Markscheme Examiners report - Peda.net · photovoltaic (PV) cells convert this solar energy with an...

Energy ans Astro revision [191 marks]

1a. [1 mark]

Two renewable energy sources are solar and wind.

Describe the difference between photovoltaic cells and solar heating panels.

Markschemesolar heating panel converts solar/radiation/photon/light energy into thermal energy AND photovoltaic cell convertssolar/radiation/photon/light energy into electrical energy

Accept internal energy of water.

Examiners report[N/A]

1b. [2 marks]A solar farm is made up of photovoltaic cells of area 25 000 m . The average solar intensity falling on the farm is 240 W m andthe average power output of the farm is 1.6 MW. Calculate the efficiency of the photovoltaic cells.

Markschemepower received = 240 × 25000 = «6.0 MW»

efficiency « = 0.27 / 27%


2 –2

= 1.66.0

1c. [3 marks]

An alternative generation method is the use of wind turbines.

The following data are available:

Length of turbine blade = 17 mDensity of air = 1.3 kg mAverage wind speed = 7.5 m s

Determine the minimum number of turbines needed to generate the same power as the solar farm.

Markschemearea = × 17 «= 908m »

power = «= 0.249 MW»

number of turbines « » = 7

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)


–3

–1

π 2 2

× 908 × 1.3 × 7.5312

= = 6.41.60.249

1d. [2 marks]Explain two reasons why the number of turbines required is likely to be greater than your answer to (c)(i).

Markscheme«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. [2 marks]Outline, with reference to energy changes, the operation of a pumped storage hydroelectric system.

MarkschemePE 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 asurplus of energy


–1

2b. [2 marks]The hydroelectric system has four 250 MW generators. The specific energy available from the water is 2.7 kJ kg . Determine themaximum time for which the hydroelectric system can maintain full output when a mass of 1.5 x 10 kg of water passes through theturbines.

Markschemetotal energy = «2.7 x 10 x 1.5 x 10 =» 4.05 x 10 «J»

time = « » 11.1h or 4.0 x 10 s

For MP2 the unit must be present.


–1

10

3 10 13

4.0×1013

4×2.5×1084

2c. [1 mark]Not all the stored energy can be retrieved because of energy losses in the system. Explain one such loss.

Markschemefriction/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

2d. [2 marks]At the location of the hydroelectric system, an average intensity of 180 W m arrives at the Earth’s surface from the Sun. Solarphotovoltaic (PV) cells convert this solar energy with an efficiency of 22 %. The solar cells are to be arranged in a square array. Determinethe length of one side of the array that would be required to replace thehydroelectric system.

Markschemearea required «= 2.5 x 10 m »

length of one side k«m»


–2

= 1×109

0.22×1807 2

= √area = 5.0

3a. [2 marks]Outline the conditions necessary for simple harmonic motion (SHM) to occur.

Markschemeforce/acceleration proportional to displacement «from equilibrium position»

and directed towards equilibrium position/pointORand 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–= x with a and x defined.


2

3b. [3 marks]

A buoy, floating in a vertical tube, generates energy from the movement of water waves on the surface of the sea. When the buoymoves up, a cable turns a generator on the sea bed producing power. When the buoy moves down, the cable is wound in bya 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 . Calculate the maximum vertical speed of thebuoy.

Markschemefrequency of buoy movement or 0.097 «Hz»

OR

time period of buoy or 10.3 «s» or 10 «s»

v = « or » or

2.6 «m s »


–1

= 3.435

= 353.4

2πx0

T2πfx0 = 2×π×4.3

10.32 × π × 0.097 × 4.3

–1

3c. [2 marks]Sketch a graph to show the variation with time of the generator output power. Label the time axis with a suitable scale.

Markschemepeaks 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 or sin graphAt least two peaks needed.Do not allow square waves or asymmetrical shapes.Allow ECF from (b)(i) value of period if calculated.


2 2

3d. [2 marks]

Water can be used in other ways to generate energy.

Outline, with reference to energy changes, the operation of a pumped storage hydroelectric system.

MarkschemePE 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 asurplus of energy


3e. [2 marks]The water in a particular pumped storage hydroelectric system falls a vertical distance of 270 m to the turbines. Calculate thespeed at which water arrives at the turbines. Assume that there is no energy loss in the system.

