Energy ans Astro revision [191 marks]

Transcription

1 Energy ans Astro revision [191 marks] Two renewable energy sources are solar and wind. 1a. Describe the difference between photovoltaic cells and solar heating panels. [1 mark] solar heating panel converts solar/radiation/photon/light energy into thermal energy AND photovoltaic cell converts solar/radiation/photon/light energy into electrical energy Accept internal energy of water. 1b. A solar farm is made up of photovoltaic cells of area m 2. The average solar intensity falling on the farm is 240 W m 2 and the average power output of the farm is 1.6 MW. Calculate the efficiency of the photovoltaic cells. power received = = «6.0 MW» efficiency «= 1.6 = 0.27 / 27% 6.0

2 An alternative generation method is the use of wind turbines. The following data are available: Length of turbine blade = 17 m Density of air = 1.3 kg m 3 Average wind speed = 7.5 m s 1 1c. Determine the minimum number of turbines needed to generate the same power as the solar farm. [3 marks] area = π 172 «= 908m 2» power = «= MW» 1.6 number of turbines «= = 6.4» = Only allow integer value for MP3. Award [2 max] for 25 turbines (ECF from incorrect power) Award [2 max] for 26 turbines (ECF from incorrect radius) Explain two reasons why the number of turbines required is likely to be greater than your answer to (c)(i). 1d.

3 «efficiency is less than 100% as» not all KE of air can be converted to KE of blades OR air needs to retain KE to escape thermal energy is lost due to friction in turbine/dynamo/generator Allow velocity of air after turbine is not zero. 2a. Outline, with reference to energy changes, the operation of a pumped storage hydroelectric system. PE of water is converted to KE of moving water/turbine to electrical energy «in generator/turbine/dynamo» idea of pumped storage, ie: pump water back during night/when energy cheap to buy/when energy not in demand/when there is a surplus of energy 1

4 The hydroelectric system has four 250 MW generators. The specific energy available from the water is 2.7 kj kg 1. Determine the 2b. maximum time for which the hydroelectric system can maintain full output when a mass of 1.5 x kg of water passes through the turbines. total energy = «2.7 x 103 x 1.5 x =» 4.05 x 1013 «J» time = «13» 11.1h or 4.0 x 104 s For MP2 the unit must be present. 2c. Not all the stored energy can be retrieved because of energy losses in the system. Explain one such loss. [1 mark] friction/resistive losses in walls of pipe/air resistance/turbulence/turbine and generator bearings thermal energy losses, in electrical resistance of components water requires kinetic energy to leave system so not all can be transferred Must see seat of friction to award the mark. Do not allow friction bald. 2

5 At the location of the hydroelectric system, an average intensity of 180 W m 2 arrives at the Earth s surface from the Sun. Solar 2d. photovoltaic (PV) cells convert this solar energy with an efficiency of 22 %. The solar cells are to be arranged in a square array. Determine the length of one side of the array that would be required to replace the hydroelectric system. area required = «= 2.5 x 107 m 2» length of one side = area = 5.0 k«m» 3a. Outline the conditions necessary for simple harmonic motion (SHM) to occur. force/acceleration proportional to displacement «from equilibrium position» and directed towards equilibrium position/point OR and directed in opposite direction to the displacement from equilibrium position/point Do not award marks for stating the defining equation for SHM. Award [1 max] for a ω = 2x with a and x defined.

6 A buoy, floating in a vertical tube, generates energy from the movement of water waves on the surface of the sea. When the buoy moves up, a cable turns a generator on the sea bed producing power. When the buoy moves down, the cable is wound in by a mechanism in the generator and no power is produced. The motion of the buoy can be assumed to be simple harmonic. A wave of amplitude 4.3 m and wavelength 35 m, moves with a speed of 3.4 m s 1. Calculate the maximum vertical speed of the 3b. buoy. [3 marks] frequency of buoy movement OR time period of buoy or «Hz» or 10.3 «s» or 10 «s» 2πx0 v = «or 2πfx 0» = 2 π 4.3 or 2 π T «m s 1» = =

7 3c. Sketch a graph to show the variation with time of the generator output power. Label the time axis with a suitable scale. peaks separated by gaps equal to width of each pulse «shape of peak roughly as shown» one cycle taking 10 s shown on graph Judge by eye. Do not accept cos 2 or sin 2 graph At least two peaks needed. Do not allow square waves or asymmetrical shapes. Allow ECF from (b)(i) value of period if calculated. Water can be used in other ways to generate energy. 3d. Outline, with reference to energy changes, the operation of a pumped storage hydroelectric system.

