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2012. május 17 Azonosító jel: FIZIKA ANGOL NYELVEN EMELT SZINTŰ ÍRÁSBELI VIZSGA 2012. május 17 8:00 ÉRETTSÉGI VIZSGA Az írásbeli vizsga időtartama: 240 perc Fizika angol nyelven Pótlapok száma Tisztázati Piszkozati NEMZETI ERŐFORRÁS MINISZTÉRIUM emelt szint írásbeli vizsga 1112 Fizika angol nyelven emelt szint Azonosító jel: Instructions for the examinee The time allowed for the examination is 240 minutes. Read the instructions for the problems very carefully and use your time wisely. You may solve the problems in arbitrary order. Allowable materials: pocket calculator, data tables Should the space provided for the solution of a problem be insufficient, ask for an extra sheet. Please indicate the number of the problem on the extra sheet. írásbeli vizsga 1112 2 / 16 2012. május 17 Fizika angol nyelven emelt szint Azonosító jel: PART ONE Precisely one of the possible solutions for each of the following questions is correct. Write

the letter corresponding to the answer you think is correct in the white square on the right. You may write calculations or draw figures on this problem sheet if necessary. 1. The acceleration of a body at a given moment points east Can its velocity at the same moment point south? A) B) C) D) No, its velocity can only point east. No, its velocity can only point west or east. Yes, its velocity can point south but it may not point north. Yes, its velocity can point in any direction. 2 points 2. How does the capacitance of a parallel-plate capacitor change, if the full thickness of the gap between its plates is filled by an iron slab? A) B) C) D) It is reduced approximately by half. It is approximately doubled. Its capacitance is reduced to zero. Its capacitance does not change. 2 points 3. What would happen, if we would shrink the Sun to a thousandth of its original size while maintaining its original mass? A) B) C) Earth and the rest of the planets would continue their motion

along their orbits. Earth and the rest of the planets would plunge towards the Sun. Earth and the rest of the planets would escape. 2 points írásbeli vizsga 1112 3 / 16 2012. május 17 Fizika angol nyelven emelt szint Azonosító jel: 4. We hang a pulley, pass a rope over it and place identical weights on both ends of the rope, two on each side. We let go of the weights and measure the tension force in the rope supporting the pulley. We then move a weight from one side to the other one and let the system go. How does the tension in the rope supporting the pulley change? A) B) C) The tension in the rope increases. The tension in the rope does not change. The tension in the rope decreases. 2 points 5. In container A we have 10 liters of 0 oC water, while in container B we have 10 liters of 100 oC water. Using a small cup we remove some water from container A, and then replace the missing quantity using water from container B. We repeat the process until the A B hot water

in container B is completely exhausted. What will the temperature of the hot water cold water water in container A be at this point? A) B) C) It will be colder than 50 oC. It will be precisely 50 oC. It will be warmer than 50 oC. 2 points 6. We change the current of a solenoid at a uniform rate of 1 A/s When is the voltage induced in the solenoid greater? A) B) C) D) While the strength of the current increases from zero to 1 A. While the strength of the current increases from 1 A to 2 A. The voltage induced in the solenoid is the same in the above two cases. The information at hand is not sufficient to resolve the question. 2 points írásbeli vizsga 1112 4 / 16 2012. május 17 Fizika angol nyelven emelt szint Azonosító jel: 7. The Guiness record for long-distance egg throwing is over 98 meters The fresh egg must be caught on arrival of course, it must not break. What could be the key to achieving such a record? A) B) C) The egg should be thrown spinning, because it

is much easier to catch a spinning egg. The egg should be slowed down gradually over the longest possible path when catching it. The egg should be thrown at a very sharp angle (almost horizontally), so it does not drop from a great height. 2 points 8. The 235U isotope is radioactive, ie it decays spontaneously – yet it can still be found naturally. What is the reason for that? A) B) C) Its half-life is very long, so the time that elapsed since it was created was not sufficient for all of it to decay. It is continuously being created by cosmic radiation in the upper atmosphere. It was scattered in great quantities by nuclear tests in the 50-s, that is what can still be found in nature today. 2 points p 9. An enclosed gas is taken twice through the cyclic process shown on the figure. From the same initial state, it is taken through the process in one direction first, then in the other direction. What is the difference between the two processes? 1. V A) B) C) At the end of one

