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Fall 2011 Notes from R.T. DeHoff, Thermodynamics in Materials Science (McGraw-Hill, 1993; CRC, 2006)
Definitions
Thermodynamic Coefficients
Thermal Expansion Coefficient
Compressibility
Heat Capacity
Fall 2011 Notes from R.T. DeHoff, Thermodynamics in Materials Science (McGraw-Hill, 1993; CRC, 2006)
Thermal Expansion Coefficient
Volumetric Thermal Expansion Coefficient
PV T
V
V
1
...,, XPTfV
PL T
L
L
1
LV 3 321 LLL Isotropic Material
Linear Thermal Expansion Coefficient
(SI Units = K-1)
(SI Units = K-1)
Fall 2011 Notes from R.T. DeHoff, Thermodynamics in Materials Science (McGraw-Hill, 1993; CRC, 2006)
Thermal Expansion CoefficientIsotropic Material
P
V T
LLL
LLL
321
321
1
LV 3321 LLL
PPPV T
LLL
T
LLL
T
LLL
LLL3
212
311
32321
1
PPP
V T
L
LT
L
LT
L
L3
3
2
2
1
1
111
321 LLLV
&If isotropic:
Fall 2011 Notes from R.T. DeHoff, Thermodynamics in Materials Science (McGraw-Hill, 1993; CRC, 2006)
Coefficient of CompressibilityVolumetric Coefficient of Compressibility
TV P
V
V
1
...,, XPTfV
Approximately:Note negative sign in definition.
E = Elastic ModulusEV /3
jiViVj EE //
(SI Units = atm-1)
Fall 2011 Notes from R.T. DeHoff, Thermodynamics in Materials Science (McGraw-Hill, 1993; CRC, 2006)
CompressibilityIsotropic Material
T
V P
LLL
LLL
321
321
1
EV
3321 EEE
TTTV P
LLL
P
LLL
P
LLL
LLL3
212
311
32321
1
TTT
V P
L
LP
L
LP
L
L3
3
2
2
1
1
111
&If isotropic:
i
i
i
ii L
L
L
dLd
iii d
dPE
1
321 V
Fall 2011 Notes from R.T. DeHoff, Thermodynamics in Materials Science (McGraw-Hill, 1993; CRC, 2006)
Heat Capacity
At Constant Pressure:
Qrev,P CPdTP (SI Units = J/mole-K)
CP f(T,P,X,…)
Empirical Fit: CP(T) a bT c/T2
At Constant Volume:
Qrev,V CVdTV (SI Units J/mole-K)
CV f(T,P,X,…)
In General: CP CV & CP CV TV2/
Fall 2011 Notes from R.T. DeHoff, Thermodynamics in Materials Science (McGraw-Hill, 1993; CRC, 2006)
Ideal Gas
PV = nRT
= 1/T = 1/P
Monatomic: CP = 5/2 R CV = 3/2 R
Diatomic: CP = 7/2 R CV = 5/2 R
U & H depend only on temperature:
U = CV dT H = CP dT
Fall 2011 Notes from R.T. DeHoff, Thermodynamics in Materials Science (McGraw-Hill, 1993; CRC, 2006)
Ideal Gas
P
nR
nRT
P
T
V
V PV
1
TV
1
2
1
P
nRT
nRT
P
P
V
V TV
-1PnRT V
TP
nRV
P
nR
T
V
P
2
PnRTP
V
T
PV
1
