – joule per degree

4) Pulley – sketch – circuit – lab-notebook – tables – time – initial temperature – final temperature – average current – average voltage – percentage difference – lacking heat – container

Sentences:

1) Working in different ways – the batteries are connected in parallel – you have to record the temperature – the motor runs freely –draw the circuit –the motor lifts and drops a container – first you have to measure the heat capacity of the motor

2) Use the ammeter to measure the current flowing in the circuit – the voltmeter is connected in parallel – use electric wires for connecting the motor to the supply – use the stopwatch to record the time interval the current flow through the motor – Read the full scale range of the thermometer

3) The motor shaft is fixed – the motor behaves like a heater – electrical work and heat are equal – record the maximum temperature – connections between batteries are made with electric wires – voltmeter has a full scale rang of 20 V

4) Record the voltage every 10 seconds – work and heat are measured separately – the full scale range of the ammeter is 10 A – record the time the circuit is turned on – the total time for the temperature rise is more than 1 minute

5) The mass of the container is not necessary – temperature rise needs more time than the batteries work – connect the batteries in parallel – use the chronometer for timing the circuit

6) The ammeter is connected in series – total timing of the circuit is less than 1 minute – use the nylon thread to connect the container and the pulley – motor is put into a styrofoam box

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where is the heat?

Conceptual Maps

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where is the heat?

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where is the heat?

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where is the heat?

Multiple Choice:

1c, 2d, 3b, 4a, 5b, 6d, 7b, 8a, 9c, 10c

Matching:

1g, 2f, 3b, 4l, 5m, 6e, 7d, 8j, 9h, 10i, 11n, 12c, 13a, 14k

True or False:

1 T, 2 T, 3 T, 4 F, 5 T, 6 T, 7 F, 8 T, 9 F, 10 F, 11 T

Cloze:

[1] experiments, [2] the object’s temperature, [3] the motor’s position, [4] the two changes, [5] the energy, [6] gravitational potential energy [7] temperature, [8] increase, [9] quantity of heat, [10] from the outside, [11] electric current, [12] measure, [13] joule

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where is the heat?

Flow Chart:

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Start

He connected the 4-cells batteries in parallel

He connected the ammeter in series to the motor

He connected the voltmeter in parallel to the motor

He startedthe stopwatch

He turned the circuit on startingthe motor and the pulley

He calculated the average current and voltage

He waited 60 s then turned thecircuit off making the motor stop

He waited for the temperature to reach its maximum

He measured the initialtemperature of the motor

He measured voltageand current

He measured thefinal temperature

He calculatedthe electrical work

He calculated the heatproduced in the motor

He calculated the percentagedifference between work and heat

End

where is the heat?

Materiale sviluppato da eniscuola nell’ambito del protocollo d’intesa con il MIUR

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