process, the temperature of the gas will be higher than the initial temperature, at the end of the other it will be lower. During the course of one process, more energy is transferred by heat to the gas than from the gas, whereas in the other process more energy is transferred by heat from the gas than to the gas. There is no difference between the two processes. 2 points írásbeli vizsga 1112 5 / 16 2012. május 17 Fizika angol nyelven emelt szint Azonosító jel: 10. We fix two positive point charges q of magnitude Q and 2Q on the two 2Q Q ends of a section. Then we first try to place a positive q charge somewhere on the section so that it is in equilibrium. After that (removing the q charge) we try to place a -q charge on the section such that it is also in equilibrium. What can we say about the two equilibriums? A) B) C) D) The two equilibriums are at the same position. The two equilibriums are not at the same position. Only the q charge can be placed so that it is in

equilibrium. Only the -q charge can be placed so that it is in equilibrium. 2 points 11. A thick concrete column of height h and mass m falls over. How much does its potential energy change compared to its initial state after it comes to rest on the ground? A) B) C) ΔΕ < mgh/2 ΔΕ = mgh/2 ΔΕ > mgh/2 2 points 12. A point charge is moving in vacuum in a homogeneous magnetic field in a plane perpendicular to the lines of magnetic induction. Which quantity will be constant? A) B) C) D) The vector of velocity. The vector of acceleration. Both quantities will be constant. Neither of the two will be constant. 2 points írásbeli vizsga 1112 6 / 16 2012. május 17 Fizika angol nyelven emelt szint Azonosító jel: 13. What does an anti-hydrogen atom consist of? A) B) C) D) A proton and an electron. A proton and a positron. An antiproton and an electron. An antiproton and a positron. 2 points p 14. What kind of process does the arrow on the adjacent p – V diagram

depict? V A) B) C) An adiabatic process. An isothermal process. Neither one of the two. 2 points 15. What does the de Broglie wavelength of an atom depend on? A) B) C) On the type of the atom – each atom has a set of characteristic de Broglie wavelengths, which can be found in its emission spectrum. On its momentum – the de Broglie wavelength of an atom decreases if its speed or mass increases. On its mass – the heavier an atom is, the greater is its de Broglie wavelength. 2 points írásbeli vizsga 1112 7 / 16 2012. május 17 Fizika angol nyelven emelt szint Azonosító jel: PART TWO Choose one of the three topics below and write a coherent, 1.5-2 page long essay about it Make sure that the phrasing is accurate and clear, the train of thought is logical and pay attention to the spelling, as this will also affect the evaluation. You do not necessarily have to formulate your thoughts in the exact order of the aspects given. The essay may be written on the following

pages. The quantum hypothesis and the photoelectric effect My futile experiments to somehow reconcile the quantum of action with classical theory lasted several years and required a lot of effort. Some of my colleagues saw something of a tragedy in this. My opinion is different For me, the gain I obtained from the thorough exploration was more valuable. I now knew that the role played by the quantum of action in physics is more significant then I tended to assume at first. Max Planck Planck and Einstein Review the hypothesis of the quantization of light, and the role of Planck and Einstein in the creation and the verification of the hypothesis. Present the photoelectric effect and, sketching a specific experimental arrangement, explain how experimental evidence supports the hypothesis of the quantization of light. Write down the basic equation for the photoelectric effect, name and explain the physical quantities that appear in it. Write at least two areas of application for the

photoelectric effect. írásbeli vizsga 1112 8 / 16 2012. május 17 Fizika angol nyelven emelt szint Azonosító jel: Generator and motor When I created the apparatus for electric rotations discussed previously before the years 1827 and 1828 with good results, no similar conceptions could be found or read in the journals or works available to me. Because of these circumstances, it was my opinion that I am the inventor of the electric apparatus described and its method of application. Jedlik Ányos The electric motor of Jedlik Ányos. Explain how a generator creates electric current via doing mechanical work. Sketch a drawing of the system design and explain the theoretical background along with role of Lenzs law. Mention an application for the generator. Explain the functioning of a type of electric motor of your choice. Present the physical laws and interactions that are required to understand its functioning. In the course of your explanation, sketch a drawing that