Markschemespecific energy available = «gh =» 9.81 x 270 «= 2650J kg »

OR

mgh mv

OR

v = 2gh

v = 73 «ms »

Do not allow 72 as round from 72.8


–1

= 12

2

2

–1

3f. [2 marks]The hydroelectric system has four 250 MW generators. Determine the maximum time for which the hydroelectric system canmaintain full output when a mass of 1.5 x 10 kg of water passes through the turbines.

Markschemetotal energy = «mgh = 1.5 x 10 x 9.81 x 270=» 4.0 x 10 «J»

OR

total energy = « (answer (c)(ii)) =» 4.0 x 10 «J»

time = « » 11.1h or 4.0 x 10 s

Use of 3.97 x 10 «J» gives 11 h.

For MP2 the unit must be present.


10

10 13

mv2 = × 1.5 × 1010×12

12

2 13

4.0×1013

4×2.5×1084

13

3g. [2 marks]Not all the stored energy can be retrieved because of energy losses in the system. Explain two such losses.

Markschemefriction/resistive losses in pipe/fluid resistance/turbulence/turbine or generator «bearings»ORsound 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.


4a. [2 marks]State two characteristics of the cosmic microwave background (CMB) radiation.

Markschemeblack body radiation / 3 K

highly isotropic / uniform throughoutORfilling the universe

Do not accept: CMB provides evidence for the Big Bang model.

[2 marks]


4b. [1 mark]The present temperature of the CMB is 2.8 K. Calculate the peak wavelength of the CMB.

Markscheme« » ≈ 1.0 «mm»

[1 mark]


λ = 2.9×10−3

2.8

4c. [2 marks]Describe how the CMB provides evidence for the Hot Big Bang model of the universe.

Markschemethe universe is expanding and so the wavelength of the CMB in the past was much smaller

indicating a very high temperature at the beginning

[2 marks]


4d. [2 marks]

A spectral line in the light received from a distant galaxy shows a redshift of z = 0.16.

Determine the distance to this galaxy using a value for the Hubble constant of H = 68 km s Mpc .

Markscheme« » v = 0.16 × 3 × 10 «= 0.48 × 10 km s »

« » ≈ 710 «Mpc»

Award [1 max] for POT error.

[2 marks]


0–1 –1

z = ⇒vc

5 5 −1

d = ⇒ v = = 706v

H0

0.48×105

68

4e. [2 marks]Estimate the size of the Universe relative to its present size when the light was emitted by the galaxy in (c).

Markscheme

[2 marks]


z = − 1 ⇒ = 1.16R

R0

R

R0

= 0.86R0

R

5a. [1 mark]

Theta 1 Orionis is a main sequence star. The following data for Theta 1 Orionis are available.

Luminosity L = 4 × 10 L

RadiusR = 13R

Apparent brightnessb = 4 × 10 b

where L, R and b are the luminosity, radius and apparent brightness of the Sun.

State what is meant by a main sequence star.

Markschemestars fusing hydrogen «into helium»

[1 mark]


5⊙

⊙–11

⊙

⊙

⊙

⊙

5b. [1 mark]Show that the mass of Theta 1 Orionis is about 40 solar masses.

Markscheme

« »

Accept reverse working.

[1 mark]


M = M⊙(4 × 105) = 39.86M⊙1

3.5

M ≈ 40M⊙

5c. [2 marks]The surface temperature of the Sun is about 6000 K. Estimate the surface temperature of Theta 1 Orionis.

Markscheme

«K»

Accept use of substituted values into4

R T .

Award [2] for a bald correct answer.

[2 marks]


4 × 105 = 132 × T 4

60004

T ≈ 42 000

L = σ

π 2 4

5d. [2 marks]Determine the distance of Theta 1 Orionis in AU.

Markscheme

«AU»

Accept use of correct values into .

[2 marks]


4 × 10−11 = 4 × 105 × 1AU2

d2

d = 1 × 108

b = L

4πd2

5e. [2 marks]Discuss how Theta 1 Orionis does not collapse under its own weight.

Markschemethe 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".

[2 marks]


5f. [3 marks]The Sun and Theta 1 Orionis will eventually leave the main sequence. Compare and contrast the different stages in the evolution ofthe two stars.

Markschemethe 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]


6a. [2 marks]

The diagram shows the structure of a typical main sequence star.

State the most abundant element in the core and the most abundant element in the outer layer.

Markschemecore: helium

outer layer: hydrogen

Accept no other elements.