8 PE of water is converted to KE of moving water/turbine to electrical energy «in generator/turbine/dynamo» idea of pumped storage, ie: pump water back during night/when energy cheap to buy/when energy not in demand/when there is a surplus of energy 3e. The water in a particular pumped storage hydroelectric system falls a vertical distance of 270 m to the turbines. Calculate the speed at which water arrives at the turbines. Assume that there is no energy loss in the system. specific energy available = «gh =» 9.81 x 270 «= 2650J kg 1» OR mgh = 1 mv2 2 OR v 2 = 2gh v = 73 «ms 1» Do not allow 72 as round from 72.8

9 3f. The hydroelectric system has four 250 MW generators. Determine the maximum time for which the hydroelectric system can maintain full output when a mass of 1.5 x kg of water passes through the turbines. total energy = «mgh = 1.5 x x 9.81 x 270=» 4.0 x 1013 «J» OR total energy = «1 mv 2 1 = (answer (c)(ii)) 2 =» 4.0 x 1013 «J» time = «13» 11.1h or 4.0 x 104 s Use of 3.97 x 1013 «J» gives 11 h. For MP2 the unit must be present. 3g. Not all the stored energy can be retrieved because of energy losses in the system. Explain two such losses. friction/resistive losses in pipe/fluid resistance/turbulence/turbine or generator «bearings» OR sound energy losses from turbine/water in pipe thermal energy/heat losses in wires/components water requires kinetic energy to leave system so not all can be transferred Must see seat of friction to award the mark. Do not allow friction bald.

10 4a. State two characteristics of the cosmic microwave background (CMB) radiation. black body radiation / 3 K highly isotropic / uniform throughout OR filling the universe Do not accept: CMB provides evidence for the Big Bang model. 4b. The present temperature of the CMB is 2.8 K. Calculate the peak wavelength of the CMB. [1 mark] «λ = » 1.0 «mm» 2.8 [1 mark]

11 4c. Describe how the CMB provides evidence for the Hot Big Bang model of the universe. the universe is expanding and so the wavelength of the CMB in the past was much smaller indicating a very high temperature at the beginning A spectral line in the light received from a distant galaxy shows a redshift of z = d. Determine the distance to this galaxy using a value for the Hubble constant of H = 68 km s 1 0 Mpc 1. «z = v» v = «= c km s 1» v «d = v = 5 = 706» 710 «Mpc» 68 H0 Award [1 max] for POT error.

12 Estimate the size of the Universe relative to its present size when the light was emitted by the galaxy in (c). 4e. R z = 1 = 1.16 R 0 R R0 = 0.86 R R0 Theta 1 Orionis is a main sequence star. The following data for Theta 1 Orionis are available. Luminosity Radius Apparent brightness L = L R = 13R b = b where L, R and b are the luminosity, radius and apparent brightness of the Sun. 5a. State what is meant by a main sequence star. [1 mark] stars fusing hydrogen «into helium» [1 mark]

13 Show that the mass of Theta 1 Orionis is about 40 solar masses. 5b. [1 mark] M = M ( ) «M 40M» = 39.86M Accept reverse working. [1 mark] 5c. The surface temperature of the Sun is about 6000 K. Estimate the surface temperature of Theta 1 Orionis = 13 2 T 4 T «K» Accept use of substituted values into L = σ4 πr 2 T 4. Award [2] for a bald correct answer.

14 Determine the distance of Theta 1 Orionis in AU. 5d = AU2 d = «AU» d2 Accept use of correct values into b = L. 4πd2 5e. Discuss how Theta 1 Orionis does not collapse under its own weight. the gravitation «pressure» is balanced by radiation «pressure» that is created by the production of energy due to fusion in the core / OWTTE Award [1 max] if pressure and force is inappropriately mixed in the answer. Award [1 max] for unexplained "hydrostatic equilibrium is reached".

