~MERICAN ACADEMY LARNACAVII PHYSICS: SEMESTER 2: TEST 2 [Date: ]

NAME I !GRADE I

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TURN OVER FOR QUESTION I

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-2-. Questions 1- 10: Choose the right answer from choices A, B, C or D (or E).

If two systems are in thermal equilibrium with each other they musto be at the same temperature.B have the same thermal capacity.C have the same internal energy.D be at the same pressure.

What is the internal energy of a system?

A the maximum amount of work that can be extracted from the system

® the sum of kinetic energies and potential energies of the molecules

C the total amount of work which has been done on the system

o the thermal energy needed to raise the temperature of the system by one kelvin

E the thermal energy which remains in the system when it is cooled to absolute zero

Which of the following statements about heat and work is not-true?

:~;;. In an adiabatic change, no heat transfer takes place.

® In an isothermal change, no work is done.e Internal energy of an ideal gas depends only on temperature.D Internal energy can be changed by heat transfer and by work input.E When the volume of gas changes gradually, work is done.

~ Air contains a mixture of gases with different molar masses M. In a sample of air at constanttemperature, the Lm.S. speed of the molecules of each of the different constituents is proportional to

A l/M ® 1/.jM e .jM D M E M2

1.. f-.\ <c,"-7 - ~~,-" ~

:: (4W>~

< c..~7 01.... -L~

j<"'~~7 0/.... 1-41'-\

N -----m

IIIIIII

o I

Vrn V

The graph shows how the number of molecules Nwith speeds between v and v + Llv in a fixed mass ~fgas ~t kelvin temperature T varies with v. Nm is themaximum value of N., which occurs when v = vrn• Ifthe temperature is doubled

A the peak in the graph is sharper

B the area under the graph increases'

C the value of Nm increases

® the value of Vrn increases to flvrn

E the value of Vrn increases to 2vm

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~

III~II~

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If the amount of fissile material in the reactor exceeds the critical mass, the fission reactions

®BCD

can be controlled by a suitable absorber of neutrons.can be controlled by a suitable moderating material.can be controlled if the coolant flows at a fast rate.cannot be controlled.

~ Which-line, A to D, in the table gives a combination of materials that is commonly used formoderating, controlling and shielding respectively in a nuclear reactor?

moderating controlling shielding

A graphite carbon lead

B cadmium carbon concrete

C cadmium boron lead

@ graphite boron concrete

"Which one of the following statements correctly describes the changes that occur when auranium nucleus undergoes fission?

g) /A, The binding energy per nucleon decreases and one or more neutrons are released.B The binding energy per nucleon decreases and one or more protons are released.© The binding energy per nucleon increases and one or more neutrons are released.D The binding energy per nucleon increases and one or more protons are released.

A nucleus of 2~~Uabsorbs a neutron and undergoes fission. Which one of the following givespossible products of this process?

A 2:.-7..%

9'" n~A 22He -S8Ra 7.."\6 qL C(c...~ ~ V\ -~ Lt

Cl !("{.

® 141 92 " 1 Z.>fo Cf"L56Ba + 36 Kr + .J on

@o ?36 1..>(. '{"LC 2_le 94PU

'1' ~ I 21b ~"LD -g,jPo 4 2 He 8 on

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bindingenergy pernucleon

P

Q R

o~------------------------------Ao

The graph shows how the binding energy per nucleon of a nucleus varies with nucleon number, A.

Which one of the following statements is not true?

Energy is released in nuclear fission reactions from nuclei in region P.Nuclei in region Q are more stable than nuclei in region R.Nuclear fusion reactions bring nuclei closer to region Q.The binding energy per nucleon increases most significantly at lower nucleon numbers.

