New test - April 20, 2017 [274 marks]

Transcription

1 New test - April 20, 2017 [274 marks] The following data are available for a natural gas power station that has a high efficiency. Rate of consumption of natural gas = 14.6 kg s 1 Specific energy of natural gas = 55.5 MJ kg 1 Efficiency of electrical power generation = 59.0 % Mass of CO 2 generated per kg of natural gas = 2.75 kg One year = s 1a. Calculate, with a suitable unit, the electrical power output of the power station. [1 mark] « » = W A unit is required for this mark. Allow use of J s 1. No sf penalty. 1b. Calculate the mass of CO 2 generated in a year assuming the power station operates continuously. [1 mark] « =» «kg» If no unit assume kg

2 1c. Explain, using your answer to (b), why countries are being asked to decrease their dependence on fossil fuels. CO 2 linked to greenhouse gas OR greenhouse effect leading to «enhanced» global warming OR climate change OR other reasonable climatic effect 1d. Describe, in terms of energy transfers, how thermal energy of the burning gas becomes electrical energy. Internal energy of steam/particles OR KE of steam/particles «transfers to» KE of turbine «transfers to» KE of generator or dynamo «producing electrical energy» Do not award mark for first and last energies as they are given in the question. Do not allow gas for steam Do not accept reference to moving OR turning generator

3 This question is in two parts. Part 1 is about energy resources. Part 2 is about thermal physics. Part 1 Energy resources Electricity can be generated using nuclear fission, by burning fossil fuels or using pump storage hydroelectric schemes. Outline which of the three generation methods above is renewable. 2a. pump storage; renewable as can be replaced in short time scale / storage water can be pumped back up to fall again / source will not run out; } (do not accept because water is used ) In a nuclear reactor, outline the purpose of the 2b. heat exchanger. [1 mark] (allows coolant to) transfer thermal/heat (energy) from the reactor/(nuclear) reaction to the water/steam; Must see reference to transfer cooling reactor/heating up water is not enough.

4 moderator. 2c. reduces speed/kinetic energy of neutrons; (do not allow particles ) improves likelihood of fission occurring/u-235 capturing neutrons; Fission of one uranium-235 nucleus releases 203 MeV. 2d. Determine the maximum amount of energy, in joule, released by 1.0 g of uranium-235 as a result of fission. [3 marks] (203 MeV is equivalent to) (J); nuclei have a mass of 235 (g) / evaluates number of nuclei; ( nuclei produce) (J) / multiplies two previous answers; Award [3] for bald correct answer. Award [1] for correct conversion from ev to J even if rest is incorrect.

5 Describe the main principles of the operation of a pump storage hydroelectric scheme. 2e. [3 marks] water flows between water masses/reservoirs at different levels; flow of water drives turbine/generator to produce electricity; at off peak times the electricity produced is used to raise water from lower to higher reservoir; 2f. A hydroelectric scheme has an efficiency of 92%. Water stored in the dam falls through an average height of 57 m. Determine the rate of flow of water, in kgs 1, required to generate an electrical output power of 4.5 MW. [3 marks] mgh use of ; t m t = 6 ; (t is usually ignored, assume 1 s if not seen) (kg s 1 ); Award [3] for a bald correct answer.

6 This question is in two parts. Part 1 is about energy resources. Part 2 is about thermal physics. Part 2 Thermal physics Distinguish between specific heat capacity and specific latent heat. 2g. specific heat capacity is/refers to energy required to change the temperature (without changing state); specific latent heat is energy required to change the state/phase without changing the temperature; If definitions are given they must include salient points given above. A mass of 0.22 kg of lead spheres is placed in a well-insulated tube. The tube is turned upside down several times so that the spheres fall through an average height of 0.45 m each time the tube is turned. The temperature of the spheres is found to increase by 8 C. 2h. Discuss the changes to the energy of the lead spheres.

7 gravitational potential energy kinetic energy; kinetic energy internal energy/thermal energy/heat energy; Do not allow heat. Two separate energy changes must be explicit. 2i. The specific heat capacity of lead is Jkg 1 K 1. Deduce the number of times that the tube is turned upside down. [4 marks] use of mcδt; use of n mgδh; equating (cδt = ngδh) ; 236 or 240; or use of ΔU = mcδt; ( =) 229 (J); n mgδh = 229 (J); n = = Award [4] for a bald correct answer. or 240; } (allow if answer is rounded up to give complete number of inversions)

8 This question is about energy sources. A small island is situated in the Arctic. The islanders require an electricity supply but have no fossil fuels on the island. It is suggested that wind generators should be used in combination with power stations using either oil or nuclear fuel. 3a. Suggest the conditions that would make use of wind generators in combination with either oil or nuclear fuel suitable for the islanders. [3 marks] needs to be windy/high average wind speeds; space/land/room for wind turbines; ability to import oil/nuclear fuel; ability to dispose of nuclear waste; comment relating to need for geological stability; 3b. Conventional horizontal-axis wind generators have blades of length 4.7m. The average wind speed on the island is 7.0ms 1 and the average air density is 1.29kgm 3. (i) Deduce the total energy, in GJ, generated by the wind generators in one year. (ii) Explain why less energy can actually be generated by the wind generators than the value you deduced in (b)(i). [5 marks] (i) π4.7 2 or 69.4 m 2 ; power = to W; 470 to 490 GJ; (ii) wind must retain kinetic energy to escape or not all KE of wind can be converted to KE of blades; energy lost to thermal energy (due to friction) in generator/turbine/dynamo; turbine will suffer downtime when no wind/too much wind; Allow any two relevant factors.

