Solutions to Thermodynamics & Statistical Mechanics 08/09 SEM 2: Questions 1-6, Exams of Mechanics

Download Solutions to Thermodynamics & Statistical Mechanics 08/09 SEM 2: Questions 1-6 and more Exams Mechanics in PDF only on Docsity! 1 PC2230 Thermodynamics & Statistical Mechanics 08/09 SEM 2 Solutions PART I Question 1 Adiabatic, đ = 0, ⇒ đ = = ,   =   ∴  =    =   − 1 1   =  − 1 1   − 1   =  − 1    −    =  − 1     − 1 Question 2 ! = " − #$ = %& − # ln  )!%! +) − %,!  1# = -$-" = -$-% -%-" = & -$-% $ = 2 /ln)! − ln %! − ln+) − %,!0 -$-% = 2 − --% ln%! − --% ln+) − %,! = −2  --% +% ln % − %, + --% 2+) − %, ln+) − %, − ) + %3 = −2 /ln % + 1 − 1 − 1 − ln+) − %, + 10 = −2 ln 4 %) − %5 &2 # = ln ) − %%  6 789 = )% − 1 %) = 16 789 + 1 2 PC2230 Thermodynamics & Statistical Mechanics 08/09 SEM 2 Solutions Question 3 : = ;+2< + 1,6=>7?@?A ℏCD+DA,E D = ;6=7?@? D ;+2< + 1,6=7??F@ D = :GDHIJ:DKG :GDHIJ =  L+M,6= NOPQ M =  4SMℎU 6= NOP Q M =  2SV #ℎ  U :DKG = 1 + 36=ℏC + 56=UℏC + ⋯ Let ] = <+< + 1,, ] = +2< + 1, < :DKG ≈  +2< + 1,PQ 6= ℏCD+DA, < =  6=ℏC_PQ ] ⇒ 2`aℏ for &D # ≪ 1. ∴ : = 2SV #ℎ  U  2`aℏ = 2SVℎ  2`ℏag "h = −-+ln :,-a = − --a ln  2`ℏ  + 32 ln 2SVℎ  − 52 ln a = 52 # i = ) -"h-# = 52) Question 4(i) :+ , #, = ;;…26=I76=I76=Ik7k …3 II = ;6=I7 I ;6=I7 I ;6=Ik7k Ik … = 11 − 6=7 11 − 6=7 11 − 6=7k … = l 11 − 6=7? P Dm Question 4(ii) %hD = − 1a -+ln:,-&D = − 1a --&D ln  11 − 6=7 11 − 6=7 11 − 6=7k … = 1a --&D ;ln21 − 6=7n3o = 1a a6 =7? 1 − 6=7? = 16=7? − 1