Problem

If a cylindrical rod of nickel 100.00 mm long and 8.000 mm in diameter is heated from 20°C...

If a cylindrical rod of nickel 100.00 mm long and 8.000 mm in diameter is heated from 20°C to 200°C while its ends are maintained rigid, determine its change in diameter. You may want to consult Table 7.1.

Table 17.1 Thermal Properties for a Variety of Materials

Material

cp(J/kg K)a

αl [(°C)–1 × 10–6]b

k (W/m K)c

L [Ω W/(K)2 × 10–8]

Aluminum

900

23.6

247

2.20

Copper

386

17.0

398

2.25

Gold

128

14.2

315

2.50

Iron

448

11.8

80

2.71

Nickel

443

13.3

90

2.08

Silver

235

19.7

428

2.13

Tungsten

138

4.5

178

3.20

1025 Steel

486

12.0

51.9

316 Stainless steel

502

16.0

15.9

Brass (70Cu–30Zn)

375

20.0

120

Kovar (54Fe–29Ni–17Co)

460

5.1

17

2.80

Invar (64Fe–36Ni)

500

1.6

10

2.75

Super Invar (63Fe–32Ni–5Co)

500

0.72

10

2.68

Ceramics

Alumina (Al2O3)

775

7.6

39

Magnesia (MgO)

940

13.5d

37.7

Spinel (MgAl2O4)

790

7.6d

15.0e

Fused silica (SiO2)

740

0.4

1.4

Soda–lime glass

840

9.0

1.7

Borosilicate (Pyrex) glass

850

3.3

1.4

Polymers

Polyethylene (high density)

1850

106–198

0.46–0.50

Polypropylene

1925

145–180

0.12

Polystyrene

1170

90–150

0.13

Polytetrafluoroethylene (Teflon)

1050

126–216

0.25

Phenol-formaldehyde, phenolic

1590–1760

122

0.15

Nylon 6,6

1670

144

0.24

Polyisoprene

220

0.14

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