9 The energy flow diagram (Sankey diagram) below is for an oil-fired power station that the islanders might use. 3c. [4 marks] (i) Determine the efficiency of the power station. (ii) Explain why energy is wasted in the power station. (iii) The Sankey diagram in (c) indicates that some energy is lost in transmission. Explain how this loss occurs. (i) indication that energy supplied to islanders is output and chemical energy input / 8 used; 25 32% / 0.32; (ii) energy/it is wasted due to inefficient burning of oil / thermal/heat energy loss to surroundings/environment / electrical energy is used to run the power station s systems / energy/it is wasted due to frictional losses in the turbine/generator; (iii) heating of wires by electric current / inefficient transformers;

10 The emissions from the oil-fired power station in (c) are likely to increase global warming by the enhanced greenhouse effect. 3d. Outline the mechanism by which greenhouse gases contribute to global warming. [3 marks] radiation emitted by Earth in (long wavelength) infrared region; frequency corresponds to resonant frequency of greenhouse gases (either vibration or difference in energy levels); radiation absorbed by greenhouse gases is (partly) re-radiated back to Earth; 3e. Nuclear fuel must be enriched before it can be used. Outline why fuel enrichment is needed. percentage of U-235 in naturally occurring ores is too low to support fission or naturally occurring U-238 does not undergo fission; percentage of U-235 (which can usefully capture thermal neutrons) is increased; 3f. The nuclear equation below shows one of the possible fission reactions in a nuclear reactor. Identify the missing numbers in the equation. ( 1 0n+ 92 U 92 Kr Ba+ 1 0n) [3 marks]

11 ( 1 0n U 92 36Kr Ba n) 235; 36; 3; The number of neutrons must be consistent with chosen isotope of uranium. 3g. A nuclear reactor requires both control rods and a moderator to operate. Outline, with reference to neutrons, one similarity and two[3 marks] differences in the function of each of these components. control rods absorb neutrons; moderators slow down neutrons; both affect the rate of reaction; both rely on the neutrons colliding with their atoms/nuclei; Must see reference to collision/interaction for fourth marking point. This question is in two parts. Part 1 is about renewable energy. Part 2 is about nuclear energy and radioactivity. Part 1 Renewable energy A small coastal community decides to use a wind farm consisting of five identical wind turbines to generate part of its energy. At the proposed site, the average wind speed is 8.5ms 1 and the density of air is 1.3kgm 3. The maximum power required from the wind farm is 0.75 MW. Each turbine has an efficiency of 30%. 4a. (i) Determine the diameter that will be required for the turbine blades to achieve the maximum power of 0.75 MW. (ii) State one reason why, in practice, a diameter larger than your answer to (a)(i) is required. (iii) Outline why the individual turbines should not be placed close to each other. [8 marks] (iv) Some members of the community propose that the wind farm should be located at sea rather than on land. Evaluate this proposal.

12 (i) total wind power required = ; maximum wind power required per turbine, P = (= 500kW) ; d = ( 8P ρπv =) 40(m) Award [1 max] for an answer of 48.9 (m) as it indicates 5 and 0.3 ignored. Award [2 max] for 22 (m) as it indicates 0.3 ignored. Award [2 max] for 89 (m) as it indicates 5 ignored. (ii) not all kinetic energy can be extracted from wind / losses in cables to community / turbine rotation may be cut off/ feathered at high or low wind speeds; Do not allow wind speed varies as question gives the average speed. (iii) less kinetic energy available / wind speed less for turbines behind; turbulence/wake effect; (do not allow turbines stacked too close ) (iv) implications: average wind speeds are greater / more space available; limitations: installation/maintenance cost / difficulty of access / wave damage; Must see one each for [2]. 4b. Currently, a nearby coal-fired power station generates energy for the community. Less coal will be burnt at the power station if the wind farm is constructed. [7 marks] (i) The energy density of coal is 35 MJ kg 1. Estimate the minimum mass of coal that can be saved every hour when the wind farm is producing its full output. (ii) One advantage of the reduction in coal consumption is that less carbon dioxide will be released into the atmosphere. State one other advantage and one disadvantage of constructing the wind farm. (iii) Suggest the likely effect on the Earth s temperature of a reduction in the concentration of atmospheric greenhouse gases.

13 (i) mass of coal per second (= kg); 77.1 (kg); or energy saved per hour= (=2700MJh-1) ; 2700 mass of coal saved = ( =) 77.1(kg) ; 35 Award [2] for a bald correct answer. (ii) advantage: energy is free (apart from maintenance and start-up costs) / energy is renewable / sufficient for small community with predominance of wind / supplies energy to remote community / independent of national grid / any other reasonable advantage; Answer must focus on wind farm not coal disadvantages. disadvantage: wind energy is variable/unpredictable / noise pollution / killing birds/bats / large open areas required / visual pollution / ecological issues / need to provide new infrastructure; (iii) greenhouse gas molecules are excited by/absorbed by/resonate as a result of infrared radiations; { (must refer to infrared not heat ) this radiation is re-emitted in all directions; less greenhouse gas means less infrared/heat returned to Earth; { (consideration of return direction is essential for mark) temperature falls (to reach new equilibrium); Part 2 Nuclear energy and radioactivity The graph shows the variation of binding energy per nucleon with nucleon number. The position for uranium-235 (U-235) is shown. State what is meant by the binding energy of a nucleus. 4c. [1 mark]

