Aligarh Muslim University (AMU) 2009 B.Sc Physics Thermal and statistical - Question Paper
4291
2008-2009
B.Sc.(HONS.) (PART-III) EXAMINATION PHYSICS
THERMAL AND STATISTICAL PHYSICS (PH-304)
Maximum Marks: 40 Duration : Three Hours.
Answer all questions.
The marks are shown against the questions.
The symbols have their usual meanings.
Use of calculator is permitted.
j. ..
1 .(a) Starting with the expression for the flux of 0 v molecules at a surface, derive
the equation of state of an ideal gas. 05
(b) Briefly discuss what do you understand by fluctuations and Brownian motion? 02
OR
1 (a) How do you define the microscopic and macroscopic cross-sections? Obtain an
expression for the mean free path of gas molecules. 05
(b) A beam of molecules of radius 2 x 10 -16 m strikes a gas composed of molecules whose radii are 3 x 10' m. There are 10 24 gas molecules per m 3. Determine
(i) the radius of exclusion and
(ii) the fraction of molecules left in the beam after it travels 106 m in the gas. 02
2.(a) Define the empirical and thermodynamic temperatures. How are the two temperatures related?
03
03
(b) Derive the following thermodynamical relations:
(i) Ct- Cv =
3T >V
3.(a) S|tate the Clausuis and the Kelvin-Planck statements of the second Law and show that the two statements are equivalent. 04
(b) Sketch a Carnot cycle for an ideal gas on a (i) T-S diagram and (ii) u - v diagram. 02
4.(a) Discuss the porous plug experiment and draw the isenthalpic curves and inversion
I
chrve for a gas. Show that the Joule- Kelvin coefficient for a gas is given by
What is the importance of this experiment in liquefaction of gases? 2+3+1
-2-
(9v_\ _vl ' 3T Ip J
OR
4(a) Define the first order and the second order phase transitions and obtain the
Clapeyron equation. 04
(b) Derive the following Maxwells relations 03
' 9T /v [ av It Ut/p IttIt
5.(a) Define the ensemble, the micro and macro-states and the thermodynamic probability. 02
(b) What is the statistical definition of entropy? Show that the entropy of a system is given by
S = KnQ ,
where Q is the thermodynamic probability of the system. 05
6. What is a quantised linear oscillator? Show that the partition function for an assembly of such oscillators is given by
exP(-0/2T)
Z -
1 - exp('0/T)
where G is the characteristic temperature. ' 07
OR
6. Smarting from first principles, obtain the Rayleigh-Jean formula for the black body
radiation. Whal is the ultra-violet catastrophe? 6
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