SECOND SEMESTER – NOVEMBER 2003

CH-2800/815 – THERMODYNAMICS & STATISTICAL MECHANICS

28-10-2003 Max:100 marks

1.00 – 4.00

PART – A (10×2=20 marks)

Answer ALL questions.

If V = for 1mole of an ideal gas show that dV is a complete differential.
K_p for the reaction at 500^oC is 3.99×10^-3 atm^-1 Calculate DG^o for the reaction.
Show that .
What is chemical potential? Is it extensive or intensive?
How many components are present in a system in which NH₄Cl (s) undergoes thermal decomposition?
Calculate the number of ways of distributing 20 identical objects with the arrangement 1, 0, 3, 5, 10, 1.’
What is the significance of partition function?
What is the residual molar entropy of CO at T = O?
Identify the systems for which it is essential to include a factor of on going from molar partition function to molecular partition function a) a sample of CO₂ (g) b) water vapour.
Calculate the ratio of the translation partition functions of D₂ and H₂ at the same temperature and pressure.

PART – B (8×5=40 marks)

Answer any EIGHT questions.

Derive expressions for isothermal reversible expansion of 1 mol of Vander Waal’s gas for a) W b) D
DS of a solid in cal/k/mole is given by the equation C_p = 6.2 + 1.3 x 10^-3T in the temperature range 27^oC to 600^o Calculate DS when 1 mole of this metal is heated from 300 k to 600 k.
Derive any two Maxwell equations.
The volume of an aqueous soltuon of NaCl at 25^oC was measured in series of molalities (m) and it was found that the volume fitted the expression

V (CC) = 1003 + 16.62m + 1.77 m^3/2 + 0.km² where V is the volume of a solution of molality 1. Calculate the partial molar volume of a the components in a solution of molality 0.1.

325 g of N₂O₄ when heated was found to occupy a volume of 500 ml at 45^oC and at 800 mm Hg pressure Calculate i) Kp ii) pressure at which the degree of dissociation is 50%.
Explain how partition functions can be separated.
Calculate the standard molar entropy of Xenon gas at 100 K.
Calculate the electronic partition function of a Tellurium atom at 500 K using the following data.

Term Degeneracy Wave number (cm^-1)

Ground 5 0

1 1 4707

2 3 4751

3 5 10559

Explain how the absolute entropy of a gas at 25^oC can be determined using third law of thermodynamics.
Compare Maxwell – Bolltzmann, Fermi – Dirac and Bose – Einstein statistical distributions.
Calculate the molecular rotational partition function for N₂ (g) at 27^o

(I = 13.9 x 10^-47 kgm^-2).

Derive an expression for transnational partition function.

PART – C (4×10=40 marks)

Answer any FOUR questions.

a) Derive Gibbs – Duhem equation.
b) Show that for 1 mole of a van der waal’s gas.
a) Explain how activity coefficient of an electrolyte be determined using EMF data.
b) Derive thermodynamically phase rule equation.
a) The virial equation of state for N₂(g) at O^oC is

PV = RT – 1.051 x10^-2 P + 8.63 x 10^-5 P² + ….

Where P is in atm; V is in litres. Find the fugacity of N₂ at O^oC and 100 atm.

pressure.

b) Deduce the expression for the variation of chemical potential with i) temperature ii)

pressure.

State the postulates of Maxwell – Boltzmann statistics and hence derive an expression for the most probable distribution.
Compare Einstein’s theory of heat capacity of solids with Debye’s theory.
a) Explain how equilibrium constant of a reaction be obtained using statistical mechanics.
b) Explain transition state theory using statistical concepts.
a) Derive the relation

E = .

b) Calculate the vibrational contribution to the entropy of Cl₂ at 500K if the wave

number of the vibration is 560 cm^-1.

Go To Main Page