14 energy released when a nucleus forms from constituent nucleons / (minimum) energy needed/work done to break a nucleus up into its constituent nucleons; Award [0] for energy to assemble nucleus. Do not allow particles or components for nucleons. Do not accept energy that binds nucleons together OWTTE. 4d. (i) On the axes, sketch a graph showing the variation of nucleon number with the binding energy per nucleon. (ii) Explain, with reference to your graph, why energy is released during fission of U-235. [5 marks] (i) generally correct shape with maximum shown, trending down to U-235; maximum shown somewhere between 40 and 70; Award [0] for straight line with positive gradient from origin. Award [1] if maximum position correct but graph begins to rise or flatlines beyond or around U-235. (ii) identifies fission as occurring at high nucleon number / at right-hand side of graph; fission means that large nucleus splits into two (or more) smaller nuclei/nuclei to left of fissioning nucleus (on graph); (graph shows that) fission products have higher (average) binding energy per nucleon than U-235; energy released related to difference between initial and final binding energy; Award [2 max] if no reference to graph. 4e. U-235 ( U) can undergo alpha decay to form an isotope of thorium (Th). (i) State the nuclear equation for this decay. (ii) Define the term radioactive half-life. [4 marks] (iii) A sample of rock contains a mass of 5.6 mg of U-235 at the present day. The half-life of U-235 is years. Calculate the initial mass of the U-235 if the rock sample was formed years ago.

15 235 (i) 92 U Th α ; (allow He for α; treat charge indications as neutral) (ii) time taken for number of unstable nuclei/(radio)activity to halve; Accept atom/isotope. Do not accept mass/molecule/amount/substance. (iii) three half-lives identified; 45 (mg); Award [2] for bald correct answer. This question is in two parts. Part 1 is about energy resources. Part 2 is about electric fields. Part 1 Energy resources 5a. The Sun is a renewable energy source whereas a fossil fuel is a non-renewable energy source. Outline the difference between renewable and non-renewable energy sources. renewable sources: rate of use/depletion of energy source; is less than rate of production/regeneration of source; Accept equivalent statement for non-renewable sources. or mention of rate of production / usage; comparison of sources in terms of being used up/depleted/lasting a long time etc; Award [1] if answer makes clear the difference but does not address the rate of production.

16 5b. With reference to the energy transformations and the operation of the devices, distinguish between a photovoltaic cell and a solar heating panel. solar heating panel converts solar/radiation/photon/light energy into thermal/heat energy and photovoltaic cell converts solar/radiation/photon/light energy into electrical energy; } (both needed) in solar heating hot liquid is stored/circulated and photovoltaic cell generates emf/pd; } (both needed) A photovoltaic panel is made up of a collection (array) of photovoltaic cells. The panel has a total area of 1.3 m 2 and is mounted on the roof of a house. The maximum intensity of solar radiation at the location of the panel is 750 Wm 2. The panel produces a power output of 210 W when the solar radiation is at its maximum intensity. 5c. Determine the efficiency of the photovoltaic panel. (power available at roof) = (= 975 W) ; 210 efficiency = ( =) 0.22 or 22%; 975

17 State two reasons why the intensity of solar radiation at the location of the panel is not constant. 5d depends on time of day; depends of time of year; depends on weather ( eg cloud cover) at location; power output of Sun varies; Earth-Sun distance varies; The owner of the house chooses between photovoltaic panels and solar heating panels to provide 4.2 kw of power to heat water. The solar heating panels have an efficiency of 70%. The maximum intensity of solar radiation at the location remains at 750 Wm 2. 5e. Calculate the minimum area of solar heating panel required to provide this power. area of panel = 4200 ; m 2 ;

18 5f. Comment on whether it is better to use a solar heating panel rather than an array of photovoltaic panels for the house. Do not consider the installation cost of the panels in your answer. calculates area of photovoltaic panels needed as about 26 m 2 / makes a quantitative comparison; solar heating takes up less area/more efficient/faster; further energy conversion needed, from electrical to thermal, with photovoltaic panels, involving further losses / OWTTE; Allow ECF from (d)(i) with appropriate reverse argument. Part 2 Electric fields An isolated metal sphere is placed in a vacuum. The sphere has a negative charge of magnitude 12 nc. 5g. Using the diagram, draw the electric field pattern due to the charged sphere. radial field with arrows and direction correct towards the sphere; (both needed) no field inside sphere; At least four lines of force to be shown on diagram.

19 Outside the sphere, the electric field strength is equivalent to that of a point negative charge of magnitude 12 nc placed at the centre of the sphere. The radius r of the sphere is 25 mm. Show that the magnitude of the electric field strength at the surface of the sphere is about h. 5 N C 1 use of E = kq ; r N C 1 ; (must see answer to 2+ significant figures) 5i. On the axes, draw a graph to show the variation of the electric field strength E with distance d from the centre of the sphere. line drawn showing zero field strength inside sphere; decreasing in inverse square-like way from a value of N C 1 or N C 1 at the surface, d = 25 mm;

20 An electron is initially at rest on the surface of the sphere. 5j. Calculate the initial acceleration of the electron. force = ; (allow use of NC 1 ) acceleration = ( 14 =) ms 2 ; k. Discuss the subsequent motion of the electron. radially away from sphere / away from centre of sphere; velocity increasing but at a decreasing rate / accelerating with decreasing acceleration; because (electric) field (strength) is decreasing;

21 This question is in two parts. Part 1 is about solar radiation and the greenhouse effect. Part 2 is about a mass on a spring. Part 1 Solar radiation and the greenhouse effect The following data are available. State the Stefan-Boltzmann law for a black body. 6a. power/energy per second emitted proportional to surface area; and proportional to fourth power of absolute temperature / temperature in K; Accept equation with symbols defined. 6b. Deduce that the solar power incident per unit area at distance d from the Sun is given by σr 2 T 4 d 2 solar power given by 4πR 2 σt 4 ; spreads out over sphere of surface area 4πd 2 ; Hence equation given.

