The difference between the specific heats at constant pressure and constant volume is described by the expression
where αv is the volume coefficient of thermal expansion, v0 is the specific volume (i.e., volume per unit mass, or the reciprocal of density), β is the compressibility, and T is the absolute temperature. Compute the values of cv at room temperature (293 K) for copper and nickel using the data in Table 17.1, assuming that αv = 3αl and given that the values of β for Cu and Ni are 8.35 × 10−12 and 5.51 × 10−12 (Pa)−1, respectively.
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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