University of the PhilippinesCollege of SciencePhysics 731st Long Problem Set A2nd Semester 2012-2013A - 1INSTRUCTIONS: Choose the best answer and shade the corresponding circle in your answer sheet. To change your answer, cross-out and sign your originalanswer and then shade your new answer. US!U" CONST#NTS: ideal gas constant: R $ %.&'( )*+ol , $ -.-%.-/ " at+*+ol ,0olt1+ann constant: 2 $ '.&%' 3 '--.& )*+olecule ,Ste4an-0olt1+ann constant: 5 $ 6./7 3 '--% 8*+. ,(' at+osphere $ '.-'&3 '-6 9ascal'--- liter $ ' +:ogadro;s nu+ber: N# $ /.-.. 3 '-.& +olecules*+olIN!OR+olar +ass $ &..- g*+ol@ +aintained at a te+perature o4 6(( ,. #. &7/ +*s0. .-./ +*sC. 76. +*sE. /6' +*s. '.(. 3 '-& +*sThe 4ollowing table gi:es the 4raction o4 +olecules with :*:r+s below a gi:en :alue.:*:r+s4raction-.. -.-''-.( -.-77-./ -..'%-.% -.('''.- -./-%'.. -.77''.( -.%%.'./ -.A(7'.% -.A7A..- -.AA&'7. # gas +ade o4 Be +olecules satis4ies the an ideal+onato+ic gas@inside acylinderwitha piston e3pand 4ro+ an initial pressure o4 '.-- 3 '-(9a, :olu+e o4 '.-- +&, and te+perature /-' ,. The e3pansion occurs so that it traces a straight line on a pJ diagra+, and the 4inal state has te+perature /-' ,, :olu+e ..-- +&, and pressure -.6-- 3 '-( 9a. 8hat is the wor2 done by the gasC >Bint: Eraw a pJ diagra+ be4ore you co+puteO@#. 7.6- 3 '-& )0. 6.-- 3 '-& )C. /.A& 3 '-& )E. '.-- 3 '-( ). -.-- ) A - 7.&. (.7A +oles o4 a polyato+ic ideal gas >K $ '.'.7@ is allowed to e3pand at a constant te+perature T $ A-- , 4ro+ a :olu+e o4 ..6- +& to a 4inal :olu+e o4 '-.- +&. The initial pressure is '.(& 3 '-(9a. 8hat is the wor2 done by the gasC#.'.-7 3 '-6 )0. (.A7 3 '-( )C. (.6( 3 '-( )E. &..& 3 '-( ). '.(& 3 '-6 ) .(. 8hat state+ent can be directly concluded 4ro+ the 4igure belowC#. The syste+ does a positi:e a+ount o4 wor2 in going 4ro+ # to 0.0. 9oint # has a higher a+ount o4 heat co+pared to point 0.C. The syste+ absorbs heat in going 4ro+ # to 0.E. 9oint # has a higher a+ount o4 wor2 co+pared to point 0.. No conclusion can be +ade.Bour '-.6. Calculatethechangeininternal energyo4 7..6+oleso4 anideal gas undergoing isother+al co+pression at a te+perature o4 &(( ,.#. &'.' 2)0. .-6 )C. .-.7 2)E. &-7 ). - ) ./. 8hat can be said about the 4igure gi:en abo:e i4 the process 4ro+ point # to 0 is an isother+al e3pansion o4 an ideal gasC#. L $ -0. U $ 8C. U $ -E. 8 P -. L $ 8A - 8.7. The internal energy o4 an ideal gas depends on:#. the pressure only0. the :olu+e onlyC. the te+perature onlyE. te+perature, pressure, and :olu+e. the te+perature and pressure onlyBour ''.%. hot@houseto the>cold@ground. would only wor2 i4 the ground and the house were at the sa+e te+peratureBour '6(-. # Carnot heat engine using ideal gas as wor2ing substance has a Carnot e44iciency o4 -.6/6. I4 a water :apor >a real gas@ was used instead, what can be said about the new Carnot e44iciency o4 this engineC#. It will :iolate the Carnot condition in using the real gas.0. It is greater than -.6/6.C. It is less than -.6/6.E. It is e3actly -.6/6.. It cannot be deter+inedA - 11('. # Carnot re4rigerator is 2nown to operate between the te+peratures -'- =C and &- =C.It uses a polyato+ic gas >K $ '.'.7@ as its wor2ing substance.The +ini+u+ :olu+e o4 the wor2ing substance o4 this Carnot re4rigerator is ..- liters, while the +a3i+u+ :olu+e is '- liters. The coe44icient o4 per4or+ance o4 this re4rigerator is QQQQQQQQQQQQQQ.#. '.&&0. -.'%(C. /.6%E. --..6. -.'&. Bour '/(.. # clay ball o4 +ass -.-6/ 2g was dropped 4ro+ a height o4 ..' +. Upon stri2ing the ground, it stic2s to the pa:e+ent con:erting its energy co+pletely into heat. 8hat is the change in entropy o4 the syste+ assu+ing the syste+ is at standard roo+ te+perature T $ .A% ,C#. -./7 )*, 0. &.A 3 '--& )*,C. -.A% )*,E. '.. )*,. Not enough in4or+ation(&. 8hat is the entropy change o4 '.- 2g o4 ice heated so that it starts at -.-- =C, +elts, and then ends up as li?uid water at &-.- =C."4 >water@ $ &.&( 3 '-6 )*2g": >water@ $ ..6/ 3 '-& )*2gcwater $ ('A- )*2g ,#. (&7 )*,0. '... 3 '-& )*,C. '/6A )*,E. %.7- 3 '-& )*,. %../ 3 '-& )*,Bour '7((. 8hat is the ratio o4 the 4inal to initial nu+ber o4 +icrostates o4 /.6 +oles o4 a gas gi:en a change in entropy o4 (.6 3 '--.& )*,C#. '0. './ 3 '-AC. '7-E. ./. &.( 3 '-% A - 12(6. "et 2 be the 0olt1+ann constant. I4 the con4iguration o4 the +olecules in a gas changes so that the +ultiplicity is reduced to one-third its pre:ious :alue,the entropy o4 the gas changes by:#. RS $ &2 ln .0. RS $ S&2 ln .C. RS $ -E. RS $ 2 ln &. RS $ S2 ln &NE O! T#