22 Calculate, using the data given, the solar power incident per unit area at distance d from the Sun. 6c. σr ( 2 T =) 8 [ ] 2 [ ] 4 ; d2 [ ] 2 = (Wm ); Award [2] for a bald correct answer. State two reasons why the solar power incident per unit area at a point on the surface of the Earth is likely to be different from your 6d. answer in (c). some energy reflected; some energy absorbed/scattered by atmosphere; depends on latitude; depends on time of day; depends on time of year; depends on weather (eg cloud cover) at location; power output of Sun varies; Earth-Sun distance varies; 2

23 The average power absorbed per unit area at the Earth s surface is 240Wm 2. By treating the Earth s surface as a black body, 6e. show that the average surface temperature of the Earth is approximately 250K. power radiated = power absorbed; T = = (250K); Accept answers given as 260 (K). 6f. Explain why the actual surface temperature of the Earth is greater than the value in (e). [3 marks] radiation from Sun is re-emitted from Earth at longer wavelengths; greenhouse gases in the atmosphere absorb some of this energy; and radiate some of it back to the surface of the Earth;

24 Part 2 A mass on a spring An object is placed on a frictionless surface and attached to a light horizontal spring. The other end of the spring is attached to a stationary point P. Air resistance is negligible. The equilibrium position is at O. The object is moved to position Y and released. Outline the conditions necessary for the object to execute simple harmonic motion. 6g. the force (of the spring on the object)/acceleration (of the object/point O) must be proportional to the displacement (from the equilibrium position/centre/point O); and in the opposite direction to the displacement / always directed towards the equilibrium position/centre/point O;

25 The sketch graph below shows how the displacement of the object from point O varies with time over three time periods. 6h. [4 marks] (i) Label with the letter A a point at which the magnitude of the acceleration of the object is a maximum. (ii) Label with the letter V a point at which the speed of the object is a maximum. (iii) Sketch on the same axes a graph of how the displacement varies with time if a small frictional force acts on the object.

26 (i) one A correctly shown; (ii) one V correctly shown; (iii) same period; (judge by eye) amplitude decreasing with time;

27 6i. Point P now begins to move from side to side with a small amplitude and at a variable driving frequency f. The frictional force is still[4 marks] small. At each value of f, the object eventually reaches a constant amplitude A. The graph shows the variation with f of A. (i) With reference to resonance and resonant frequency, comment on the shape of the graph. (ii) On the same axes, draw a graph to show the variation with f of A when the frictional force acting on the object is increased.

28 (i) resonance is where driving frequency equals/is close to natural/resonant frequency; the natural/resonant frequency is at/near the maximum amplitude of the graph; (ii) lower amplitude everywhere on graph, bit still positive; maximum in same place/moved slightly (that is, between the lines) to left on graph; This question is about the use of energy resources. 7a. State the difference between renewable and non-renewable energy sources. [1 mark] only non-renewable is depleted/cannot re-generate whereas renewable can / consumption rate of non-renewables is greater than formation rate and consumption rate of renewables is less than formation rate; Do not allow cannot be used again.

29 Nuclear reactors are used to generate energy. In a particular nuclear reactor, neutrons collide elastically with carbon-12 nuclei ( 12 6C) that act as the moderator of the reactor. A neutron with an initial speed of ms 1 collides head-on with a stationary carbon-12 nucleus. Immediately after the collision the carbon-12 nucleus has a speed of ms 1. 7b. (i) State the principle of conservation of momentum. (ii) Show that the speed of the neutron immediately after the collision is about ms 1. [10 marks] (iii) Show that the fractional change in energy of the neutron as a result of the collision is about 0.3. (iv) Estimate the minimum number of collisions required for the neutron to reduce its initial energy by a factor of (v) Outline why the reduction in energy is necessary for this type of reactor to function.

30 (i) (total) momentum unchanged before and after collision / momentum of a system is constant; } (allow symbols if explained) no external forces / isolated system / closed system; Do not accept conserved. (ii) final momentum of neutron = neutron mass u ; } (allow any appropriate and consistent mass unit) final speed of neutron = 8.0 or (m s 1 ); ( (m s 1 )) Allow use of 1 u for both masses giving an answer of (m s 1 ). (iii) initial energy of neutron = (J) and final energy of neutron = (J); } (both needed) ( ) fractional change in energy = ( =) 0.33; 8.04 or mv fractional change = ( 2 i 2 2 mu2 f ); }(allow any algebra that shows a subtraction of initial term from final term divided by initial value) ( (= 6 ) 2 ( ) 2 ) (allow omission of 10 6) ( ) 2 = 0.33; (allow 0.30 if 8.2 used) Do not allow ECF if there is no subtraction of energies in first marking point. (iv) (0.33) n = 10 6 ; n = 13; (allow n = 12 if 0.3 is used) 1 1 1mv 2 2 i (v) neutrons produced in fission have large energies; greatest probability of (further) fission/absorption (when incident neutrons have thermal energy or low energy); Do not accept reaction for fission reaction. This question is about nuclear power production. 8. State two advantages of power production using fossil fuels compared to using nuclear fuels. no radioactive waste; no radiation risks to users; lower expense of decommissioning / easier to decommission / easier to install / lower set-up cost; transportation and storage less hazardous/safer; simpler technology; cannot be used for military purposes; fossil fuels can be extracted/found more easily; no chance of catastrophic accident/meltdown/chernobyl;

