Ex/Met/T/224/95/2011(S)

BACHELOR OF METALLURGICAL ENGG. EXAMINATION, 2011

(2nd Year, 2nd Semester, Supplementary)

Thermodynamics of Materials

Time : Three hours Full Marks : 100

Answer any five questions : -

1. i) The heat of combustion of tungsten carbide, WC at 298K

is-1195 KJ/mol. Determine the standard heat of formation

of WC at the same temperature, w c , 298HD

Given,

3

2

wo ,

Co ,

o

o

298

298

H 832 KJ /mo l

H 394 KJ/mol

D = -

D = -6

ii) Show that for the change of state, 1 2 , for n moles ofan ideal gas

1 V 2 VS / C S / C1 1 2 2P V . e P V . e

g g- -=

Where both S and CV are molar properties. 7

iii) The molar free energy of a metal at a 1atm is consideredto vary with temperature as follows :

G = 30,000 + 175 T - 25 T lnT

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5. i) Show that the change in volume with temperature of afixed quantity of vapur which is in equilibrium with theliquid phase is given by the expression.

evap( d V / d T ) / V (1 H / R T ) / T= - D 10

ii) The activity coefficient of Cd in liquid Cd-Zn alloys at4350C can be represented by log g cd = 0.185

2 3zn znX 0.13X+ . Calculate the corresponding expression

for the composition dependence of log zng and hencecalculate a

Zn in the X

cd = 0.6 alloy at 4350C. 10

6. i) Three moles of O2 is passed over a bed of hot carbon

(excess) at 950 K and 1atm pressure in a flow reactor.The exit gas, which essentially containts CO and CO

2(with negligible O

2), leaves the reactor under equilibrium

with C. Find the moles and partial pressures of CO, CO2

and O2 in the exit gas.

(for data, refer to Question 3.) 15

ii) Calculate the difference ( )H UD - D for the reaction

23O (g)3

O (g)2

=

Occurring at 500C and 1atm pressure. 5

( 4 )

x

( 2 ) ( 3 )

Find the molar entropy S and molar heat capacity CP of

the metal at 500 K. 7

2. i) Carbon has two allotropes, graphite and diamond. At 250Cand 1atm pressure, graphite is the stable form. Calculatethe pressure which must be applied to graphite at 250Cin order to bring about its transformation to diamond.

Given,

H298

(graphite)

= H298

(diamond

) = -1900 J/mol

S298

(graphite)

= 5.73 J/K. mol

S298

(diamond)

= 2.43 J/K.mol

rgraphi te,25

oC=2.22gm/cc; r

diamond,25o

C=3.515 gm/cc

10

ii) For the reaction 2 n On ( V )1

0 (g) Z ( s )2

Z + =

0G 482 ,920 18.80TInT 344.7 T JD = - - +

Find 0 0 0PH , S , and ( C )D D D for the reaction at 1000K.10

3. i) Show that for fixed mass and fixed composition systems

2

2

PT

S V

p

p

C Va) T

P T

Cpb)

V C Vb

= -

= -

8

ii) Is it possible to bring a CO-CO2 gas mixture, at a total

pressure of 1atm, into contact with liquid A1 at 7000Cwithout having either solid Al

2O

3 or solid AI

4C

3 form?

Given :

0

2

0

2 2

0

2 2 3

0

4 3

1a)C(s) O (g) CO (g); G 111, 700 87.65TJ

2

b)C(s) O (g) CO (g); G 394,100 0.84T J

3c)2AI(1) O (g) AI O ( s ) ; G 1687,000 326.8TJ

2

d)4AI(1) 3C(s) AI C (s); G 265,000 95.1T J

+ = D = - -

+ = D = - -

+ = D = - +

+ = D = - +

12

4 i) Write the Ellingham reaction for the oxide M3O

4. Find the

relation between the standard free-energy change of theEllingham reaction and the standard free energy offormation of M

3O

4.

Plot the standard free-energy change of the aboveEllinghan reaction against temperature (T), showing themelting point of M and M

3O

4 each. 10

ii) A gas mixture of 30%CO, 10%CO2, 10%H

2 and 50%N

2

(by volume) is fed to a heat treating furnace at 9270C.Calculate the equilibrium composition of the gas(CO-CO

2-H

2-H

2O-N

2) at a total pressure of 1atm.

Given :0

2 2 2

1H (g) O (g) H O ( g ) ; G 246,000 5 4 . 8 T J

2+ = D = - +

(For other data, refer to Question 3.) 10

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