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# The potential energy curve were symmetric figure

17.3 Thermal Expansion

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Table 17.1

k
(W/m-K)c

L
[-W/(K)2108]

Metals
900 23.6 247 2.20
386 17.0 398 2.25
128 14.2 315 2.50
448 11.8 80 2.71

Nickel

443 13.3 90 2.08

Silver

235 19.7 428 2.13
138 4.5 178 3.20
486 12.0 51.9
502 16.0 15.9
375 20.0 120

Kovar

460 5.1 17 2.80

(54Fe-29Ni-17Co)

500 1.6 10 2.75
500 0.72 10 2.68
Alumina (Al2O3) Magnesia (MgO) 775 7.6 39
940 13.5d 37.7
790 7.6d 15.0e
740 0.4 1.4
840 9.0 1.7

Borosilicate (Pyrex) glass

850 3.3 1.4
Polymers

Polyethylene

1850 106–198 0.46–0.50
1925 145–180 0.12
1170 90–150 0.13
1050 126–216 0.25

(Teflon)

Phenol-formaldehyde,

122 0.15
1670 144 0.24
220 0.14

a To convert to cal/g-K, multiply by 2.39 � 10�4; to convert to Btu/lbm-�F, multiply by 2.39 � 10�4. b To convert to (�F)�1, multiply by 0.56.

c To convert to cal/s-cm-K, multiply by 2.39 � 10�3; to convert to Btu/ft-h-�F, multiply by 0.578. d Value measured at 100�C.

V T (17.4)
V0

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For each class of materials (metals, ceramics, and polymers), the greater the atomic bonding energy, the deeper and more narrow this potential energy trough. As a result, the increase in interatomic separation with a given rise in temperature will be lower, yielding a smaller value of � l. Table 17.1 lists the linear coefficients of thermal expansion for several materials. With regard to temperature dependence, the magnitude of the coefficient of expansion increases with rising temperature. The values in Table 17.1 are taken at room temperature unless indicated otherwise. A more comprehensive list of coefficients of thermal expansion is provided in Table B.6 of Appendix B.

Interatomic distance Interatomic distance 0 0

(a) (b)

FIGURE 17.3 (a) Plot of potential energy versus interatomic distance,
demonstrating the increase in interatomic separation with rising temperature. With heating, the interatomic separation increases from r0 to r1 to r2, and so on. (b) For a symmetric potential energy-versus-interatomic distance curve, there is no increase in interatomic separation with rising temperature (i.e., r1 � r2 � r3 ).

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