31 Part 2 Wind power and the greenhouse effect 9a. A coal-fired power station has a power output of 4.0GW. It has been suggested that a wind farm could replace this power station. [4 marks] Using the data below, determine the area that the wind farm would occupy in order to meet the same power output as the coal-fired power station. Radius of wind turbine blades = 42 m Area required by each turbine = m2 Efficiency of a turbine = 30% Average annual wind speed = 12 m s 1 Average annual density of air = 1.2 kg m 3 power output of a turbine=0.3 ½ρAv 3= [42] 2 [12] 3(=1723kW); number of turbines needed = (= 2322) ; area needed = ; = (m 2); Award [4] for a bald correct answer. Note: Answers sometimes start with calculating power input from wind which is 5743 kw and incorporate 0.3 at a later stage. 9b. Wind power does not involve the production of greenhouse gases. Outline why the surface temperature of the Earth is higher than would be expected without the greenhouse effect. [3 marks]

32 look for these main points: the surface of Earth re-radiates the Sun s radiation; greenhouse gases (in atmosphere) readily absorb infrared; mention of resonance; the absorbed radiation is re-emitted (by atmosphere) in all directions; (some of) which reaches the Earth and further heats the surface; Award [1 max] for responses along the lines that greenhouse gases trap infrared radiation. 9c. The average solar intensity incident at the surface of the Earth is 238 W m 2. (i) Assuming that the emissivity of the surface of the Earth is 1.0, estimate the average surface temperature if there were no greenhouse effect. (ii) The enhanced greenhouse effect suggests that in several decades the predicted temperature of the atmosphere will be 250 K. The emissivity of the atmosphere is Show that this atmospheric temperature increase will lead to a predicted average Earth surface temperature of 292 K. [5 marks]

33 (i) total absorbed radiation= total emitted radiation =238(Wm -2); temperature of Earth= [ ] =255(K); Award [2] for a bald correct answer. (ii) total absorbed radiation at surface=238+[( εδt 4) ]; =410.8(Wm -2); temperature of surface= [ ] =291.7(K); K 1 1 This question is about the greenhouse effect. The following data are available for use in this question: Explain why the power absorbed by the Earth is 10a. P 4πd 2 (1 α) πr 2 [3 marks] intensity of the Sun s radiation at the Earth s orbit = P ; 4πd 2 fraction absorbed by the Earth =(1- ); the surface area of the disc (absorbing the radiation) = πr 2 ; Look for statements that correctly describe each term.

34 The equation in (a) leads to the following expression which can be used to predict the Earth s average surface temperature T. 10b. [4 marks] (1 α)p T = 4 16πσd 2 (i) Calculate the predicted temperature of the Earth. (ii) Explain why the actual average surface temperature of the Earth is in fact higher than the answer to (b)(i). (i) correct substitution; to get T=250 (K); (ii) greenhouse gases in the atmosphere absorb some of the energy radiated by the Earth; and radiate some of it back to the surface of the Earth; This question is in two parts. Part 1 is about wind power. Part 2 is about radioactive decay. Part 1 Wind power Outline in terms of energy changes how electrical energy is obtained from the energy of wind. 11a. kinetic energy of wind transferred to (rotational) kinetic energy of turbine/blades; kinetic energy changed to electrical energy in generator/dynamo; Generator/dynamo must be mentioned.

35 Air of density ρ and speed v passes normally through a wind turbine of blade length r as shown below. 11b. [5 marks] (i) Deduce that the kinetic energy per unit time of the air incident on the turbine is 1 πρr 2 v 3 2 (ii) State two reasons why it is impossible to convert all the available energy of the wind to electrical energy. (i) volume of cylinder of air passing through blades per second =vπr 2; mass of air incident per second=ρvπr 2; kinetic energy per second= 1 mv 2 ; 2 leading to 1 2 πρr2 v 3 Award [3] for answers that combine one or more steps. (ii) the speed of the air/wind cannot drop to zero; wind turbulence / frictional losses in turbine/any moving part / resistive heating in wires;

36 Air is incident normally on a wind turbine and passes through the turbine blades without changing direction. The following data are [3 marks] 11c. available. Density of air entering turbine = 1.1 kg m 3 Density of air leaving turbine = 2.2 kg m 3 Speed of air entering turbine = 9.8 m s 1 Speed of air leaving turbine = 4.6 m s 1 Blade length = 25 m Determine the power extracted from the air by the turbine. kinetic energy per second of air entering turbine = 1 π = ; 2 kinetic energy per second of air leaving turbine = 1 π = ; 2 power extracted = = W; A wind turbine has a mechanical input power of W and generates an electrical power output of W. On the grid 11d. below, construct and label a Sankey diagram for this wind turbine. [3 marks]

37 correct shape of diagram (allow multiple arrows if power loss split into different components); relative width of arrows correct; labels correct; Outline one advantage and one disadvantage of using wind turbines to generate electrical energy, as compared to using fossil 11e. fuels. Advantage: Disadvantage: Advantage: wind is renewable so no resources used up / wind is free / no chemical pollution / no carbon dioxide emission / does not contribute to greenhouse effect / is scalable i.e. many sizes of turbine possible; Disadvantage: expensive initial cost / large land area needed / wind not constant / effect on movement of birds / aesthetically unpleasant / noise pollution / high maintenance costs / best locations far from population centres / low energy density; Accept any other suitable advantage or disadvantage.