[2 marks]


6b. [3 marks]The Hertzsprung–Russell (HR) diagram shows two main sequence stars X and Y and includes lines of constant radius. R is theradius of the Sun.

Using the mass–luminosity relation and information from the graph, determine the ratio .

Markschemeratio of masses is

ratio of volumes is

so ratio of densities is

Allow ECF for MP3 from earlier MPs

[3 marks]


density of star Xdensity of star Y

( ) = 102104

10−3

13.5

( )3= 10610

10−1

= 10−4102

106

6c. [1 mark]

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.

Markschemeline to the right of X, possibly undulating, very roughly horizontal

Ignore any paths beyond this as the star disappears from diagram.

[1 mark]


6d. [1 mark]Outline why the neutron star that is left after the supernova stage does not collapse under the action of gravitation.

Markschemegravitation is balanced by a pressure/force due to neutrons/neutron degeneracy/pauli exclusion principle

Do not accept electron degeneracy.

[1 mark]


6e. [2 marks]The radius of a typical neutron star is 20 km and its surface temperature is 10 K. Determine the luminosity of this neutron star.

MarkschemeL = AT = 5.67 x 10 x 4 x (2.0 x 10 ) x (10 )

L = 3 x 10 «W»ORL = 2.85 x 10 «W»

Allow ECF for [1 max] ifr used (gives 7 x 10 «W »)

Allow ECF for a POT error in MP1.

[2 marks]


6

σ 4 –8 π 4 2 6 4

26

26

π 2 26

6f. [2 marks]Determine the region of the electromagnetic spectrum in which the neutron star in (c)(iii) emits most of its energy.

Markscheme «m»

this is an X-ray wavelength

[2 marks]


λ = = 2.9 × 10−92.9×10−3

106

7a. [2 marks]Describe what is meant by the Big Bang model of the universe.

Markschemetheory 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

[2 marks]


7b. [2 marks]State two features of the cosmic microwave background (CMB) radiation which are consistent with the Big Bang model.

MarkschemeCMB 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

[2 marks]


7c. [2 marks]

A particular emission line in a distant galaxy shows a redshift z = 0.084.

The Hubble constant is H = 68 km s Mpc .

Determine the distance to the galaxy in Mpc.

0–1 –1

Markscheme «kms »

«Mpc»

Allow ECF from MP1 to MP2.

[2 marks]


= z ⇒ v = 0.084 × 3 × 105 = 2.52 × 104vc

–1

d = = = 370.6 ≈ 370v

H0

2.52×104

68

7d. [3 marks]Describe how type Ia supernovae could be used to measure the distance to this galaxy.

Markschemetype Ia have a known luminosity/are standard candles

measure apparent brightness

determine distance from d =

Must refer to type Ia. Do not accept other methods (parallax, Cepheids)

[3 marks]


√ L

4πb

8a. [2 marks]Outline, with reference to star formation, what is meant by the Jeans criterion.

Markschemea 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 cloudORthe mass exceeds a critical mass for a particular radius and temperature

[2 marks]


8b. [2 marks]In the proton–proton cycle, four hydrogen nuclei fuse to produce one nucleus of helium releasing a total of 4.3 × 10 J of energy.The Sun will spend 10 years on the main sequence. It may be assumed that during this time the Sun maintains a constant luminosity of 3.8× 10 W.

Show that the total mass of hydrogen that is converted into helium while the Sun is on the main sequence is 2 × 10 kg.

Markschemenumber of reactions is

H mass used is «kg»

[2 marks]

–12

10

26

29

= 2.79 × 10551010×365×24×3600×3.8×1026

4.3×10−12

2.79 × 1055 × 4 × 1.67 × 10−27 = 1.86 × 1029


8c. [2 marks]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.

Markschemenuclear 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

[2 marks]


9a. [1 mark]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 isignored.

On the axes above draw a graph to show the variation of R with time, when dark energy is present.

Markschemecurve starting earlier, touching at now and going off to infinity

[1 mark]


–26 –3

9b. [1 mark]

Recent evidence from the Planck observatory suggests that the matter density of the universe is ρ = 0.32 ρ , where ρ ≈ 10 kg mis 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.

Markschemethere is dark matter that does not radiate / cannot be observed

Unexplained mention of "dark matter" is not sufficient for the mark.