15 5f. The Sun and Theta 1 Orionis will eventually leave the main sequence. Compare and contrast the different stages in the evolution of[3 marks] the two stars. the Sun will evolve to become a red giant whereas Theta 1 Orionis will become a red super giant the Sun will explode as a planetary nebula whereas Theta 1 Orionis will explode as a supernova the Sun will end up as a white dwarf whereas Theta 1 Orionis as a neutron star/black hole [3 marks]

16 The diagram shows the structure of a typical main sequence star. 6a. State the most abundant element in the core and the most abundant element in the outer layer. core: helium outer layer: hydrogen Accept no other elements.

17 6b. The Hertzsprung Russell (HR) diagram shows two main sequence stars X and Y and includes lines of constant radius. R is the radius of the Sun. [3 marks] density of star X Using the mass luminosity relation and information from the graph, determine the ratio. density of star Y 10 ratio of masses is ( ) = 10 2 ratio of volumes is 10 3 ( 10 ) 3 = so ratio of densities is 2 = Allow ECF for MP3 from earlier MPs [3 marks]

18 Star X is likely to evolve into a neutron star. On the HR diagram in (b), draw a line to indicate the evolutionary path of star X. 6c. [1 mark] line to the right of X, possibly undulating, very roughly horizontal Ignore any paths beyond this as the star disappears from diagram. [1 mark] 6d. Outline why the neutron star that is left after the supernova stage does not collapse under the action of gravitation. [1 mark] gravitation is balanced by a pressure/force due to neutrons/neutron degeneracy/pauli exclusion principle Do not accept electron degeneracy. [1 mark]

19 6e. The radius of a typical neutron star is 20 km and its surface temperature is 10 6 K. Determine the luminosity of this neutron star. L = σat 4 = 5.67 x 10 8 x 4 π x (2.0 x 104) 2 x (106) 4 L = 3 x 1026 «W» OR L = 2.85 x 1026 «W» Allow ECF for [1 max] if πr 2 used (gives 7 x «W») Allow ECF for a POT error in MP1. 6f. Determine the region of the electromagnetic spectrum in which the neutron star in (c)(iii) emits most of its energy.

20 λ = = «m» this is an X-ray wavelength 7a. Describe what is meant by the Big Bang model of the universe. theory in which all space/time/energy/matter were created at a point/singularity at enormous temperature with the volume of the universe increasing ever since or the universe expanding OWTTE

21 State two features of the cosmic microwave background (CMB) radiation which are consistent with the Big Bang model. 7b. CMB has a black-body spectrum wavelength stretched by expansion is highly isotropic/homogenous but has minor anisotropies predicted by BB model T «= 2.7 K» is close to predicted value For MP4 and MP5 idea of prediction is needed A particular emission line in a distant galaxy shows a redshift z = The Hubble constant is H = 68 km s 1 0 Mpc 1. 7c. Determine the distance to the galaxy in Mpc.

22 v = z v = = «km s 1 c» v d = = 4 = «Mpc» 68 H0 Allow ECF from MP1 to MP2. 7d. Describe how type Ia supernovae could be used to measure the distance to this galaxy. [3 marks] type Ia have a known luminosity/are standard candles measure apparent brightness determine distance from d = L 4πb Must refer to type Ia. Do not accept other methods (parallax, Cepheids) [3 marks]

23 Outline, with reference to star formation, what is meant by the Jeans criterion. 8a. a star will form out of a cloud of gas when the gravitational potential energy of the cloud exceeds the total random kinetic energy of the particles of the cloud OR the mass exceeds a critical mass for a particular radius and temperature 8b. In the proton proton cycle, four hydrogen nuclei fuse to produce one nucleus of helium releasing a total of J of energy. The Sun will spend years on the main sequence. It may be assumed that during this time the Sun maintains a constant luminosity of W. Show that the total mass of hydrogen that is converted into helium while the Sun is on the main sequence is kg. number of reactions is = H mass used is = «kg»