(Total for Questions 1 - 10 = 10 marks)

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A heating coil is used to warm water that flows past it at a steady rate of 0.24 kg S-i. The I Leaveheating coil remains at a constant working temperature of 350 DC. blank

Wanner water at 19.0 DC

Insulation

/Heating coil

Cold water at 17.0 DC

The specific heat capacity of water is 4200 J kg' K-1• Calculate the rate of absorption ofenergy by the cold water assuming no energy is lost to the surroundings .

. ..~.~ ~ ~ ..~ ~~ ~ 0..:. 7:-~.~.~~~ ~ 41:tr.o..2.\~.§~~..~.~ ..X ·0\:,:

..........~~ ~ ~~ .

Rate of absorption = h~.Q..\~~ .~ (3)

The heating coil is operating at its normal working temperature of 350 DC. The equation~u= ~Q + ~wmay be applied to the coil. State and explain the value of each quantity foreach second of operation.

boU= 0 .

Reason ~~ ~ .

"0 = - 2.O\JV">L.l_ ........................•..................................................................................•...............................................••....

Reason k~\.k ~~ ~..~~ .

- ''LOG\)"">boW - :1:: .

Reason ~er.<h. cXo~ . ~ 4:,+; ~ ..~;, ~ f Q.~.e.y. .

........................... ~~.\~ .(6)

(Total 9 marks)

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OJ (a) Explain what is meant by

(i) the specific heat capacity of water,

··········~········~tw.·~········~ ··VlA.\Y.··· ..···~ ~.:tM..~

...........~ .\~b ~ J.k .

(ii) the specific latent heat of fusion of ice .

.............~-t ~~.~d ~ ~.\:\ ·I·.···~..·········.

.............t ~:) .

(b) A sample of solid material, which has a mass of 0.15 kg, is supplied with energy at aconstant rate. The specific heat capacity of the material is 1200 J kg'" K-1 when in the solidstate. During heating, its temperature is recorded at various times and the following graphis plotted.

temperature/'C

94 ----------------------------

58 --------~----------~

18

o 12 165time/minutes

Assume there is no heat exchange with the surroundings.

(i) Show that energy is supplied to the material at a rate of 24 W.

·······~·····~·..····~·~..k~..··..;.::······~·~··~········· .~~ ~ O-~

.....................................................~ .....O':~>..~>..~....\~~.~.~£~.s.~\...~..1Q.k I

..................................................................................................................................... ~.~ .

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(4)

::z.-r-t

(ii) Calculate the specific latent heat of fusion of the material .

......b "? »..~ ~ 6-:t.~..?:':: .. A:1-.Q ..~ .-""'- 6 . , S \..::.j

" L;:t k> k --,••.......•••.••.....••.•..•..•....•.•.•••••••••• 90 •.••••••••••.•••••• ~ ••.•••••.••••••••.•...•••.•..........•..••••••..........•.•...••..

(iii) Calculate the specific heat capacity of the material when in the liquid state .

....... ( ::: ~ ..!>..:Q ~~ -a , ::= ~.~ .. ~~ .-

................................................. C."?: l~ ::: ~1..~ ..~ ~::ty...~ .:-~ C)"~s.~ '>C )C:.~

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.....................................................................................::: l.J.~.2.~;;~..~~~..... (6)

(c) (i) On the axes below, the original graph is shown by a dotted line. Sketch a graph on thesame axes indicating how you would expect the results of the experiment in part (b) todiffer if there were a significant heat loss from the material to surroundings whichwere at 15°C.

94 /

/ .:temperaturef'C //

//

/

58 /

18

o I5 1612

time/minutes

(ii) Explain the shape of the first section of the graph you have drawn in part (c)(i) .

...............§>~.It:.:: ~ :;"? ~~ ~ ~ ~ t: .- Ii'...............~ ~ t .

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(13)

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I~ (a) A student investigates how the pressure of a gas depends on its temperature.

(i) To carry out this experiment, two variables must be kept constant. What arethey?

1 ~S~ .2 ~~!.r.. c\- ~.Q.~ {. ~~~~ .

