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1 No. of Printed Pages : 8 BP11E-106/PHE-06 BACHELOR OF SCIENCE (B.Sc.) Term-End Examination June, 2018 PHYSICS BPHE-106/PHE-06 : THERMODYNAMICS AND STATISTICAL MECHANICS Time : 2 hours Maximum Marks : 50 Note : All questions are compulsory, but internal choices are given. You can use calculators or log tables. Symbols have their usual meanings. The marks for. each question are indicated against it. 1. Answer any three parts : 3x5=15 (a) Two identical gaseous systems, each containing 0.06 mol of ideal gas are at 300 K and 2.0 atm pressure. The ratio of heat capacities of the gas is F4. One of the gases is made to expand adiabatically and the other isothermally until they are at normal pressure. Calculate the final volumes in each case. BPHE-106/PHE-06 1 P.T.O.
2 (b) (c) (d) Derive Clausius-Clapeyron equation for the first-order phase transition. Starting from the equation of motion of a linear harmonic oscillator, show that its phase space is an ellipse. Calculate van der Waals' constants for helium using the data Tc = 5.3 K, pc = 2.25 atm and R = 8.31 J morl K Establish Boltzmann's entropy relation. OR Derive an expression for adiabatic lapse rate Using Maxwell's relations for a van der Waals gas, show that au av T v2 (--) = a 10 OR (a) One mole of an ideal gas is expanded isothermally to four times its initial volume. Calculate the entropy change in terms of R, the gas constant. 4 BPHE-106/PHE-06 2
3 (b) Draw a labelled diagram for the experimental arrangement used in adiabatic demagnetization of a paramagnetic substance. State the lowest temperature attainable with this method What is Brownian motion? Give two examples of Brownian motion. Discuss Perrin's experiment to determine Avogadro's number OR What is transport phenomena? Obtain the expression for viscosity of gas by assuming that the number of particles crossing the plane from either side per unit area per second is 1 nvr Discuss its temperature and pressure dependence BPHE-106/PHE-06 3 P.T.O.
4 5. The thermodynamic probability for a Fermi-Dirac system is given by w.n gi!. (g. N.)!N.! Using this, derive an expression for the distribution function and plot it for T = 0 K and T > 0 K. 8+2 OR Write Planck's formula for energy density of a black body radiation. Show that Rayleigh-Jeans law, Wien's law and Stefan's law are contained in it BPHE-106/PHE-06 4
5 I littit.w.i.-106fift.7.f.-06 (*.TT ift.) Tiftwr T'4, 2018 Ofkaefd,M w.i.406/Eft.7w.i.-o6 wen tll?mt : 2 Eir7 ariii*vg 37-W : 50 3e4FITef TRT. feheif 777 g arm 4.15ckj Ri7T fll(1447 3iT Pik wf fond g 1N-d* anf ff / Stre?ch * flog dff fist 1. f*- 1 R9T tf'4r : 3x5=15 atiim C I 300 K 311K '4T4 2.0 atm t I 51co)ch A mol 3TT filtt tir WsrfT VerdTall 3137M 1.4 t I * ter Tr tem t1 4-1C11 3ruR Ref! 7r-dr t 74 imich T R Tef 3u70 I * *RR atr4-dq 4114)1Zio *1.1* BPHE-106/PHE-06 5 P.T.O.
6 (w) 'm.1;1p. 31T-4p-u witi-44r-.04th cntui 9Frff *C.-4R I (Tr) IRsich 31T-4-41 A'r ti41.ntui -srritt *Cr-A7 ITF*r 3rrap-rr TrITR teir t I (1:0 3ft-4 Tc = 5.3 K, pc = 2.25 atm a* R = 8.31J mo1-1 K-1 1 dqq)ii clity*1 PR* 1.41.kcni *=rnr tfk41:f* 2. Vft # :21TRIff trpa I 5 te=4i wt TETT etolch mre:ff te4r I 5 3. ctti t1 el krt.! ATI filog*ii7r : (u) a v TerIT () 1-I (I 3110 "A.q NtIlk srri- RF: 3.171R *1 9R "T4T t I ttl R tr-41 7V:11 trk yldr I 4 BPHE-106/PHE-06 6
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8 5. 1:541-Ivi dv=4.11, 16t) NI 4)11 eeiact, : gi (gi Ni )!Ni! *-Zq th eq otiach 9-0:FW tor 31ITT=OK3t T>OK*Te.R PcIA tilrizr I 8+2 3T2TerT TRW f44->tui d),71 (energy density) rffk To fair I Ri4 te4r Att -PelH 'a1t 14WR ill *ti4 Trgrfta- I BPHE-106/PHE ,000
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