illustrates the motors functioning and mention an application for the electric motor. The whistle sounds The whistle is a cylindrical tube closed at the top end and open at the bottom end and is made of wood, bone or glass. It has a sharp-edged opening for the mouth under its closed end and has several smaller sideholes along it. If the air is blown towards the sharp edge of the opening for the mouth in an oblique direction, while the side-holes are all closed, the oscillation with a node at its middle that is generated is the lowest sound for the whistle. Schirkhuber Móricz: Elméleti és tapasztalati természettan alaprajza (1851) Review the concept of standing waves and how they are created. Review the most important physical properties of the sound created in a whistle, their relationship, the type of wave created and the factors affecting the pitch of the sound. Explain the properties of the sound created in an open whistle and in a closed whistle, the relationship between the

wavelength and the length of the whistle. Explain the role of the harmonics in the forming of the sound of the whistle. írásbeli vizsga 1112 9 / 16 Total Presentation 18 points 5 points 2012. május 17 Fizika angol nyelven emelt szint Azonosító jel: PART THREE Solve the following problems. Justify your statements using calculations, diagrams or explanations, depending on the nature of the questions. Make sure that the notations you use are unambiguous. 1. A hard disk used in computers nowadays consists of one or more platters rotating at a high speed and a reading head that moves close to the surface of the platter. The data is contained on the platter in tiny magnetic grains; the head interprets the alignment of the tiny magnets as a bit of information, a “1” or a “0”. The machinery of the drive moves the head in a radial direction and the bits at the current radius are read by the head sequentially as they pass before it because of the rotation of the

platter. In a particular type of hard disk, the distance between two tiny magnetic grains both representing a bit is about 30 nm. a) b) c) What is the maximum rate at which the head may possibly be able to read data from the outermost edge of the platter of a hard disk, whose platter diameter is 3.5” (inch) and speed of rotation is 7200 RPM (rounds per minute)? (1 inch = 2.54 cm, the rate for reading data is usually given in Gbit/s nowadays.) What maximum rate may be attained for reading data which are located at a distance of 3 cm from the center of rotation? Approximately how many Gbytes of information may the disk be able to store, if the data is located between a distance of 1 cm and 4.5 cm from the center of rotation on the platter and one byte is composed of eight bits? a) b) c) Total 6 points 2 points 3 points 11 points írásbeli vizsga 1112 10 / 16 2012. május 17 Fizika angol nyelven emelt szint Azonosító jel: 2. A car battery is composed of six identical

cells connected in series The open circuit voltage (electromotive force) of the battery is 13.2 V When the load on the battery is 54 W, the terminal voltage decreases to 10.8 V What is the internal resistance of a single cell? What is short-circuit current of the battery? Total 11 points írásbeli vizsga 1112 11 / 16 2012. május 17 Fizika angol nyelven emelt szint Azonosító jel: 3. We fill a V=200 dm3 container, whose walls are thin, with helium gas of temperature t0= -123 ºC. There is a safety valve on the side of the container. This is basically a small hole with an area of A=5 cm2, onto which a small plate is pressed by a spring. The force in the spring is F=25 N The N initial pressure of the gas is p0 = 10 . The cm 2 temperature of the gas slowly increases to that of its environment t1=27 ºC. J ) ( R = 8300 K ⋅ kmol a) b) c) What is the mass of the helium gas enclosed in the container initially? What is the temperature of the gas when the safety valve opens?

What is the mass of the helium gas enclosed in the container when the temperature reaches that of the environment? a) b) c) Total 3 points 6 points 4 points 13 points írásbeli vizsga 1112 12 / 16 2012. május 17 Fizika angol nyelven emelt szint Azonosító jel: 4. We are looking at a point-like light source which is located at a distance of 2 meters from us and radiates light in all directions evenly. The power of the light source is 10 W, the wavelength of the emitted light is λ = 450 nm. Approximately how many photons pass through our pupil in a second, if the diameter of our pupil at the time of the observation is 4 mm? m c = 3 ⋅108 , h = 6.62 ⋅10 −34 Js s Total 12 points írásbeli vizsga 1112 13 / 16 2012. május 17 Fizika angol nyelven emelt szint írásbeli vizsga 1112 Azonosító jel: 14 / 16 2012. május 17 Fizika angol nyelven emelt szint írásbeli vizsga 1112 Azonosító jel: 15 / 16 2012. május 17 Fizika angol nyelven