38 This question is in two parts. Part 1 is about a nuclear reactor. Part 2 is about simple harmonic oscillations. Part 1 Nuclear reactor The reactor produces 24 MW of power. The efficiency of the reactor is 32 %. In the fission of one uranium-235 nucleus J[4 marks] 12a. of energy is released. Determine the mass of uranium-235 that undergoes fission in one year in this reactor. 24 power produced ( ) =75MW; 0.32 energy produced in a year ( =) J; number of reactions required in one year ( ) = ; mass used ( ) 29kg; or mass used ( ) = 29kg; Explain what would happen if the moderator of this reactor were to be removed. 12b. [3 marks] the neutrons would not be slowed down; therefore they would not be/have less chance of being captured/induce fission; so (much) less/no power would be produced;

39 During its normal operation, the following set of reactions takes place in the reactor. 12c. 1 0n U U U Np e + v Np Pu e + v (I) (II) (III) [3 marks] (i) State the name of the process represented by reaction (II). (ii) Comment on the international implications of the product of these reactions. (i) beta decay; (ii) the reactions end up producing plutonium (from uranium 238); (this isotope of) plutonium may be used to manufacture nuclear weapons / can be used as fuel in other reactors / plutonium is extremely toxic; or the products of the reactions are radioactive for long periods of time / OWTTE; therefore posing storage/safety problems; 13. A radioactive isotope has a half-life of two minutes. A sample contains sixteen grams of the isotope. How much time elapses until one gram of the isotope remains? [1 mark] A. 6 minutes B. 8 minutes C. 10 minutes D. 12 minutes B

40 Data concerning nuclides are plotted using the axes below. 14. [1 mark] What are the axis labels for this graph? A 15. Which of the following is true about beta minus ( β ) decay? A. An antineutrino is absorbed. B. The charge of the daughter nuclide is less than that of the parent nuclide. C. An antineutrino is emitted. D. The mass number of the daughter nuclide is less than that of the parent nuclide. [1 mark] C

41 A student performs an experiment with a paper toy that rotates as it falls slowly through the air. After release, the paper toy quickly attains a constant vertical speed as measured over a fixed vertical distance. The aim of the experiment was to find how the terminal speed of the paper toy varies with its weight. The weight of the paper toy was changed by using different numbers of paper sheets in its construction. The graph shows a plot of the terminal speed v of the paper toy (calculated from the raw data) and the number of paper sheets n used to construct the toy. The uncertainty in v for n = 1 is shown by the error bar. The fixed distance is 0.75 m and has an absolute uncertainty of 0.01 m. The percentage uncertainty in the time taken to fall through the fixed distance is 5%. Calculate the absolute uncertainty in the terminal speed of the paper toy for n = 6. 16a. [3 marks]

42 0.01 percentage uncertainty in distance ( =) 1.3% ; 0.75 percentage uncertainty in v = ( =) 6.3% ; absolute uncertainty in n = 6 point is ( = ) ms 1 ; 16b. On the graph, draw an error bar on the point corresponding to n = 6. [1 mark] overall length of error bar drawn correct to within half a small square; Consistent with (a)(i). On the graph, draw a line of best-fit for the data points. 16c. [1 mark] any reasonable smooth curve/straight-line passing through error bars Do not award where abrupt change of gradient occurs at n = 5. The student hypothesizes that v is proportional to n. Use the data points for n = 2 and n = 4 from the graph opposite to show 16d. that this hypothesis is incorrect. [3 marks]

43 v n tests for n or v; v v n = 0.12 for n = 2 and n = for n = 4; (both needed) hypothesis incorrect because two values should be equal; Accept for [3] read-off of both 0.24 and 0.34 together with the comment that 0.34 is not double Award [2 max] if no use of data but candidate has drawn curve with no straight portion and comments that line is not straight and does not go through origin. Award [1 max] if no use of data but candidate has drawn a straight line and comments that line is straight but not through origin. 16e. Another student hypothesized that v might be proportional to n. To verify this hypothesis he plotted a graph of v 2 against n as shown below. [3 marks] Explain how the graph verifies the hypothesis that v is proportional to n.

44 (if v n)v 2 n; graph of v 2 against n is a straight-line; that goes through the origin; In 1997 a high-speed car of mass kg achieved the world land speed record. The car accelerated uniformly in two stages as shown in the table. The car started from rest. Use the data to calculate the 16f. average acceleration of the car in stage 1. [1 mark] 11 ms 2 ; average net force required to accelerate the car in stage 2. 16g. [3 marks] Δv = 236; 236 a = ( =) 29.5 (ms 2 ); 8 (F = ) = N; Award [2 max] for omission of initial speed (answer is 390 kn). Award [3] for correct bald answer. total distance travelled by the car in 12 s. 16h.

45 phase 1 distance 88 m / phase 2 distance 1296 m; total 1400 m; Award [2] for correct bald answer. Watch for significant figure penalty in this question (1384 m). 1 Award [1 max] for at 2 substituted correctly for first phase, if no distances 2 evaluated and answer incorrect. Award [1 max] for correct addition of incorrect phase 1 and/or 2 distance(s). 16i. Draw the complete diagram of the circuit that uses a potential divider, ammeter, voltmeter and cell to measure the current-voltage characteristics for component X. [3 marks]

46 voltmeter in parallel across X; ammeter in series with X; correct circuit; (allow ecf from 1st and 2nd marking points) Accept voltmeter connections that include ammeter (in series with X) Condone re-drawing of resistor X closer to variable resistor. The graph shows the current-voltage characteristics for the component X. 16j. Component X is now connected across the terminals of a cell of emf 2.0 V and negligible internal resistance. Use the graph to show that the resistance of X is 0.83 Ω. I = 2.4 A at 2.0 V; 2 ; 2.4 = 0.83 Ω Award [1 max] for use of gradient of graph from (2,2.4) to origin.