24 8c. Massive stars that have left the main sequence have a layered structure with different chemical elements in different layers. Discuss this structure by reference to the nuclear reactions taking place in such stars. nuclear fusion reactions produce ever heavier elements depending on the mass of the star / temperature of the core the elements / nuclear reactions arrange themselves in layers, heaviest at the core lightest in the envelope

25 9a. The graph shows the variation with time t of the cosmic scale factor R in the flat model of the universe in which dark energy is ignored. [1 mark] On the axes above draw a graph to show the variation of R with time, when dark energy is present. curve starting earlier, touching at now and going off to infinity [1 mark] 26 3

26 Recent evidence from the Planck observatory suggests that the matter density of the universe is ρ = 0.32 ρ, where ρ kg m 3 m c c is the critical density. The density of the observable matter in the universe is only 0.05 ρ. Suggest how the remaining 0.27 ρ is accounted for. 9b. c c [1 mark] there is dark matter that does not radiate / cannot be observed Unexplained mention of "dark matter" is not sufficient for the mark. [1 mark] 9c. The density of dark energy is ρλc 2 where ρ = ρ ρ. Calculate the amount of dark energy in 1 m 3 Λ c m of space. ρ = 0.68ρ = «kgm 3 Λ c» energy in 1 m 3 is therefore «J»

27 Derive, using the concept of the cosmological origin of redshift, the relation 10a. T 1 R between the temperature T of the cosmic microwave background (CMB) radiation and the cosmic scale factor R. the cosmological origin of redshift implies that the wavelength is proportional to the scale factor: λ R combining this with Wien s law λ 1 T OR use of kt hc λ «gives the result» Evidence of correct algebra is needed as relationship T = k R is given. The present temperature of the CMB is 2.8 K. This radiation was emitted when the universe was smaller by a factor of b. Estimate the temperature of the CMB at the time of its emission.

28 use of T 1 R = 2.8 x 1100 x «K» State how the anisotropies in the CMB distribution are interpreted. 10c. [1 mark] CMB anisotropies are related to fluctuations in density which are the cause for the formation of structures/nebulae/stars/galaxies OWTTE [1 mark] Describe what is meant by dark matter. 11a.

29 dark matter is invisible/cannot be seen directly OR does not interact with EM force/radiate light/reflect light interacts with gravitational force OR accounts for galactic rotation curves OR accounts for some of the missing mass/energy of galaxies/the universe OWTTE [6 marks] The distribution of mass in a spherical system is such that the density ρ varies with distance r from the centre as 11b. k ρ = r 2 [1 mark] where k is a constant. Show that the rotation curve of this system is described by v = constant. «from data booklet formula» v = 4πGρ 3 r substitute to get v = 4πGk 3 Substitution of ρ must be seen. [1 mark]

30 Curve A shows the actual rotation curve of a nearby galaxy. Curve B shows the predicted rotation curve based on the visible stars 11c. in the galaxy. Explain how curve A provides evidence for dark matter. curve A shows that the outer regions of the galaxy are rotating faster than predicted this suggests that there is more mass in the outer regions that is not visible OR more mass in the form of dark matter OWTTE

31 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 Calculate, with a suitable unit, the electrical power output of the power station. 12a. [1 mark] « » = W A unit is required for this mark. Allow use of J s 1. No sf penalty. Calculate the mass of CO generated in a year assuming the power station operates continuously. 12b. 2 [1 mark] « =» «kg» If no unit assume kg

32 Explain, using your answer to (b), why countries are being asked to decrease their dependence on fossil fuels. 12c. CO 2 linked to greenhouse gas OR greenhouse effect leading to «enhanced» global warming OR climate change OR other reasonable climatic effect Describe, in terms of energy transfers, how thermal energy of the burning gas becomes electrical energy. 12d. 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

33 Alpha Centauri A and B is a binary star system in the main sequence. State what is meant by a binary star system. 13a. [1 mark] two stars orbiting about a common centre «of mass/gravity» Do not accept two stars orbiting each other. b A apparent brightness of Alpha Centauri A 13b. (i) Calculate =. apparent brightness of Alpha Centauri B b B [4 marks] (ii) The luminosity of the Sun is W. Calculate the radius of Alpha Centauri A.

