IGNOU BPHCT-135 June 2022 Previous Year Question Paper

Q1.Attempt any five parts : 2x5=10

(a) Define degree of freedom of a molecule. Calculate the degree of freedom for a rigid diatomic molecule.

(b) The coefficient of viscosity of helium is

Q2.6 x 10-6 Nsm2, M = 4 kg K mol! and Cy =12.5x10? JK mol. Calculate thermal conductivity of helium.

(c) Define entropy and state second law of thermodynamics in terms of entropy.

(d) Planck’s law is given by : a 2° | exp he/ARBT -1 Using this relation deduce Rayleigh-Jean’s law.

(e) Write one example each of

(i) diathermal and

(ii) adiabatic boundary of a thermodynamic system.

(f) Write down the differential form of the first law of thermodynamics explaining all the parameters.

(g) What do you understand by a phase space ?

(h) Show that in the high energy range, the Bose-Einstein distribution reduces to the Maxwell-Boltzmann distribution.

Q3.Answer any two parts :

(a) The expression of the number of molecules in Maxwellian gas having speeds in the range v to v+dvu is given by: 3/2 2 dNy = 4nN|—“—| v2 exp| -| 2° | |av 2nkgT 2kpT Using this expression, show that the expression of the most probable speed Up of a molecule in a Maxwellian gasis: 5 P m

(b) Derive the survival equation : N x =Noexp| -— 0 of for distribution of free paths. Hence, plot distribution of free paths as a function of ~. 5

(c) What is Brownian motion ? Write any four characteristics of Brownian motion.

Q4.Attempt any two parts:

(a) Obtain the values of isothermal compressibity Bp and coefficient of volume expansion « for an ideal gas. 8+2

(0) Is work a function of the state ? Explain its path dependent behaviour with the help of an indicator diagram. 1+4

(c) Three moles of an ideal gas at STP is expanded isothermally to twice its volume. It is then made to undergo isochoric change to attain its original pressure. Calculate the total work done in these processes. (Given : R= 8.3 JK mol"!).

Q5.Attempt any two parts:

(a) A freezer operates between —13°C and 33°C. Calculate (j) maximum value of coefficient of performance (w) of this refrigerator and

(ii) the amount of electrical energy required to freeze 0.5 kg of water, initially at 0°C. It is given that : Latent heat of fusion = 334 kJ kg“. 243

(b) Using Maxwell’s relations, obtain first and second energy equations. 5

(c) State Stefan-Boltzmann’s law. Write its mathematical expression. Plot spectral energy density of a black body with wavelength at different temperatures. 2+1+2

Q6.Attempt any two parts:

(a) Suppose two indistinguishable particles are placed in four states. Enumerate the possible macrostates and the corresponding microstates. 5

(b) Write down the expression for the single- particle partition function in space. Use this relation to derive expressions for entropy and pressure. 1+24+2

(c) Derive Planck’s law using the Bose- Einstein’s distribution law for photons. 5 wd, = ean a |” m pe mv2 = 2 exp] —| Ze