Solutions Manual
to accompany
INTRODUCTION TO
THE THERMODYNAMICS OF MATERIALS
Fifth Edition
David R. Gaskell
School of Materials Engineering
Purdue University
West Lafayette, IN
INTRODUCTION
This solutions manual provides worked-out answers to all problem
A
Quiz Introduction to Thermodynamics of Materials Dec. 19h 2013 /
i=1
Namemm omsxs
1 . .
l. (a) Start with d8 = EdU+dV, derrveASln terms of CWT and V, as T and V go from T1 to T2 and
V1 to V2, respectively. q 3
7
(b) calculate AS for an ideal gas at
Page 47
Solving for v and substituting the given values of p, b and I) gives
e 0.00167 -12 -1
=_=0.734.10 m-s
1 p~b 1014-0248-10-9
-7
10_T=4.032-1012 m-s'12
10 0243-10
&1
111 =
5.20 Necking of a tensile specimen begins at a true strain of 0.20. The corr
Page 52
6.2 According to quantitative metallography, N1, the average number of grain-boundary
intercepts per unit length of a line laid over a microstructure is directly related to S, Wrea
f as:
per unit volume, by the relation
A~f f
Su=2NI
(3) Determine
Page 45
5.16 For the case of tensile deformation considered in Prob. 5.14, determine the indices of the
primary, conjugate and cross-slip systems as well as those for the critical plane.
Solution:
(a) The primary system is (111) [011].
(b) The conjugate s
Page 43
muss Fri Jun 07 xa-Jtzli Isul
5.14 (a) The diagram accompanying this problem shows a 111 standard projection of a fee
crystal in which the standard stereographic triangles are outlined. Assuming that point a in the gure
represents the orientatio
Page 48
area, A5, or
P
of = " = _100_ = 1.273 .107 Pa. = 12.73 MPa
A.- (1: - (.01?)
4
al area minus the nal area divided by the initial
(c) The reduction in area, RA, is dened as the initi
0-7 A:
areaor
A.-A
where RA = 0.3, Ai = 7.85 - 10'5 m, thus h 3
Page 50
Now solve for p
where do is the intercept of the straight line, through the data in Fig. 5,35, with the stress axis. The
value of arc, is 39 kg/mm2 and k = 2.55-10"l kg2-cm. Accordingly for the 60 kg/rm-n2 stress we
mm
have
_ 6039 2_ 9 3_ 13 3
g
/
12.2, A diffusion couple, made by weldin a thin one-centimeter uare slab of pure metal A to a
similar slab of pure metal B, was given a diffusion anneal at an elevated temperature and then cooled
to room temperature. On chemically analyzing successive l
8.2 (a)Using the 283K data, given ain Sec. 8.5 for the Drouard, Washburn and Parker
zinc single crystal, determine the value of A in the rate equation, Eq. 8.2.
(b) Next determine the temperature at which the crystal should recover one-fourth
of its yield
Introduction To The Thermodynamics of Materials
2nd midterm solutions
Graders: (#1, #2, #4),
(#3, #5, #6), (#7, #8)
1.
<sol>
2.
<sol>
(a)
Total number of lattice site is N
Total number of lattice site for A is NA
Total number of lattice site for B is NB
Multi-element high entropy alloys
( )
Thermodynamics in Materials Science
Alloys evolution
Traditional alloys (~1930)
one major element. Total element # usually 3
major element usually 50%
Fe-Al alloys
Super alloys (after 1940)
applications in aircraf
Introduction to the thermodynamics of materials
science (II)
Final solutions
Exam time: June 17th, 2010
#3, #4,#5 graded by ; #1, #2graded by
;
1.
(a
) G M RT X A ln X A X B ln X B RT X A ln A X B ln B
(b (total 7 points)
2
2
;
Q
ln
X
ln
X
)
A
B
B
A
an
Introduction to the thermodynamics of materials
science
Final exam solutions
Exam time: Jan. 5th, 2010
#1,#2,#8 were graded by ; #3,#4 were
graded by ; #5,#6,#7 were graded by
1.
A: 1st law : dU q w(micro world) or U q w(macro world)
The increase in the
Introduction to the thermodynamics of materials
science (II)
Final solutions
Exam time: June 17th, 2010
#3, #4,#5 graded by ; #1, #2graded by
;
1.
(a
) G M RT X A ln X A X B ln X B RT X A ln A X B ln B
(b (total 7 points)
2
2
;
Q
ln
X
ln
X
)
A
B
B
A
an
Introduction to the thermodynamics of materials
science (II)
2st midterm solutions
Exam time: May 20th, 2010
#1, #5,#7 graded by ; #2 #3, #4, ,#6
graded by
1.
(a
)
3 points for each one
(b
)
The non-ideality for gases is because (i) the molecular attract
Midterm score distribution
1.(a)
U = Ufinal-Uinitial
= (0.17Tfinal+C)- (0.17Tinitial+C)
=0.17(Tfinal-Tinitial )
=0.17(315-40)
=46.75(kJ/kg)
Since volume is fixed, W=0 (2 )
U= Q= 46.75(kJ/kg) (4 )
6
This one was graded by
1.(b)
From q=Tds , dS=q/T=dU/T
Midterm score distribution
Avg. 84.8 .too high, I need to raise the difficulty of
the problems next time.
1.(a)
U = Ufinal-Uinitial
= (0.17Tfinal+C)- (0.17Tinitial+C)
=0.17(Tfinal-Tinitial )
=0.17(315-40)
=46.75(kJ/kg)
Since volume is fixed, W=0 (2 )
U=
I apologize for skipping the details of the derivation, plus there are some
corrections in solving this problem.
Problem 10.5
There are SiO2 and TiO2, so you should use the following equation for mixing:
G M RT X A ln a A X B ln aB
RT X A ln X A X B ln
/ 12.2., A diffusion couple, made by welding a thin one-centimeter mug-g slab of pure metal A to a
similarFsl/ab of pure metal B, was given a diffusion anneal at an elevated temperature and then cooled
to room temperature. On chemically analyzing successi
5.5 Defamation twins are also able to form along the cfw_111 planes of fee crystals, as a re5ult of the
application of a shear stress across this type of plane. In twinning. the shear directions are
< 211 as.
cfw_a Prove. using Eo. 5.3, that the [1Z1]ancl
IM [a] How rnan'g.r eduivalent cfw_111: 115 :3 slip svsterns are there In the fcc lattice?
[bl Indentifv each svstem bv writing out its slip plane and slip direction indices.
Solution:
[a] The various slip svsterns are listed below.
(111J[1Io] (TI1)[110]
7.1 Gold has a melting point of 1,063 and its latent heat of fusion is 12,700 J/mol.
Determine the entropy change due to the freezing of one mole of gold and indicate
whether it is positive or negative.
7.8 Compute the equilibrium concentration of vacanci
Chapter. 3
3.9 Do you except a correlation between bonding energy and melting points of
metals? Justify your answer.
Solution.
,. .,
.(bonding energy)
(melting point)
3.10 The lattice energy of an ionic solid, U, is the amount of energy required to
separa
6.1 (a) Given a small angle tilt boundary, whose angle of tilt is 0.1 deg., find the spacing
between dislocations in the boundary if the Burgers vector of the dislocations is 0.33 nm.
(b) On the assumption that the dislocations conform to the conditions i