Physics 123. Exam #1. October 11, 2006

Transcription

1 hyscs Exa # October, 006 roble /0 roble /0 roble /0 roble 4 /0 roble 5 /0 roble 6 /0 roble 7 /0 roble 8 /0 roble 9 /0 roble 0 /0 Total /00

2 Free-Response robles: lease show all work n order to receve partal credt I your solutons are llegble no credt wll be gven lease use the back o the page necessary, but nuber the proble you are workng on Each proble s worth 0 ponts ressure, volue, and teperature T are related, or a certan ateral, AT BT by = where A and B are constants What s the work done by the ateral the teperature changes ro T to T whle the pressure reans constant? Snce the pressure s constant, the work s gven by AT BT The ntal volue s = AT BT The nal volue s = Thereore the work done sw =, where, where [ A( T T ) B( T T )] T T ( ) s the ntal teperature W = s the nal teperature A contaner encloses two deal gases Two oles o the rst gas are present, wth olar ass M The second gas has olar ass M = M, and ½ ole o ths gas s present What racton o the total pressure on the contaner wall s attrbutable to the second gas? n RT The pressure due to the rst gas s =, and the pressure due to the nrt second gas s = Thus the total pressure on the contaner wall s ( ) RT = + = n + n The racton o the total pressure due to the second gas s then n RT 05 = = = = ( n + n ) n + n RT n

3 A dvergng lens wth a ocal length o agntude 5c and a convergng lens wth a ocal length o agntude c have a coon central axs and are separated by c An object o heght c s 0c n ront o the dvergng lens, on the coon central axs (The orderng, ro let to rght s objectdvergng lens-convergng lens) What are the nal age propertes and where s the locaton o the nal age? The rst age locaton s gven by + = d = = 60c The agncaton o the do d 5c 0c rst lens s the negatve rato o the age dstance to the object dstance and s 06 Now the new object dstance s gven as c + 6c = 8c Thereore the nal age locaton s + = d = = 6c Ths do d c 8c gves a agncaton or the nd lens o - The total agncaton s the product o that or lens and lens, or - Ths eans the age s c tall, and the nal age s real, nverted and enlarged 4 A bubble o 50 oles o helu s suberged at a certan depth n lqud water when the water (and thus the helu) undergoes a teperature ncrease T o 0 o C at constant pressure As a result the onatoc and deal gas bubble expands How uch energy s added as heat to the helu durng the ncrease and expanson and how uch work s done by the helu as t expands aganst the pressure o the surroundng water? Snce the pressure s constant, the heat Q = nc T, where C = C +R or an deal 5 J gas Thereore we have Q = n( C + R) T = 5 ol 8 ( 0K ) = 077 5J ol K The change n nternal energy s J Ent = nc T = 5ol 8 ( 0K ) = 46 5J ol K

4 5 The yrex glass rror n the telescope at the Mt aloar Observatory has a daeter o 00 nches The teperature ranges ro -0 o C to 50 o C on Mt aloar Assung that the glass can reely expand and contract, what s the axu change n daeter o the rror n croeters? (Hnts: There are 54c n 00 nch and the coecent o lnear expanson or yrex glass s x0-6 / o C) The change n daeter s gven by L = Lα T Thereore, 6 6 o o 54c 0 µ L = 00n 0 ( C) 60 C = 84 0 n n 00c = 9754µ 6 Lght o wavelength 440n passes through a double slt, yeldng a dracton pattern whose graph o ntensty I versus angular poston θ s shown below What are the slt wdth and slt separaton? The rst dracton nu occurs at 5o Thus asnφ = λ a = = = 5 05µ o sn 5 The nuber o spots s related to the rato o d to a The total nuber o spots s 9, d d then # = + = 9 = 4 d = 4 505µ = 0 µ a a

5 7 A che, on ndng the stove out o order, decdes to bol the water or a custoer s coee by shakng t n a Theros lask Suppose that he uses tap water (c = 490 J/kgK) at 5 o C and that the water all 0c each shake and that the che akes 0 shakes per nute Neglectng any loss o theral energy by the lask, how long ust the che shake the lask untl the water reaches 00 o C? The ass M o water ust be rased ro T = 5 o C to T = 00 o C I c s the specc heat o water, then the energy requred s Q=Mc(T T) Each shake supples energy gh, where h s the dstance oved durng the downward stroke o the shake I N s the total nuber o shakes then Ngh = Q I t s the te Ngh Q taken to rase the water to ts bolng pont then = The nuber o t t shakes per nute s the rate, so the te t J Q Mc( T ) c( T T ) ( K ) T 490 kg K 85 t = = = = s Rate Mgh Rate Mgh Rate gh 0 n = 97 0 n = 8days s 8 Gas wthn a closed chaber undergoes the cycle shown below n the dagra What s the net energy added to the syste as heat durng one coplete cycle? Over a cycle the nternal energy ust be the sae so the heat Q absorbed equals the work done W Over the porton o the cycle ro A to B, the pressure s a lnear uncton o the 0 N 0 N volue Thus = + where the coecents were chosen so that = 0N/ when = and = 0N/ when = 4 Thus the work done by the gas durng ths porton o the cycle sw = AB d = + d = + = 60J The porton BC o the cycle s at constant pressure, so the work done s = - 90J The CA porton s a t constant volue, so no work s done Thus the total work done by the gas s W net = 60J 90J + 0J = -0J The heat absorbed s -0J, so the gas loses 0J o heat energy Another, easer ethod, s to realze that the work done s the area under the curve, so N N N W = W W = = 90J 60J ( ) ( ) ( ) = J net BC AB 0 and thus the gas loses 0J as heat 4

6 9 We know that or an adabatc process γ = a constant What s the constant or an adabatc process nvolvng exactly 0 oles o an deal gas passng through the state havng = 0at and T = 00 K, the gas s datoc and the olecules have rotaton but no oscllatons? γ γ 7 nrt γ 5 N 5 = = nrt = ( 0 0 ) ol K = 5 0 N ( ol 8 J 00K ) 0 A whte dwar s the core o a dead edu szed star lke the Sun When a star lke the Sun des, t passes through several phases endng soetes as a Red Gant When the orces o gravty cannot hold onto the solar atosphere, the atosphere dsspates nto space and what s let s a whte hot core called a whte dwar How long (n years) wll t take or a whte dwar (at a teperature o 4,000K) to radate away all o ts energy to space (at a teperature o K) the whte dwar has a ass o x0 0 kg? Assue urther that the whte dwar s an deal etter, coposed entrely o carbon (wth an atoc ass o,) and that the radus o the whte dwar s 5500 k The te s gven by Nk 56 J B K t = = 8 W σεa T T nal ntal K 4 yr 6 = 6 0 sec = 4 0 yrs 6 0 s 4 ( K ) ( 4000K )