BACHELOR OF SCIENCE (B.Sc.) Term-End Examination

Transcription

1 No. of Printed Pages : 8 PHE-06 BACHELOR OF SCIENCE (B.Sc.) Term-End Examination June, 2016 PHYSICS PHE-06 : THERMODYNAMICS AND STATISTICAL MECHANICS Time : 2 hours Maximum Marks : 50 Note : All questions are compulsory. However, internal choices are given. You can use non-scientific calculator or log table. Symbols have their. usual meanings, unless stated otherwise. Marks are indicated against each question. 1. Answer any three parts : 3x5=15 (a) Calculate the thermal conductivity of a gas using the following data : p = 1.6 kg m-3, = 480 ms-1, X = 8 x 10-8 m, M = 32, y 1.4 and R = 8.31 kj kmorl K-1. (b) Calculate the change in temperature when oxygen gas at 27 C is made to undergo adiabatic throttling and the pressure is reduced by 50 atm. Given a = 132 x 10-2 Nm4, b = 31'2 x 10-6 Itt3 mo1-1, R = 8.3 J mol-1 K-1 and Cp 3-5 R. PHE-06 1 P.T.O.

2 (c) A student is working in a physics laboratory on sonometer, whose wire has cross-sectional area 0.86 x 10-6 m2. A tension of 20 N is applied at the free end. The wire is stretched between two rigid supports 1.2 m apart. If the temperature is reduced by 12 C, calculate the final tension in the wire. The coefficient of linear expansion and isothermal Young's modulus may be assumed to be constant at the values 1.5 x 10-5 K-1 and 2.0 x 1011 IsTm-2. (d) Consider a one level system having energy E = kbt /n (V/V0), where V is the volume and Vo is a constant. Obtain an expression for pressure for this system. Discuss the significance of your result. 2. What is thermocouple? How is it used to measure temperature? Discuss its merits and limitations OR State zeroth law of thermodynamics and write parametric as well as exact equation of state for one mole of a real gas and a paramagnetic substance PHE-06 2

3 3. (a) What do you understand by the term second order phase transition? Show that for a second order phase transition : 1+4 (C Cpl) AP P2 AT = [Tv (02 (l1)] (b) Define entropy and show that entropy increases when two gases mix Write van der Waals' equation for one mole of a real gas. Show that the critical coefficient is independent of the nature of gas. 2+8 OR (a) State two characteristics of Brownian motion. Write down the equation of motion of a free Brownian particle moving along a particular direction using Langevin's arguments. Why do we work with mean squared displacement rather than mean displacement? (b) Calculate the diameter of a molecule of helium using the following data : van der Waals' constant b = 2.42 x 10-5 m3 mo PHE-06 3 P.T.O.

4 5. (a) Show that the phase space of a linear harmonic oscillator is an ellipse. 3 (b) Obtain an expression for BE condensation temperature. 7 OR (a) (b) Write down Planck's formula for black body radiation and show that it contains Wien's law, Rayleigh-Jeans law and Stefan-Boltzmann law Plot Fermi-Dirac, Bose-Einstein and Maxwell-Boltzmann distribution functions at a finite temperature as a function of energy on the same graph. 3 Physical constants : NA = 6.02 x 1023 morl kb = 1.38 x J K-1 l K-1 R= 8.31 kj kmor PHE-06 4

5 tft.l.. -O6 I "1 l inch (*.KR ;ft.) MiW VNTr 'V', 2016 fftwiimr-4 : ssvoilit tii6/41t4 EON. : 2 F:14 alftffq NW: 50 Oz. ; I7 raw. arftref, ff, 1.4.hr1 mr( 34oi/2w 4-ff-da 3r2r47 eipi inud Tpir)7T tfan- ff Nee. NO Ws/fret ff,v4ch ? filq4 ft Ffiv TA *28T e4r : 3x5=15 PHroRgi 3ft-41 * 31111R IR 4ff vochcrirrc11 *OR : p = F6 kg m-3, i = 48O ms-1, X = 8 x 10-8 m, M = 32, y = 1-4 MIT R 8-31 kj kmorl NO 27 C IR31Tq4flc*N. *1- tog t4i 4 1-K ql , * 50 atm *-1:1 t I 1I'il.n4 t4. qic.1 tit R I ikeit TRIT : a = 13-2 x 10-2 Nm4, b = 31-2 x 10- m3 morl, R = 8 3 J mo1-1 K-1 Wifft C 3-5 R. P PHE-06 5 P.T.O.

6 (T) 'RW WQ. *1)-14.11e.t 1T chl T4T t I * e.k 0-4EFF 0.85 x io- 6 ra2 t Ili * atistp.t-trft- 20 N *T alierd t I'UR fidt Qt 4th R.11* A19- ilad 14sii TIM t I -zft C febar,'ffitx1 34 PR wa *I ctircicf *If4R 1141 ukir "MT zitt * 31WK TR 1.5 x 10-5 K-1 WiTT 2.0 x 1011 Nm-2 #1f4R (4) Ct.40-4 E = - kbt In (VIV 0)t, 3 w'c~tt V0 1 3 t I414 oeiact) 3rrqr altr4 * i=t4r 2. -Mg- IT4 SIT? 4tichl 3TTATT M. A % 14)41i? T{41- wdrc I MIZIT ilt41111 W' f611:47 ct.) fref Wall zr izgrai (cislki) Tka * 1C,R moiiciet) err zratra 3Tḏk:ZIT tii.ficrykui Air PHE-06 6

7 3. (W) th migt.vit tistam 311Er 1;EIT 1:11TO vf4-4 Ari* -1* f cflq ch1f2 tiactikut 14HRIRsiti cgia4 9 '101 : 1+4 Op (CP2 Cpl ) AT [Tv (02 PO] () R4fft *my R-11Z0 warrik4w4g * xur 3rWir 4 wilt of tr4ft-m (110i).10i' vt, frff l Ikef qiust arcytt toficku l *NR f %irda* mca trt f Tif gntcr r"4 I 2+8 () rat TA AI -k' 0 elictivt I c1i 1 q(.)44.11 (A) * 31-mm -ER feoz 4 g-* 01,141 TA TAT TA imtii7 I -qtr ITTIR 1:1414 tit iwizfier 44 Mgr WA" likcbrict cbt;" #? NO AHRI * artir tr lifezpr * apj vr el itf *1-1* : artist arc-t+ W214 b = 2.42 x 10-3 m3 mo PHE-06 7 P.T.O.

8 5. *If- 1* If et) ag-4-41 t-ew *1- pia i lteipi 3 rtanich i1ki-3ir-i-4244 (BE) Mtl ,1 surt trf4r I 7 aen' Tfik-wr fikkur fait -fflarr *AR I* AIR iii-itileviii.i Pito' *ki4 itoi t I (s) Tgfr-itk-m, ctki -41B-3TET4reriq teg 1:RTRI 411 LiRfo 1C.,R "R" ' RP:5 TR It* 3 Oft fl gruel) : NA = 6.02 x B = 1.38 x J K-1 k -1 R= &31 kj km01 PHE ,000