(2)

(ii) Draw a labelled diagram of the apparatus the student could use.

(4)

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(iii) State one precaution the student should take to improve the quality of theresults.

·······y.~~\····~·······\V·~~······ ..~·······~·~· ..·····5·~ .~~ (1)

I~

(b) In the space below sketch a graph to show how the pressure of an ideal gas dependson its temperature. Add any key values to your temperature axis, - -

\~C-.-_-----\0,0

(Total 10 marks)

The kinetic theory of gases is based on a number of assumptions. One assumption is that theaverage distance between the molecules is much larger than the molecular diameter. Asecond assumption is that the molecules are in continuous random motion. State and explainone observation in support of each assumption.

First assumption

............§.~ ~ ~.~.~ ..i.~~ .

.............s..~ ~~~.~ ~~ ~ k ~~ :.Second assumption

..............~.~.~.~.~ ~.Q.b~ ~., .

..............~.w.\~ ~ ~ ~~..'d.":' •• ~ ••••••.•• ~.~·~·4 ···..····

...............~ ~~.o ~h \.~~ ~ ~~.~O..~ f.. t?~J(..~.( -d::t.: .

...............~.~.9 ..~ ..~\ .

(Total 4 marks)

(3)

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i II !

I III

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/~ A cubic box with sides of length 0.50 m contains a gas. There are 1.5 x 1024

molecules inside the box.

Cubic box ofside 0.50m

400ms-1

MOl~~

~------~------~--~

A molecule is moving at 400 m s-I in a direction perpendicular to the shaded face.The average rate of change of momentum for this molecule at the shaded face is1.6 x 10-20 kg m S-2.

State the two assumptions that the kinetic theory makes about the collisions of thismolecule with the shaded face .

............. .~\fA.?:-: .~~ .

~~.............. ~ .

(2)

One third of all the molecules strike the shaded face. Calculate the average forceexerted by these molecules if their average speed is 400 m S-I .

..............F. :::'..J.~)( ..J.t?~4 .x....J ~.y \0 -~.~.~.i".~ .\....... ~ .•.

................................~ ~ ..:;: f. ~ ..R.~ .-.---/ ~ ~U~~-

.......................... ~~ .•...~~~.~ .~\,,~ S~C7<..AAf' Average force = .5t.Q.~~.y. .~~ m

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-If -

Hence calculate the gas pressure on the shaded face.

···..·····f·?·····f ::: ~.~ .1\ lo·c;o,",,)~

Gas pressure = 3.3..~Y.'.t.\.... .-=====-==- 1(2) I

The formula from kinetic theory for the pressure exerted by a gas is given by

State what the term (Cl) represents.

.......................~~ ~.~ ~f.~~ ., (1)

(Total 8 maJkS)

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.:

-/~-

16) Helium is a monatomic gas for which all the internal energy of the molecules may beconsidered to be translational kinetic energy.

molar mass of helium = 4.0 x 10-3 kgthe Boltzmann constant = 1.38 x 10-23 J K-1

the Avogadro constant = 6.02 x 1023 mol"

(a) Calculate the kinetic energy of a tennis ball of mass 60g travelling at 50m s" .

...........f..~..;:;~~ ..\r.~ ~ ~ ..~ .Q.:.O..~.Q..~.~ x (.s..Q..~.~"':~)~ .

.................................................~ 1.~.2. .--(b) Calculate the internal energy of 1.0g of helium gas at a temperature of 48 K.

............ E·\,c··:7:·· ..i···h1 <..~~.? :?. ~ k·::t ~ ..·..·~· ..f·~·~···

..........?E-~.~~~~ x J...~1. ; b.:y..~.~K)~~ .2. X k\~.~.l4-?- + 2... +~K

..... . ~~......... . ~ .

