No. of Printed Pages : 8
PHE-06
BACHELOR OF SCIENCE (B.Sc.)
CO (.0 0') CO CD
Term-End Examination December, 2011 PHYSICS PHE-06 : THERMODYNAMICS AND STATISTICAL MECHANICS Maximum Marks : 50
Time : 2 hours
Note : All questions are compulsory. Marks are given with each question. You can use log tables and non-programmable calculator.
Answer any three parts : 5x3=15 1. (a) Starting from the first law of thermodynamics, show that for a perfect gas : Cp- Cr= R
where symbols have their usual meanin0. (b) Define mean free path for the molecules of a gas in constant random motion. Assume that they move with average speed v . Show that their mean free path is given by : A
0.75 ird`n
where n is number density and d is diameter of gas molecules. PHE-06
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(c)
1 kg of water at 0°C is fully converted into steam at 100°C at normal pressure. Calculate the change in entropy. The specific heat capacity of water is 4-18 x 10 3J kg -1 K -1 and latent heat of vaporisation is 2.24 x 10 6J kg -1 .
(d)
Starting from Planck's radiation law, show that Stefan-Boltzmann constant is given by : 27r 5 k4B 15 h 3 C 2 •
2. When one mole of an ideal gas undergoes a quasistatic adiabatic change, its pressure and temperature are related as Tr = pl r = constant.
Use this result to obtain an expression for adiabatic lapse rate. OR
The nozzle of a bicycle is blocked. With no force on the handle, the pump contains a volume V of air at 300K and atmospheric pressure. The handle is pushed down so that the volume reduces to 3V/4. However, no air escapes from -the pump. Assume the change to be adiabatic and calculate the final temperature of air in the pump. Take 'y = 1.4. PHE-06
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3. What is Joule-Thomson Effect ? For a gas obeying
Van der Waal's equation of state, obtain an expression for Joule-Thomson coefficient. Discuss the physical implications of your result for 2+6+2 producing low temperatures. OR
(a)
Show that the fermi energy at absolute zero 5 is given by :
EF
(b)
h 2 ( 3N 2 2m 8,7V
Assume one conduction electron per atom 5 in a metal at room temperature and take N/ V = 5.86 x 10 28 m -3 . Show that the electron gas is strongly degenerate.
4. (a) The entropy is additive and Thermodynamic 5
probability is multiplicative. Using these facts, establish the relation : S = kB ln W where kB is Boltzmann constant. (b) Derive Sackur - Tetrode equation for an ideal 5 gas and show that it is free from Gibbs paradox. PHE-06
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5. (a) A steel wire of length 2.5 m and area of 5 cross-section 2-5 x 10 -6 M 2 is suspended from a torsion head. A 5 kg weight is suspended at its free-end. Calculate the work done on the wire. Take Y= 2 x 10 11 N in 2 . OR Write down Van der Waals' equation of 1,4 state. How does it compare with experiments. (b) An experimentalist observed the motion of
5
soot particles of radius 0.4 x 10 -4 cm in water - glycerine solution characterised by = 2.78 x 10 - 2 kg m -i s - 1 at 300K for 10s. The observed value of 0 x2 was 3.3 x 10 -8 cm 2 . Calculate Boltzmann constant and hence Avogadro's number. OR Calculate the change in melting print of ice 5 at 0°C when pressure is increased by 2 atm. Given L = 79.6 Cal g -1 and specific volumes of water and ice are 1.0001 cm 3 and 1.0908 cm3, respectively.
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P.T.O.
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PHE-06
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TIT
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ftTz CI I LI 4-11-1 T = 0° K "cfT 41 4-11 f97cFri ('r1 1-'1R1 RA
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/%111
.TT 5
04■31ch :
h 2 I 3N \ 2/3 2m 8.77..V
let) tiTg dr-1 4-114 -97 .) oiwzr)
(b)
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ITU:19 1:rrffcT lT N/ V=5.86 x 1028m — 3 #1-Z zff '1 *-1 3TqW t I
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PHE-06
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tI P.T.O.
5. (a)
2.5 m
rf
33 2.5 x 10 —6 m2 31-19T-21. 11-FT— Q7q 1
5
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head) tf odcbiqi 7:1* -13Wf
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(=h1-Cic1 .w1f771 Y 2 x 10 11 Nm -2 .
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(b)
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=2.78x10-2 k g m -i s -1 t
0.4 x 10 -4 cm "NwIT 1 chlrot5
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t L=79.6 Cal g -1 727 41.11
Td <3,4 fq-FTE
3TPrdi sil+-Rf: 1.0001 cm3 47 1.0908 cm3 t I
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