emelt szint Azonosító jel: To be filled out by the examiner evaluating the paper! maximum score I. Multiple choice questions II. Essay: content II. Essay: presentation III. Complex problems Total score for the written exam score attained 30 18 5 47 100 examiner Date: . Score attained rounded to the nearest integer (elért pontszám egész számra kerekítve) Integer score entered in the program (programba beírt egész pontszám) I. Multiple choice questions (Feleletválasztós kérdéssor) II. Essay: content (Esszé: tartalom) II. Essay: presentation (Esszé: kifejtés módja) III. Complex problems (Összetett feladatok) examiner (javító tanár) notary (jegyző) Date (Dátum): . Date (Dátum): írásbeli vizsga 1112 16 / 16 2012. május 17 ÉRETTSÉGI VIZSGA 2012. május 17 Fizika angol nyelven emelt szint Javítási-értékelési útmutató 1112 FIZIKA ANGOL NYELVEN EMELT

SZINTŰ ÍRÁSBELI ÉRETTSÉGI VIZSGA JAVÍTÁSI-ÉRTÉKELÉSI ÚTMUTATÓ NEMZETI ERŐFORRÁS MINISZTÉRIUM Fizika angol nyelven emelt szint Javítási-értékelési útmutató The examination papers should be evaluated and graded clearly, according to the instructions of the evaluation guide. Markings should be in red ink, using the conventional notations. PART ONE For the multiple choice questions, the two points may only be awarded for the correct answer given in the evaluation guide. The score (0 or 2) should be entered in the table next to the question as well as the table for total scores at the end of the exam paper. PART TWO The examinee should present the answers to the questions in a continuous text in whole sentences, so sketchy outlines are not to be evaluated. The only exception is any explanatory text or label of a drawing. Scores for facts or information mentioned in the evaluation guide may only be awarded if the examinee explains it in proper context. Partial

scores must be written on the margin with indication as to which item of the evaluation guide is the basis of the evaluation. The evaluated statement in the text must be ticked The scores must also be entered in the table following the questions of the second part. PART THREE The sentences printed in italics in the evaluation guide define the steps necessary for the solution. The scores indicated here may be awarded if the action or operation described by the text in italics can be clearly identified in the work of the examinee and is basically correct. Wherever the action can be broken down into smaller steps, partial scores are indicated beside each line of the expected solution. The „expected solution” is not necessarily complete; its purpose is to indicate the length and nature of the expected solution, and the depth of detail required of the examinee when writing the solution. Comments in brackets that follow provide further guidance on the evaluation of possible errors,

differences or incomplete answers. Correct answers that differ from the reasoning of the one (ones) given in the evaluation guide are also acceptable. The lines in italics provide guidance in allocating scores, eg how much of the full score may be awarded for correct interpretation of the question, for writing down relationships, for calculations, etc. Should the examinee combine some steps, or carry on calculations algebraically, he/she may skip the calculation of intermediate results shown in the evaluation guide. If these intermediate results are not being explicitly asked for in the problem, the scores indicated for them can be awarded if the reasoning is otherwise correct. The purpose of indicating scores for intermediate results is to make the evaluation of incomplete solutions easier. For errors that do not affect the correctness of reasoning (miscalculations, clerical errors, conversion errors, etc.) deduce points only once Should the examinee write more than one solutions, or

display multiple attempts at solving the problem, and does not indicate clearly which one of those he/she considers the final version, the last one should be evaluated (i.e the one at the bottom of the page if there is nothing to indicate otherwise). If the solution contains a mixture of two different trains of thought, the elements of only one of them should be evaluated: that one which is more favorable for the examinee. The lack of units during calculation should not be considered a mistake – unless it causes an error. However, the results questioned by the problem are acceptable only with proper units. írásbeli vizsga 1112 2 / 10 2012. május 17 Fizika angol nyelven emelt szint Javítási-értékelési útmutató PART ONE 1. D 2. C 3. A 4. C 5. C 6. C 7. B 8. A 9. B 10. A 11. A 12. D 13. D 14. C 15. B Award 2 points for each correct answer. Total: 30 points. írásbeli vizsga 1112 3 / 10 2012. május 17 Fizika angol nyelven emelt szint