.............•.......•..........•..............••.•......•.•.•.•.•••• ~ ..••.• I.s.9.? : ~ .=-(c) At what temperature would the internal energy of LOg of helium gas be equal to

the kinetic energy of the ball in part (a) .

............ -;r..$.2. >.<: 4.¥ ..~~ ~ Z,4-..k .-Iso-s

... /13

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(1)

(3)

(1)

-13-

It is possible to use a graph of either neutron numbers or nucleon numbers, plottedagainst proton numbers, to predict whether a given nuclide will undergo one or otherof the various kinds of nuclear decay.

(a) Sketch, on the axes provided, a graph of either neutron number or nucleonnumber against proton number for the stable isotopes. Add a scale to the axisused for proton number to illustrate the ranges of values involved. [2J

-{Vi

/' ./ /0 ':e\u..A..~ /

- ~~ /'-:

-:

v-:

I( Proton number t:

[trO

(b) Explain, with reference to your sketch graph, how predictions about the twotypes of beta decay may be made. [*1

i\ ~c>k~ -h, \Z\ tdt"\ ck \'>\~ cL ~~ \ \,\, ,\- ~, , '-hrc.2 W'.g, ,....,.. f~ \-0 '" ~ ~ \,J~\\. ,.L~

~n.+-

'" ,Se. ""-~ f --''"

LE', t\

"= !~l for Question 17= 6 marks!..

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/~ (a) Explain what is meant by radioactive decay.

........................ck..~ ~ ~.~ J~: A.~~~.~.~ ~ .

.........................~.~.~ ~.~ ~.l. w.:- ~.~.k.~ .

(b) The rate of decay of a radioactive sample was measured with a Geiger counter over aperiod of a day. The graph below shows the results of this experiment.

-? ~):._:_::~••··.:Il:I.,T.'H- ..-i-·+++·-jtJ:EnTft·±:t:l~±![tt~I:I]:J~[i:.i~lIHtl~j:rl:J.1JI!Jtt-jItj400,\~.

, 1 ; ; ; ;: ; i, ! , .

. : ; i : I

! ;; l----L: ! ;

i I! 1 ! i .

h· ..·\

j!, ! I I I , ' •• :; I ;'. .... .:

j,tJ--£Fti'_1--;'-ri-H-+"1',~~. -'i~$tf-1EJ1~tt1-..,::'j~jth-Hf- ) i

~', ~•.~t: :"'",+.'-I..!.,:.,' ...: ".I·.+,+J.,i"=+11.:;trltl ..!..,:.+ ..,..,,·+P+1fft u~I)]:~:Jhmil

O~0~~IWt~~4W=~~~+8~=+I!=t412~tq~~I'~621~WJ'==;~Ojdi+==~2+4~

-l~'L

Use the graph to estimate

(i) the background activity in becquerel,

-----i.~ Time (hours)

..............................~Q ::::... ,\. ~t- .~()~

.................................................................................................................................................................

(ii) the half-life of the sample .

....................................~ x..4..h. ?: 2..~ 2k.~.,:~ .10 i21

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Examineronly

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TURN OVER FOR QUESTION 19

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I~ A smoke detector contains a small radioactive source.

A typical source contains 1.2 x 10-8 g of americium-241 , which has a half-life of 432 years.Show that the decay constant of americium-241 is approximately 5 x 10-11

S-I .

., ~ l.,L- ~ > \" L.........A ~ ··· ······· ., tt ~"'t.. '>c' ~~ S.. "2..~ '>C 'Z..4- >c S{,(]V sJ(; ).."'-

...............................................................................................................................................

-\\ \=.. <;.. o<6")0( \ o e -...............................: ? ······························(2)

Calculate the number of nuclei in 1.2 x 10-8 g of americium- 241, given that 241 g contains6.0 x1023 nuclei .

..............\:.1.,..~ \0.-:-.~.s x 6:.Q ~ ..~.o.~~ .,;2..AtJ,

..............................................................................................................................................