47 This question is in two parts. Part 1 is about a simple pendulum. Part 2 is about the Rutherford model of the atom. Part 1 Simple pendulum A pendulum consists of a bob suspended by a light inextensible string from a rigid support. The pendulum bob is moved to one side and then released. The sketch graph shows how the displacement of the pendulum bob undergoing simple harmonic motion varies with time over one time period. On the sketch graph above, (i) 16k. (ii) label with the letter A a point at which the acceleration of the pendulum bob is a maximum. label with the letter V a point at which the speed of the pendulum bob is a maximum. (i) (ii) one A correctly shown; one V correctly shown; 16l. Explain why the magnitude of the tension in the string at the midpoint of the oscillation is greater than the weight of the pendulum bob. [3 marks] pendulum bob accelerates towards centre of circular path / OWTTE; therefore force upwards; that adds to tension produced by the weight;

48 A pendulum bob is moved to one side until its centre is 25 mm above its rest position and then released. 16m. (i) Show that the speed of the pendulum bob at the midpoint of the oscillation is 0.70 ms 1. [5 marks] (ii) The mass of the pendulum bob is kg. The centre of the pendulum bob is 0.80 m below the support. Calculate the magnitude of the tension in the string when the pendulum bob is vertically below the point of suspension. (i) evidence shown of equating kinetic energy and gravitational potential energy; v = ( ) ; = 0.70 ms 1 Allow g = 10 m s 2 answer 0.71 m s 2. v (ii) centripetal acceleration (= ) [= 2 r ] = 0.61 (ms 2 ); 0.8 net acceleration = ( =) 10.4 (ms 2 ) or T mg = m 0.61; tension = (ma =) 0.59 N; Allow g = 10 m s 2 answer 0.60 N. Award [3] for bald correct answer.

49 Part 2 Rutherford model of the atom The isotope gold-197 ( Au) is stable but the isotope gold-199 ( Au) is not. (i) Outline, in terms of the forces acting between nucleons, why, for large stable nuclei such as gold-197, the number of neutrons[4 marks] 16n. exceeds the number of protons. (ii) A nucleus of Au 199 decays to a nucleus of 80 Hg with the emission of an electron and another particle. State the name of this other particle. (i) mention of Coulomb repulsion between protons; mention of strong (nuclear) force (between nucleons); overall balance must be correct (and more neutrons needed for this); Award [0] for a statement that neutron is negative. (ii) anti neutrino / v ; This question is in two parts. Part 1 is about a lightning discharge. Part 2 is about fuel for heating. Part 1 Lightning discharge Define electric field strength. 16o. force acting per unit charge; on positive test / point charge;

50 A thundercloud can be modelled as a negatively charged plate that is parallel to the ground. 16p. [3 marks] The magnitude of the charge on the plate increases due to processes in the atmosphere. Eventually a current discharges from the thundercloud to the ground. On the diagram, draw the electric field pattern between the thundercloud base and the ground. lines connecting plate and ground equally spaced in the central region of thundercloud and touching both plates; (judge by eye) edge effects shown; (accept either edge effect A or B shown on diagram) field direction correct; The magnitude of the electric field strength E between two infinite charged parallel plates is given by the expression E = σ ε 0 where σ is the charge per unit area on one of the plates. A thundercloud carries a charge of magnitude 35 C spread over its base. The area of the base is m 2. (i) 16q. (ii) (iii) Determine the magnitude of the electric field between the base of the thundercloud and the ground. State two assumptions made in (c)(i). When the thundercloud discharges, the average discharge current is 1.8 ka. Estimate the discharge time. [12 marks] (iv) The potential difference between the thundercloud and the ground before discharge is V. Determine the energy released in the discharge.

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52 (i) σ = ( 35 =) (C m 2 ); E = ; = N C 1 or V m 1 ; Award [3] for bald correct answer. (ii) edge of thundercloud parallel to ground; thundercloud and ground effectively of infinite length; permittivity of air same as vacuum; (iii) t = Q ; I t = 35 ; 1800 = 20 ms; (iv) use of energy = p.d. charge; average p.d. = (V); energy released = ; = J; Award [3 max] for 8.8 GJ if average p.d. point omitted. charge Accept solution which uses average current (from ). time Allow ecf from (c)(ii). Part 2 Fuel for heating Define the energy density of a fuel. 16r. [1 mark] energy (released) per unit mass; Accept per unit volume or per kg or per m 3. Do not accept per unit density.