34 i stars are roughly at the same distance from Earth OR d is constant for binaries LA 1.5 L B 0.5 = = 3.0 Award [2] for a bald correct answer. ii r = π = «m» Award [2] for a bald correct answer. Show, without calculation, that the radius of Alpha Centauri B is smaller than the radius of Alpha Centauri A. 13c. «A= L» B and A have similar temperatures σt 4 so areas are in ratio of luminosities «so B radius is less than A»

35 Alpha Centauri A is in equilibrium at constant radius. Explain how this equilibrium is maintained. 13d. [3 marks] radiation pressure/force outwards gravitational pressure/force inwards forces/pressures balance A standard Hertzsprung Russell (HR) diagram is shown. 13e. Using the HR diagram, draw the present position of Alpha Centauri A and its expected evolutionary path.

36 Alpha Centauri A within allowable region some indication of star moving right and up then left and down ending in white dwarf region as indicated

37 The first graph shows the variation of apparent brightness of a Cepheid star with time. The second graph shows the average luminosity with period for Cepheid stars. 14a. Determine the distance from Earth to the Cepheid star in parsecs. The luminosity of the Sun is W. The average apparent brightness of the Cepheid star is W m 2. [3 marks] from first graph period=5.7 «days» ±0.3 «days» L from second graph = 2300 «±200» LSUN d = «26 = m» =250 «pc» 4π Accept answer from interval 240 to 270 pc If unit omitted, assume pc. Watch for ECF from mp1

38 Explain why Cephids are used as standard candles. 14b. Cepheids have a definite/known «average» luminosity which is determined from «measurement of» period OR determined from period-luminosity graph Cepheids can be used to estimate the distance of galaxies Do not accept brightness for luminosity. The peak wavelength of the cosmic microwave background (CMB) radiation spectrum corresponds to a temperature of 2.76 K. Identify two other characteristics of the CMB radiation that are predicted from the Hot Big Bang theory. 15a. isotropic/appears the same from every viewing angle homogenous/same throughout the universe black-body radiation

39 A spectral line in the hydrogen spectrum measured in the laboratory today has a wavelength of 21cm. Since the emission of the [1 mark] 15b. CMB radiation, the cosmic scale factor has changed by a factor of Determine the wavelength of the 21cm spectral line in the CMB radiation when it is observed today «cm» OR 231 «m» Describe how some white dwarf stars become type Ia supernovae. 16a. [3 marks] white dwarf must have companion «in binary system» white dwarf gains material «from companion» when dwarf reaches and exceeds the Chandrasekhar limit/1.4 M SUN supernova can occur

40 Hence, explain why a type Ia supernova is used as a standard candle. 16b. a standard candle represents a «stellar object» with a known luminosity this supernova occurs at an certain/known/exact mass so luminosity/energy released is also known OWTTE MP1 for indication of known luminosity, MP2 for any relevant supportive argument. Explain how the observation of type Ia supernovae led to the hypothesis that dark energy exists. 16c. [3 marks] distant supernovae were dimmer/further away than expected hence universe is accelerating dark energy «is a hypothesis to» explain this

41 The graph shows the observed orbital velocities of stars in a galaxy against their distance from the centre of the galaxy. The core of the galaxy has a radius of 4.0 kpc. Calculate the rotation velocity of stars 4.0 kpc from the centre of the galaxy. The average density of the galaxy is kg m 17a. 3. 4πGρ v = «r» 3 4 = π ( ) 3 v is about «m s 1» or 146 «km s 1» Accept answer in the range of to «m s 1».

42 Explain why the rotation curves are evidence for the existence of dark matter. 17b. rotation curves/velocity of stars were expected to decrease outside core of galaxy flat curve suggests existence of matter/mass that cannot be seen now called dark matter The Sun has a radius of m and is a distance m from Earth. The surface temperature of the Sun is 5800 K. Show that the intensity of the solar radiation incident on the upper atmosphere of the Earth is approximately 1400Wm 2. 18a. I = σat 4 4πd 2 = ( ) ( ) π ( ) OR 4π ( ) 2 I=1397 Wm 2 In this question we must see 4SF to award MP3. Allow candidate to add radius of Sun to Earth Sun distance. Yields 1386 Wm 2. 2