')Number of nuclei = 3.:.~ ~ ~.Q .

(1)

Hence calculate the activity of 1.2 x 10-8 g of americium-241.

...........s» ? A.~ ; ~.:.Q..~ ~Q~~.~~~~ ~.~.()?': ~U.~~ .-~~

..............................................................................................................................................

Activity = J.: ?:~..~.~.t: .- (2)

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The diagram below shows the principle of the smoke detector.

Current/ detector

Radioactive ~.--+-: l~=--_~source // ~ r----JMetalplates

Radiation from the source ionises the air between the plates, and a small current isdetected. If smoke enters the detector, the ions 'stick' to the smoke particles, reducing thecurrent and triggering an alarm.

Arnericium-241 is an alpha emitter. Explain why an alpha emitter is a suitable source forthis apparatus .

..................h~.)\.\: n:M.~"?.~ ~ ,,~ <.M..~ .

...................s~~~ ~ ~ ~~ -:-:-> ~.~ ..k.. .

Discuss other features of this americium sample which make it a suitable source for thesmoke detector.

....................\..~ h~\\ \~ .••••••••.•••••........ $:.<>. ....•.. O"'c.\;.~.~.~ (. ~.~ ~.~ ..~ O..~

................................S:~""'-A;..~ \-..%~c ~ k.~ .

••• a ••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• ,

(Total 10 marks)

(2)

(3)

I Leave 1biank .

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I ~0(a)

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II

The principal thermonuclear fusion process by which the Sun produces energy is asequence of three separate fusion reactions. This process effectively combines fourprotons into one helium nucleus, releasing an amount of energy that is equivalent to themass difference between four :H atoms and one ;He atom.

Show that the energy released by the process is about 27 MeV.

1mass of IH atom = 1.00783 u

4mass of 2He atom = 4.00260u

..······~·:·~·~··~~·9.·~·..··~·..·l·~·..~···\···q:p·~·~·>.··~~~ .

........It...~ \· qJ)..J:'.i3. ..~.~ :~ ~: ~.~.~.Q ..Y.\. 7. 9.:..Q.::?~.I.'C..~

..........0.:..Q.~~.:!.A...~ ....\:..~..~...~....~~~~.~..~~ ...2...l1:..~..~..~o..~~.\~.'.)"to\.by \0 -\~) ~V-'

..............................................................................................................................................

........................~ ?-:-.~:..~ ..K..~.v .(2 marks)

(b) It has been calculated that, in the absence of any atmospheric absorption, energy fromthe Sun would reach the Earth at a rate of 1350Wm-2

•

Show that the mean rate of energy production by the Sun is approximately4 x 1026 W. Assume that there is no absorption between the Sun and the Earth.

mean radius of Earth's orbit = 1.50 x to'' m

.r ~ ~ -::/:e;- 40 Q"t T"••••••••••••••• ~ ••••••••••••••••••••••••••••••••••••••••••••••••••••••• JIIIrjo'f •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••

................~~~~ ? :'t~~ t.\:~g..~..~.J..'..~)~ ~ \3.s..9..W.~"::: S·~ \0 lv........................................................................ ~ .

(2 marks)

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(c) From parts (a) and (b), and any data needed from the Data Sheet, calculate

(c) (i) the rate at which the mass of the Sun is decreasing,

...1.~ ::=: \ a.~ :: 1:.r ~ ~Q~.~.ty :~ 1.:..'!-:..~ \Q~~~. c.,"'- T~ (vo « \0 ¥ "",s~')" tc.~ <;.--,

(c) (ii) the number of ~He nuclei that are produced per day by the fusion processdescribed in part (a) .

.......~:.¥...~ \0.~~.~ ~ (}.'i..~..~.~.~.~~ .

.............~.~~..~.\Q~..~ ~..~..~ \!-?~~~~ .

~"'L........~ ?:.:..=f x..io .

=-

(5 marks)