Javítási-értékelési útmutató PART TWO Each of the scores may be divided in all three topics. 1. The quantum hypothesis and the photoelectric effect Reviewing the content and the creation of the quantum hypothesis: 6 points Light is composed of portions or quanta of energy. (1 point) The energy of a photon is proportional to the frequency of light. (1 point) Writing down the relationship. (1 point) Planck formulated the hypothesis of the quantization of energy. (1 point) Einstein applied it to light (1 point) and confirmed it for the photoelectric effect (1 point). Explaining the photoelectric effect: 6 points Delineating the effect. (1 point) A possible experimental setup. (1 point) The relationship between the change in frequency and the emission of electrons. (1 point) The relationship between the intensity of light (the power of the light source) and the emission of electrons. (1 point) Summarizing and interpreting the observations. (2 points) The basic equation for the

photoelectric effect: 4 points Writing down the equation. (1 point) The concept of the work function. (2 points) The velocity of the emitted electrons. (1 point) Mentioning applications: 2 points 1 point for each application. Total: 18 points írásbeli vizsga 1112 4 / 10 2012. május 17 Fizika angol nyelven emelt szint Javítási-értékelési útmutató 2. Generator and motor Explaining how the generator creates electric current: 10 points The correct indication of the magnetic field on the sketch. (1 point) Indicating the rotating frame (coil) on the sketch. (1 point) Indicating the Lorentz force acting on the charges of the conducting frame. (2 points) (2 points may only be awarded if the examinee indicates the Lorentz force at several different sections on the frame, at different locations in the magnetic field.) Stating the direction of the induced current correctly. (1 point) (The 3 points due for the two previous steps may also be awarded if the examinee justifies

the creation of current with the changing of the magnetic flux through the frame instead of the charge separation induced by the Lorentz force and states the direction of the current correctly.) Formulating Lenzs law. (1 point) Applying it to the current situation. (1 point) Analyzing its manifestation in the case of the generator. (2 points) The induced current is such that the secondary Lorentz force acting on it in the magnetic field hampers the rotation of the coil. Or the interaction between the magnetic field of the induced current and the external magnetic field hampers rotation. An example for an application. (1 point) Reviewing how the electric motor works: 8 points A sketch showing the functioning of a type of electric motor. (2 points) Stating the direction of the current. (1 point) Indicating the forces that create rotation. (2 points) Explaining how a persistent rotation is sustained. (2 points) Presenting an application. (1 point) Total: 18 points írásbeli vizsga 1112

5 / 10 2012. május 17 Fizika angol nyelven emelt szint Javítási-értékelési útmutató 3. The whistle sounds Explaining the concept of the standing wave: 2 points The explanation must contain a mentioning of nodes and antinodes. (A drawing is also acceptable for an explanation; illustration with a transversal wave is of full value.) Creation of standing waves: 2 points The sound created in a whistle: 7 points The concepts of frequency, speed of propagation and wavelength, and defining the relationship between them (1+1+1+1 points) Mentioning the longitudinal nature of sound waves (1 point) The relationship between the pitch of the sound and the frequency (2 points) Introducing the open and the closed whistle: 4 points Presenting an open whistle and defining nodes, antinodes and wavelength of the sound created in it. (2 points) Presenting a closed whistle and defining nodes, antinodes and wavelength of the sound created in it. (2 points) Stating he role of harmonics: 3

points The sound of the whistle contains a number of harmonics in addition to the fundamental frequency. These create the characteristic sound of the whistle together (The detailed analysis of the nature of the harmonics is not necessary.) Total: 18 points Evaluation of the style of the expression for all three topics based on the exam description: Lingual correctness: 0–1–2 points • The text contains accurate, comprehensible, well structured sentences; • there are no errors in the spelling of technical terms, names and notations. The text as a whole: 0–1–2–3 points • The review is a cohesive, unified whole; • individual parts, subtopics relate to each other along a clear, comprehensible train of thought. If the review is no more than 100 words in length, no points may be awarded for the style of expression. If the examinees choice of topic is ambiguous, the style of expression of the last one written down should be evaluated. írásbeli vizsga 1112 6 / 10 2012.