[1 mark]


m c c–26 –3

c c

9c. [2 marks]The density of dark energy is ρ c where ρ = ρ – ρ . Calculate the amount of dark energy in 1 m of space.

Markschemeρ = 0.68ρ = 0.68 × 10 «kgm »

energy in 1 m is therefore 0.68 × 10 × 9 × 10 ≈ 6 × 10 «J»

[2 marks]


Λ 2 Λ c m3

Λ c−26 −3

3 −26 16 −10

10a. [2 marks]Derive, using the concept of the cosmological origin of redshift, the relation

T

between the temperature T of the cosmic microwave background (CMB) radiation and the cosmic scale factor R.

Markschemethe cosmological origin of redshift implies that the wavelength is proportional to the scale factor: R

combining this with Wien’s law

OR

use of kT

«gives the result»

Evidence of correct algebra is needed as relationship T = is given.

[2 marks]


∝ 1R

λ ∝

λ ∝ 1T

∝ hc

λ

k

R

10b. [2 marks]The present temperature of the CMB is 2.8 K. This radiation was emitted when the universe was smaller by a factor of 1100.Estimate the temperature of the CMB at the time of its emission.

Markschemeuse of T

= 2.8 x 1100 x 3080 ≈ 3100 «K»

[2 marks]


∝ 1R

10c. [1 mark]State how the anisotropies in the CMB distribution are interpreted.

MarkschemeCMB anisotropies are related to fluctuations in density which are the cause for the formation of structures/nebulae/stars/galaxies

OWTTE

[1 mark]


11a. [2 marks]Describe what is meant by dark matter.

Markschemedark matter is invisible/cannot be seen directlyORdoes not interact with EM force/radiate light/reflect light

interacts with gravitational forceORaccounts for galactic rotation curvesORaccounts for some of the “missing” mass/energy of galaxies/the universe

OWTTE

[6 marks]


11b. [1 mark]The distribution of mass in a spherical system is such that the density ρ varies with distance r from the centre as

ρ =

where k is a constant.

Show that the rotation curve of this system is described by

v = constant.

Markscheme«from data booklet formula» substitute to get

Substitution of ρ must be seen.

[1 mark]


k

r2

v = √ r4πGρ

3v = √ 4πGk

3

11c. [2 marks]Curve A shows the actual rotation curve of a nearby galaxy. Curve B shows the predicted rotation curve based on the visible starsin the galaxy.

Explain how curve A provides evidence for dark matter.

Markschemecurve 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 visibleORmore mass in the form of dark matter

OWTTE

[2 marks]


12a. [1 mark]

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

Specific energy of natural gas = 55.5 MJ kg

Efficiency of electrical power generation = 59.0 %

Mass of CO generated per kg of natural gas = 2.75 kg

One year = 3.16 × 10 s

Calculate, with a suitable unit, the electrical power output of the power station.

Markscheme«55.5 × 14.6 × 0.59» = 4.78 × 108 W

A unit is required for this mark. Allow use of J s 1.

No sf penalty.


–1

–1

27

–

12b. [1 mark]Calculate the mass of CO generated in a year assuming the power station operates continuously.

Markscheme«14.6 × 2.75 × 3.16 × 10 =» 1.27 × 10 «kg»

If no unit assume kg


2

7 9

12c. [2 marks]Explain, using your answer to (b), why countries are being asked to decrease their dependence on fossil fuels.

MarkschemeCO linked to greenhouse gas OR greenhouse effect

leading to «enhanced» global warmingORclimate changeORother reasonable climatic effect


2

12d. [2 marks]Describe, in terms of energy transfers, how thermal energy of the burning gas becomes electrical energy.

MarkschemeInternal 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


13a. [1 mark]

Alpha Centauri A and B is a binary star system in the main sequence.

State what is meant by a binary star system.

Markschemetwo stars orbiting about a common centre «of mass/gravity» Do not accept two stars orbiting each other.


13b. [4 marks](i) Calculate .

(ii) The luminosity of the Sun is 3.8 × 10 W. Calculate the radius of Alpha Centauri A.

=bA

bB

apparent brightness of Alpha Centauri Aapparent brightness of Alpha Centauri B

26

Markschemeistars are roughly at the same distance from EarthORd is constant for binaries


ii

= 8.4 × 10 «m»



= = 3.0LA

LB

1.50.5

r = √ 1.5×3.8×1026

5.67×10−8×4π×58004

8

13c. [2 marks]Show, without calculation, that the radius of Alpha Centauri B is smaller than the radius of Alpha Centauri A.