43 18b. The albedo of the atmosphere is Deduce that the average intensity over the entire surface of the Earth is 245Wm 2. «transmitted intensity =» «= 980Wm 2» πr 2 980Wm 2 4πR2 245Wm 2 Estimate the average surface temperature of the Earth. 18c T 4 = 245 T = 256K Describe one key characteristic of a nebula. 19a. [1 mark] made of dust and/or gas formed from supernova can form new stars some radiate light from enclosed stars some absorb light from distant stars

44 19b. Beta Centauri is a star in the southern skies with a parallax angle of arc-seconds. Calculate, in metres, the distance of this star from Earth. 3 d = 1 OR 120pc = m Answer must be in metres, watch for POT. Outline why astrophysicists use non-si units for the measurement of astronomical distance. 19c. [1 mark] distances are so big/large OR to avoid using large powers of 10 OR they are based on convenient definitions Aldebaran is a red giant star with a peak wavelength of 740 nm and a mass of 1.7 solar masses. Show that the surface temperature of Aldebaran is about 4000 K. 20a.

45 T = K Answer must be to at least 2SF. The radius of Aldebaran is m. Determine the luminosity of Aldebaran. 20b. L= π ( ) = W Accept use of to give W. Outline how the light from Aldebaran gives evidence of its composition. 20c. absorption lines in spectra are specific to particular elements Accept emission lines in spectra.

46 20d. Identify the element that is fusing in Aldebaran s core at this stage in its evolution. [1 mark] helium Predict the likely future evolution of Aldebaran. 20e. [3 marks] helium flash expansion of outer shell OR surface temperature increase planetary nebula phase only the core remains if below 1.4M S/Chandrasekhar limit then white dwarf Light reaching Earth from quasar 3C273 has z= a. [4 marks] (i) Outline what is meant by z. (ii) Calculate the ratio of the size of the universe when the light was emitted by the quasar to the present size of the universe. (iii) Calculate the distance of 3C273 from Earth using H =68kms 1 o Mpc 1.

47 (i) z = Δλ where Δλ is the redshift of a wavelength and λ 0 is the wavelength measured at rest on Earth OR it is a measure of λo cosmological redshift Do not allow just redshift. R R 1 R 1 (ii) z = 1, = so = = 0.86 Ro Ro z+1 Ro 1.16 Do not accept answer (iii) v=zc= = kms-1 v d = = 4 = 706Mpc OR m 68 Ho Explain how cosmic microwave background (CMB) radiation provides support for the Hot Big Bang model. 21b. as the universe expanded it cooled/wavelength increased the temperature dropped to the present approximate 3K OR wavelength stretched to the present approximate 1mm Value is required for MP2.

48 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. 22a. 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 heat exchanger. 22b. [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.

49 moderator. 22c. 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. Determine the maximum amount of energy, in joule, released by 1.0 g of uranium-235 as a result of fission. 22d. [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.

50 Describe the main principles of the operation of a pump storage hydroelectric scheme. 22e. [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; A hydroelectric scheme has an efficiency of 92%. Water stored in the dam falls through an average height of 57 m. Determine the 22f. 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.

51 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. 22g. 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. The essential difference between specific heat capacity and specific latent heat is that the former refers to a change of temperature without changing state; whereas the latter refers to a change of state without changing temperature. Most candidates just wrote definitions which they had learnt by rote and omitted the constant temperature for a substance changing state.

52 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. Discuss the changes to the energy of the lead spheres. 22h. gravitational potential energy kinetic energy; kinetic energy internal energy/thermal energy/heat energy; Do not allow heat. Two separate energy changes must be explicit. This is a question specifically about energy changes so candidates are expected to use accurate language and spell out the changes one by one. Common mistakes were omitting the gravitational in gravitational potential energy; referring to heat rather than thermal energy; and saying that gravitational potential energy changed to thermal and kinetic energy as if it were a single process.

53 The specific heat capacity of lead is Deduce the number of times that the tube is turned upside down. 22i. 2 Jkg 1 K 1 [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) This was generally well done. There were four marks and the question asks the candidates to deduce so it is essential that the argument is transparent. The examiner cannot be expected to search through a mass of numbers in order to carry forward an error.