május 17 Fizika angol nyelven emelt szint Javítási-értékelési útmutató PART THREE Problem 1 Data: f1 = 7200 RPM, d = 30 nm/bit, D1 = 3.5”, R2 = 3 cm, R3 = 10 – 445 cm a) Realizing that at a given radius on the platter, the tangential velocity and the distance between two grains are the two factors that define the maximum rate at which data can be read: 2 points As the magnetic grains on the platter pass before the head one after another because of the platters rotation, the maximum possible rate at which data may be read is given by the ratio of the tangential velocity belonging to the given radius on the platter and the d v distance between two grains: η = R (If the examinee does not write this recognition d down, but later carries on calculations according to this formula, the two points should be awarded.) Calculating the radius and tangential velocity belonging to the outermost part of the platter: 1 + 2 points As D1 = 3.5" = 89 cm so R1 =445 cm (1 point)

1 m v R = R ⋅ ω = R ⋅ f ⋅ 2π = 4.45 cm ⋅ 7200 RPM ⋅ 2π = 445 cm ⋅ 120 ⋅ 2π = 336 (2 points) s s Calculating the maximum possible rate of reading data: 1 point vR Gbit The rate of reading data: η1 = = 1.12 . d s b) Calculating the rate of reading data in the second case: 2 points (may be divided) As the rate of reading data is proportional to the tangential velocity, which is, in turn, proportional to the radius, the quantity we seek may be calculated from the previous data reading rate using the ratio of radii, or by using the new tangential velocity: R Gbit or η 2 = η1 ⋅ 2 = 0.75 s R1 v 1 m Gbit v R = R2 ⋅ ω = 3 cm ⋅ 120 ⋅ 2π = 22.4 and η 2 = R = 0.75 s s s d c) Calculating the amount of data that may be stored: 3 points (may be divided) As the approximate distance between grains that store one bit is 30 nm, the “space” required for one bit is Abit = d 2 = 900 nm 2 = 9 ⋅10 −16 m 2 (1 point). írásbeli vizsga 1112 7 / 10 2012. május 17

Fizika angol nyelven emelt szint Javítási-értékelési útmutató The effective area of the platter (between the radii 1.0 cm and 445 cm): Aplatter = (4.45) 2 cm 2 ⋅ π − 10 cm 2 ⋅ π = 59 cm 2 ≈ 6 ⋅10 −3 m 2 (1 point) From which the number of bytes that may reside on the platter: C platter = Aplatter = 838 Gbyte . (1 point) 8 ⋅ Abit If it is known to the examinee that in computer science 1 Gbyte is not simply 109 bytes, but rather (1024)3 bytes, the result for the capacity of the disk will be 780 Gbyte, so this value must also be accepted. Total: 11 points Problem 2 Data: U0 =13.2 V, P = 54 W, U1 = 108 V Formulating and calculating the current of the battery under load: 3 points (may be divided) As the power of the battery is P = I ⋅ U1 (1 point), P = 5 A (transforming and calculation 1 + 1 points). so I = U1 Determining the voltage drop on the total internal resistance of the battery: 1 point U internal = U 0 − U1 = 2.4 V Formulating and calculating the

total internal resistance of the battery: 2 points U internal Ri = = 0.48 Ω I Recognizing that with cells connected in series the total internal resistance of the battery is equal to the sum the internal resistances of all six cells: 2 points (Should the examinee fail to write down this recognition, but carries on with calculations in accordance with it, the two points are to be awarded. The recognition may also be expressed with a schematic drawing of the battery, provided that all six cells connected in series are drawn with the internal resistance indicated separately for each cell.) Calculating the internal resistance for one cell: 1 point U internal = 0.48 Ω ⇒ Ri = 008 Ω I Formulating and calculating the short-circuit current for the battery: 6 ⋅ Ri = 1 + 1 points I short U = 0 = 27.5 A Ri Total: 11 points írásbeli vizsga 1112 8 / 10 2012. május 17 Fizika angol nyelven emelt szint Javítási-értékelési útmutató Problem 3 Data: V = 200 dm3 , t0 = -123