Markscheme«A=

» B and A have similar temperatures

so areas are in ratio of luminosities

«so B radius is less than A»


L

σT 4

13d. [3 marks]Alpha Centauri A is in equilibrium at constant radius. Explain how this equilibrium is maintained.

Markschemeradiation pressure/force outwards

gravitational pressure/force inwards

forces/pressures balance


13e. [2 marks]A standard Hertzsprung–Russell (HR) diagram is shown.

Using the HR diagram, draw the present position of Alpha Centauri A and its expected evolutionary path.

MarkschemeAlpha Centauri A within allowable region

some indication of star moving right and up then left and down ending in white dwarf region as indicated


14a. [3 marks]

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.

Determine the distance from Earth to the Cepheid star in parsecs. The luminosity of the Sun is 3.8 × 10 W. The averageapparent brightness of the Cepheid star is 1.1 × 10 W m .

Markschemefrom first graph period=5.7 «days» ±0.3 «days»

from second graph « »

d = « » =250 «pc»

Accept answer from interval 240 to 270 pc If unit omitted, assume pc.Watch for ECF from mp1


26

–9 –2

= 2300L

LSUN±200

√ = 8.3 × 1018m2500×3.8×1026

4π×1.1×10−9

14b. [2 marks]Explain why Cephids are used as standard candles.

Markscheme Cepheids have a definite/known «average» luminosity

which is determined from «measurement of» periodORdetermined from period-luminosity graph

Cepheids can be used to estimate the distance of galaxies

Do not accept brightness for luminosity.


15a. [2 marks]

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.

Markschemeisotropic/appears the same from every viewing angle

homogenous/same throughout the universe

black-body radiation


15b. [1 mark]A spectral line in the hydrogen spectrum measured in the laboratory today has a wavelength of 21cm. Since the emission of theCMB radiation, the cosmic scale factor has changed by a factor of 1100. Determine the wavelength of the 21cm spectral line in the CMB

radiation when it is observed today.

Markscheme23 100 «cm»OR231 «m»


16a. [3 marks]Describe how some white dwarf stars become type Ia supernovae.

Markschemewhite dwarf must have companion «in binary system»

white dwarf gains material «from companion»

when dwarf reaches and exceeds the Chandrasekhar limit/1.4 M supernova can occur


SUN

16b. [2 marks]Hence, explain why a type Ia supernova is used as a standard candle.

Markschemea 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.


16c. [3 marks]Explain how the observation of type Ia supernovae led to the hypothesis that dark energy exists.

Markschemedistant supernovae were dimmer/further away than expected

hence universe is accelerating

dark energy «is a hypothesis to» explain this


17a. [2 marks]

The graph shows the observed orbital velocities of stars in a galaxy against their distance from the centre of the galaxy. The core of thegalaxy 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 5.0 × 10 kg m.

Markschemev = « »

v is about 146000 «m s » or 146 «km s »Accept answer in the range of 140000 to 160000 «m s ».


–21 –

3

√ r4πGρ

3= √ × π × 6.67 × 10−11 × 5.0 × 10−21 × (4000 × 3.1 × 1016)4

3

–1 –1

–1

17b. [2 marks]Explain why the rotation curves are evidence for the existence of dark matter.

Markschemerotation 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


18a. [2 marks]

The Sun has a radius of 7.0×10 m and is a distance 1.5×10 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 .

Markscheme

OR

I=1397 Wm

In this question we must see 4SF to award MP3.Allow candidate to add radius of Sun to Earth–Sun distance. Yields 1386 Wm


8 11

−2

I = σAT 4

4πd2

=5.67×10−8×(7.0×108)2

×58004

(1.5×1011)2

5.67×10−8×4π×(7.0×108)2×58004

4π×(1.5×1011)2

−2

–2.

−2

18b. [2 marks]The albedo of the atmosphere is 0.30. Deduce that the average intensity over the entire surface of the Earth is 245Wm .

Markscheme«transmitted intensity =» 0.70 × 1400 «= 980Wm »

245Wm


−2

–2

× 980Wm−2πR2

4πR2

–2

18c. [2 marks]Estimate the average surface temperature of the Earth.

Markscheme5.67 × 10 × T = 245

T = 256K


–8 4

19a. [1 mark]Describe one key characteristic of a nebula.