53 A room heater burns liquid fuel and the following data are available. Density of liquid fuel Energy produced by 1 m 3 of liquid fuel Rate at which fuel is consumed Latent heat of vaporization of the fuel = kgm 3 = J = 0.13 g s 1 = 290 kj kg 1 (i) Use the data to calculate the power output of the room heater, ignoring the power required to convert the liquid fuel into a 16s. gas. [5 marks] (ii) Show why, in your calculation in (b)(i), the power required to convert the liquid fuel into a gas at its boiling point can be ignored. rate (i) volume of fuel used per second = (= (m 3 )); density energy = ; = ( =) 4.4 kw; Award [3] for bald correct answer. (ii) power required = ( =) 38 W; small fraction/less than 1% of overall power output / OWTTE; State, in terms of molecular structure and their motion, two differences between a liquid and a gas. 16t

54 sensible comment comparing molecular structure; e.g. liquid molecular structure (more) ordered than that of a gas. in gas molecules far apart/about 10 molecular spacings apart / in liquid molecules close/touching. sensible comment comparing motion of molecules; e.g. in liquid: molecules interchange places with neighbouring molecules / no long distance motion. in gases: no long-range order / long distance motion. This question is in two parts. Part 1 is about the production of energy in nuclear fission. Part 2 is about collisions. Part 1 Production of energy in nuclear fission A possible fission reaction is U n Kr Ba + x 1 0n. (i) State the value of x. 16u. (ii) Show that the energy released when one uranium nucleus undergoes fission in the reaction in (a) is about J. [6 marks] Mass of neutron Mass of U nucleus Mass of Kr - 92 nucleus Mass of Ba nucleus = u = u = u = u (iii) State how the energy of the neutrons produced in the reaction in (a) is likely to compare with the energy of the neutron that initiated the reaction.

55 (i) 3; (ii) Δm = [ ] ; = (u); energy released = = 173 (MeV); ; (= 2.768) (J) or Δm = [ ] ; = (u); mass converted = (= ); (use of E = mc 2 ) energy = ; (= 2.77) (J) Award [2 max] if mass difference is incorrect. If candidate carries forward an incorrect value from (a)(i) [2 is common], treat this as ecf in (a)(ii). Award [3 max] if the candidate uses a value for x inconsistent with (a)(i). (iii) greater/higher energy; Outline the role of the moderator. 16v. reduces neutron speed to (thermal) lower speeds; so that chance of initiating fission is higher; Accept fast neutrons cannot cause fission for 2nd marking point.

56 A nuclear power plant that uses U-235 as fuel has a useful power output of 16 MW and an efficiency of 40%. Assuming that each [4 marks] 16w. fission of U-235 gives rise to J of energy, determine the mass of U-235 fuel used per day. 40% efficient so 40 (MW) required; = per second; number of fissions per day = ; (= ) = 48 g per day; Part 2 Collisions 16x. State the principle of conservation of momentum. the total momentum of a system is constant; provided external force does not act; or the momentum of an isolated/closed system; is constant; Award [1] for momentum before collision equals collision afterwards.

57 In an experiment, an air-rifle pellet is fired into a block of modelling clay that rests on a table. The air-rifle pellet remains inside the clay block after the impact. As a result of the collision, the clay block slides along the table in a straight line and comes to rest. Further data relating to the experiment are given below. Mass of air - rifle pellet Mass of clay block Velocity of impact of air - rifle pellet Stopping distance of clay block = 2.0 g = 56 g = 140 ms 1 = 2.8 m (i) 16y. Show that the initial speed of the clay block after the air-rifle pellet strikes it is 4.8 ms 1. (ii) Calculate the average frictional force that the surface of the table exerts on the clay block whilst the clay block is moving. [6 marks]

58 (i) initial momentum = ; final speed ; = 4.8 ms 1 Watch for incorrect mass values in equation. 1 (ii) initial kinetic energy of pellet + clay block = mv 2 ; ( = 0.67 J) ; work done force = ; distance travelled = 0.24 N; or use of appropriate kinematic equation with consistent sign usage e.g. a = u2 v 2 ; 2s a = 4.82 ; F = = 0.24 N; ; Discuss the energy transformations that occur in the clay block and the air-rifle pellet from the moment the air-rifle pellet strikes the [3 marks] 16z. block until the clay block comes to rest. kinetic energy of pellet is transferred to kinetic energy of clay block; and internal energy of pellet and clay block; clay block loses kinetic energy as thermal energy/heat;

59 The clay block is dropped from rest from the edge of the table and falls vertically to the ground. The table is 0.85 m above the 16aa. ground. Calculate the speed with which the clay block strikes the ground. v = 2gs; = 4.1 ms 1 ; Allow g = 10 m s 2 answer 4.1 m s 2 Award [2] for bald correct answer. 17. Emission and absorption spectra provide evidence for A. the nuclear model of the atom. B. natural radioactivity. C. the existence of isotopes. D. the existence of atomic energy levels. [1 mark] D 18. Which of the following is true in respect of both the Coulomb interaction and the strong interaction between nucleons in an atom? [1 mark] C

60 Which of the following correctly identifies the three particles emitted in the decay of the nucleus 20 Ca into a nucleus of Sc? A. α, β, γ B. β, γ, ν C. α, γ, ν D. α, β, ν [1 mark] B 20. The nuclear reaction is an example of A. nuclear fission. B. radioactive decay. C. nuclear fusion. D. artificial transmutation. 2 1 H +3 1 H 4 2 He +1 0 n [1 mark] C The number of neutrons and the number of protons in a nucleus of an atom of the isotope of uranium 92U are [1 mark] B 22. A sample contains an amount of radioactive material with a half-life of 3.5 days. After 2 weeks the fraction of the radioactive material [1 mark] remaining is A. 94 %. B. 25 %. C. 6 %. D. 0 %. C

61 23. The rest mass of a proton is 938 MeV c 2. The energy of a proton at rest is A J B ( ) 2 J C ev D ( ) 2 ev [1 mark] C International Baccalaureate Organization 2017 International Baccalaureate - Baccalauréat International - Bachillerato Internacional Printed for George Washington High School