ºC, t1 = 27 ºC, A = 5 cm2 , F = 25 N, p0 = 10 R = 8300 N , cm 2 J kg , M =4 . K ⋅ kmol kmol a) Formulating and calculating the mass of the helium gas filled into the container: 3 points (may be divided) m p ⋅V ⋅ M ⋅ R ⋅T ⇒ m = from which m = 64 g. (Writing down the ideal gas law M R ⋅T 1 point, substituting the corresponding data into it 1 point, calculation of the mass in question 1 point.) p ⋅V = b) Formulating and calculating the pressure at which the safety valve opens: 3 points (may be divided) The valve opens when the force on the plate from the inside just exceeds the sum of the forces due to outside atmospheric pressure and the spring. A ⋅ pmax = A ⋅ p0 + F (2 points) F N The pressure of the gas in the container is then pmax = p0 + = 15 . (1 point) A cm 2 Formulating and calculating the temperature in question: 3 points (may be divided) Because the volume does not change during the process, Gay-Lussacs law is p ⋅T p p applicable: 0 = max (1

point), from which T = max 0 = 225 K i.e t’= -48 ºC p0 T0 T (transformation and calculation 1 + 1 point). (The temperature in question need not be transformed to degrees Celsius, if the temperature given in Kelvin is correct, full points are to be awarded.) c) Recognizing that heating the gas further does not increase the pressure any more, because some of the gas continuously escapes through the safety valve: 2 points If the examinee does not write this recognition down, but expresses it with a formula somewhere (e.g p final = pmax or using pmax later as the final pressure in the calculation), the two points are to be awarded. Formulating and calculating the mass of the helium gas remaining in the container: 1 + 1 point As the final pressure of the gas in the container is pmax at the end of the temperature m change pmax ⋅ V = 1 ⋅ R ⋅ T1 ⇒ m1 = 48 g. M Should the examinee use the outside pressure as the final pressure of the enclosed gas (saying that the valve has

“opened”), at most two points may be awarded for question c). Total: 13 points írásbeli vizsga 1112 9 / 10 2012. május 17 Fizika angol nyelven emelt szint Javítási-értékelési útmutató Problem 4 m , h = 6.62 ⋅10 −34 Js s Determining the number of photons emitted by the light source in a second: 6 points (may be divided) The power of the light source is equal to the product of the number of photons emitted in a second and the photon energy: P = N ⋅ E (2 points). h⋅c = 4.4 ⋅10-19 J (formulation and calculation, The energy of one photon E = Data: P = 10 W, λ = 450 nm, d = 4 mm, R = 2 m, c = 3 ⋅108 1 + 1 points), λ P 1 = 2.27 ⋅1019 E s (formulation and calculation, 1 + 1 point). Calculating the photon energy is not essential P Should the examinee write the expression for the photon energy directly into the N = E formula and the final result is correct, full points are to be awarded. However, if the expression for the photon energy does not appear

somewhere explicitly, only four points are to be awarded for this question even if the final answer is correct. From which the number of photons emitted in a second: N = Determining the number of photons passing through our pupil in a second: 6 points (may be divided) The number of photons passing through our pupil in a second is that part of the full photon number, which leaves the light source in the direction of our pupil. That is, the product of the full photon number and the ratio of the area of our pupil and the surface area of a full sphere with a radius of 2 meters: Apupil N= N (3 points). Asphere 2 ⎛d ⎞ The area of the pupil: Apupil = ⎜ ⎟ ⋅ π = 12.6 ⋅10 −6 m 2 (1 point) ⎝2⎠ The area of the spheres surface: Asphere = 4 ⋅ R 2 ⋅ π = 50.3 m 2 (1 point) 1 (1 point). s (The numerical calculation of the areas is not necessary. Should the examinee use the formal expressions and the final result is correct, full points are to be awarded.) II. solution: The

problem may also be solved in a reverse order. The examinee may first calculate the power of the light passing through the pupil using the quotient of the areas, and then calculate the corresponding photon number. A In this case P = P pupil = 2.5 ⋅10 −6 W (6 points overall, which may be divided in the Asphere same manner as in the previous case), 1 P and N = = 5.68 ⋅1012 (6 points overall, which may be divided in the same manner as s E Total: 12 points in the previous case). The photon number in question is therefore: N = 5.68 ⋅1012 írásbeli vizsga 1112 10 / 10 2012. május 17