Markschememade of dust and/or gasformed from supernovacan form new starssome radiate light from enclosed starssome absorb light from distant stars


19b. [2 marks]Beta Centauri is a star in the southern skies with a parallax angle of 8.32×10 arc-seconds. Calculate, in metres, the distance ofthis star from Earth.

Markscheme OR 120pc

120×3.26×9.46×10 =3.70×10 m

Answer must be in metres, watch for POT.


−3

d = 18.32×10−3

15 18

19c. [1 mark]Outline why astrophysicists use non-SI units for the measurement of astronomical distance.

Markschemedistances are so big/large OR to avoid using large powers of 10 OR they are based on convenient definitions


20a. [2 marks]

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.

Markscheme

3900 KAnswer must be to at least 2SF.


T = 2.9×10−3

740×10−9

20b. [2 marks]The radius of Aldebaran is 3.1×10 m. Determine the luminosity of Aldebaran.

MarkschemeL=5.67×10 ×4π×(3.1×10 ) ×4000

=1.8×10 W

Accept use of 3900 to give 1.6×10 W.


10

-8 10 2 4

29

4 29

20c. [2 marks]Outline how the light from Aldebaran gives evidence of its composition.

Markschemeabsorption lines in spectra

are specific to particular elements

Accept “emission lines in spectra”.


20d. [1 mark]Identify the element that is fusing in Aldebaran’s core at this stage in its evolution.

Markschemehelium


20e. [3 marks]Predict the likely future evolution of Aldebaran.

Markschemehelium flashexpansion of outer shell OR surface temperature increaseplanetary nebula phaseonly the core remainsif below 1.4M /Chandrasekhar limit then white dwarf


S

21a. [4 marks]Light reaching Earth from quasar 3C273 has z=0.16.

(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 Mpc .o−1 −1

Markscheme(i) where Δλ is the redshift of a wavelength and λ is the wavelength measured at rest on Earth OR it is a measure of

cosmological redshift

Do not allow just “redshift”.

(ii)

Do not accept answer 1.16.

(iii) v=zc=0.16×3×10 =4.8×10 kms

OR 2.2×10 m


z = Δλ

λo0

≪ z = − 1, = ≫ so =≪ ≫= 0.86R

Ro

R

Ro

1z+1

R

Ro

11.16

8 4 -1

d = = = 706Mpcv

Ho

4.8×104

6825

21b. [2 marks]Explain how cosmic microwave background (CMB) radiation provides support for the Hot Big Bang model.

Markschemeas 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.


22a. [2 marks]

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.

Markschemepump 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 notaccept “because water is used”)


22b. [1 mark]

In a nuclear reactor, outline the purpose of the

heat exchanger.

Markscheme(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.


22c. [2 marks]moderator.

Markschemereduces speed/kinetic energy of neutrons; (do not allow “particles”)

improves likelihood of fission occurring/U-235 capturing neutrons;


22d. [3 marks]

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.

Markscheme(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.


3.25 × 10−11

6.02 × 1023

2.56 × 1021 8.32 × 1010

22e. [3 marks]Describe the main principles of the operation of a pump storage hydroelectric scheme.

Markschemewater 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;


22f. [3 marks]A hydroelectric scheme has an efficiency of 92%. Water stored in the dam falls through an average height of 57 m. Determine therate of flow of water, in , required to generate an electrical output power of 4.5 MW.

Markschemeuse of ;

; (t is usually ignored, assume 1 s if not seen)

;



kgs−1

mgh

t

=m

t

4.5×106

0.92×9.81×57

8.7 × 103 (kg s−1)

22g. [2 marks]

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.

Markschemespecific 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.

Examiners reportThe essential difference between specific heat capacity and specific latent heat is that the former refers to a change of temperaturewithout changing state; whereas the latter refers to a change of state without changing temperature. Most candidates just wrotedefinitions which they had learnt by rote – and omitted the constant temperature for a substance changing state.

22h. [2 marks]

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 spheresfall 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.

Markschemegravitational potential energy kinetic energy;

kinetic energy internal energy/thermal energy/heat energy;

Do not allow heat.

Two separate energy changes must be explicit.

Examiners reportThis is a question specifically about energy changes so candidates are expected to use accurate language and spell out the changesone by one. Common mistakes were omitting the “gravitational” in gravitational potential energy; referring to “heat” rather than thermalenergy; and saying that gravitational potential energy changed to thermal and kinetic energy as if it were a single process.