54 This question is about the Hertzsprung Russell (HR) diagram and the Sun. A Hertzsprung Russell (HR) diagram is shown. The following data are given for the Sun and a star Vega. 23a. Luminosity of the Sun = W Luminosity of Vega = W Surface temperature of the Sun = 5800 K Surface temperature of Vega = 9600 K [3 marks] Determine, using the data, the radius of Vega in terms of solar radii. LV LS σav[tv] = ( 4 σ[r V] =) 2 [TV] 4 ; σas[ts] 4 σ[rs] 2 [TS] [rv]2 = ; [rs] r V = ( r S =) 2.3 r S ; Do not award third marking point if radius of the Sun is lost. candidates notably addressed absolute magnitude without referring to apparent magnitude as the question asked. Well-prepared candidates (both HL and SL) only had a problem with the part related to the use of a non-linear temperature scale. Average prepared candidates displayed difficulty in the experimental measurement of the temperature of the distant star and also with details of nuclear processes occurring in the Sun during transformation to a red giant.

55 Outline how observers on Earth can determine experimentally the temperature of a distant star. 23b. [3 marks] obtain the spectrum of the star; measure the position of the wavelength corresponding to maximum intensity; use Wien s law (to determine temperature); } (allow quotation of Wien s equation if symbols defined) Award [3 max] for referring to identification of temperature via different ionizations of different elements. candidates notably addressed absolute magnitude without referring to apparent magnitude as the question asked. Well-prepared candidates (both HL and SL) only had a problem with the part related to the use of a non-linear temperature scale. Average prepared candidates displayed difficulty in the experimental measurement of the temperature of the distant star and also with details of nuclear processes occurring in the Sun during transformation to a red giant. This question is about the Hertzsprung Russell (HR) diagram and the Sun. A Hertzsprung Russell (HR) diagram is shown. The Sun will remain on the main sequence of the HR diagram for about another five billion years. After this time it will become a red giant, following the evolutionary path shown in the diagram.

56 Outline why the Sun will leave the main sequence, and describe the nuclear processes that occur as it becomes a red giant. 24a. [4 marks] insufficient hydrogen (to continue fusion); star collapses (under gravity); temperature increases; initiated fusion of helium, (energy released causes) rapid expansion of star; Well-prepared candidates (both HL and SL) only had a problem with the part related to the use of a non-linear temperature scale. Average prepared candidates displayed difficulty in the experimental measurement of the temperature of the distant star and also with details of nuclear processes occurring in the Sun during transformation to a red giant.

57 Describe two physical changes that the Sun will undergo as it enters the red giant stage. 24b. rapid expansion / increase of size; decrease in temperature / cooler stars appear red in colour / increase of luminosity; Well-prepared candidates (both HL and SL) only had a problem with the part related to the use of a non-linear temperature scale. Average prepared candidates displayed difficulty in the experimental measurement of the temperature of the distant star and also with details of nuclear processes occurring in the Sun during transformation to a red giant. This question is about cosmic microwave background (CMB) radiation. A line in the hydrogen spectrum is measured in the laboratory to have a wavelength of 656 nm. The same line from a distant galaxy is measured to have a wavelength of 730 nm. Assuming that the Hubble constant H 0 is 69.3 kms 1 Mpc 1, calculate the distance of this galaxy from Earth. 25a. Δλ v ( = ) v = ( 8 74 =) (ms 1 ); λ c 656 v d = = 4 = 488 Mpc; 69.3 H0

58 Well done by candidates, weaker candidates did not write their ideas clearly enough in (a)(ii). Part (b) was also quite well done, but only better candidates mentioned uncertainty in measurement of distances to galaxies. 25b. discuss why different measurements of the Hubble constant do not agree with each other. [1 mark] measurements from distant galaxies have large uncertainties; Well done by candidates, weaker candidates did not write their ideas clearly enough in (a)(ii). Part (b) was also quite well done, but only better candidates mentioned uncertainty in measurement of distances to galaxies. International Baccalaureate Organization 2017 International Baccalaureate - Baccalauréat International - Bachillerato Internacional Printed for Jyvaskylan Lyseon lukio