→

→

−

22i. [4 marks]The specific heat capacity of lead is . Deduce the number of times that the tube is turned upside down.

Markschemeuse of ;

use of ;

equating ;

236 or 240;

or

use of ;

;

;

or 240; } (allow if answer is rounded up to give complete number of inversions)


Examiners reportThis was generally well done. There were four marks and the question asks the candidates to “deduce” so it is essential that theargument is transparent. The examiner cannot be expected to search through a mass of numbers in order to carry forward an error.

1.3 × 102 Jkg−1K−1

mcΔT

n × mgΔh

(cΔT = ngΔh)

ΔU = mcΔT

(0.22 × 1.3 × 102 × 8 =) 229 (J)

n × mgΔh = 229 (J)

n = = 2362290.22×9.81×0.45

23a. [3 marks]

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.

Luminosity of the Sun

Luminosity of Vega

Surface temperature of the Sun

Surface temperature of Vega

Determine, using the data, the radius of Vega in terms of solar radii.

Markscheme;

;

;

Do not award third marking point if radius of the Sun is lost.

Examiners reportcandidates notably addressed absolute magnitude without referring to apparent magnitude as the question asked. Well-preparedcandidates (both HL and SL) only had a problem with the part related to the use of a non-linear temperature scale. Average preparedcandidates displayed difficulty in the experimental measurement of the temperature of the distant star and also with details of nuclearprocesses occurring in the Sun during transformation to a red giant.

= 3.85 × 1026 W

= 1.54 × 1028 W

= 5800 K

= 9600 K

= ( =)LV

LS

σAV[TV]4

σAS[TS]4

σ[rV]2[TV]4

σ[rS]2[TS]4

= ×1.54×1028

3.85×1026

[rV]2

[rS]296004

58004

rV = (√ × rS =) 2.3 rS1.54×1028

3.85×1026

58004

96004

23b. [3 marks]Outline how observers on Earth can determine experimentally the temperature of a distant star.

Markschemeobtain 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.

Examiners reportcandidates notably addressed absolute magnitude without referring to apparent magnitude as the question asked. Well-preparedcandidates (both HL and SL) only had a problem with the part related to the use of a non-linear temperature scale. Average preparedcandidates displayed difficulty in the experimental measurement of the temperature of the distant star and also with details of nuclearprocesses 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 redgiant, following the evolutionary path shown in the diagram.

24a. [4 marks]Outline why the Sun will leave the main sequence, and describe the nuclear processes that occur as it becomes a red giant.

Markschemeinsufficient hydrogen (to continue fusion);

star collapses (under gravity);

temperature increases;

initiated fusion of helium, (energy released causes) rapid expansion of star;

Examiners reportWell-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 withdetails of nuclear processes occurring in the Sun during transformation to a red giant.

24b. [2 marks]Describe two physical changes that the Sun will undergo as it enters the red giant stage.

Markschemerapid expansion / increase of size;

decrease in temperature / cooler stars appear red in colour / increase of luminosity;

Examiners reportWell-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 withdetails of nuclear processes occurring in the Sun during transformation to a red giant.

25a. [2 marks]

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 ismeasured to have a wavelength of 730 nm. Assuming that the Hubble constant is ,

calculate the distance of this galaxy from Earth.

Markscheme;

;

H0 69.3 kms−1Mpc−1

( = ⇒) v = ( =) 3.38 × 107 (ms−1)Δλ

λ

vc

3.00×108×74656

d = = = 488 Mpcv

H0

3.38×104

69.3

Printed for Jyvaskylan Lyseon lukio

© International Baccalaureate Organization 2017

International Baccalaureate® - Baccalauréat International® - Bachillerato Internacional®

Examiners reportWell done by candidates, weaker candidates did not write their ideas clearly enough in (a)(ii). Part (b) was also quite well done, but onlybetter candidates mentioned uncertainty in measurement of distances to galaxies.

25b. [1 mark]discuss why different measurements of the Hubble constant do not agree with each other.

Markschememeasurements from distant galaxies have large uncertainties;

Examiners reportWell done by candidates, weaker candidates did not write their ideas clearly enough in (a)(ii). Part (b) was also quite well done, but onlybetter candidates mentioned uncertainty in measurement of distances to galaxies.

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