Question 19.3: Resistivity of Pure Copper Calculate the electrical conducti......
Resistivity of Pure Copper
Calculate the electrical conductivity of pure copper at (a) 400°C and (b) -100°C.
Step-by-Step
The resistivity of copper at room temperature is 1.67 × 10^{-6} ohm · cm, and the temperature resistivity coefficient is 0.0043 ohm/(ohm · °C). (See Table 19-3.)
(a) At 400°C:
ρ = ρ_{RT} (1 + α_{R}ΔT) = (1.67 × 10^{-6})[1 + 0.0043(400 \ – \ 25)]
ρ = 4.363 × 10^{-6} \ ohm ⋅ cm
σ = 1/ρ = 2.29 × 10^5 \ ohm^{-1} ⋅ cm^{-1}
(b) At -100°C:
ρ = (1.67 × 10^{-6})[1 + 0.0043(-100 – 25)] = 7.724 × 10^{-7} \ ohm ⋅ cm
σ = 1.29 × 10^{6} \ ohm^{-1} ⋅ cm^{-1}
| Table 19-3 The temperature resistivity coefficient α_{R} for selected metals | ||
| Metal | Room Temperature Resistivity (ohm · cm) |
Temperature Resistivity Coefficient (α_{R}) [ohm/(ohm· °C)] |
| Be | 4.0 × 10^{-6} | 0.0250 |
| Mg | 4.45 × 10^{-6} | 0.0037 |
| Ca | 3.91 × 10^{-6} | 0.0042 |
| Al | 2.65 × 10^{-6} | 0.0043 |
| Cr | 12.90 × 10^{-6}(0°C) | 0.0030 |
| Fe | 9.71 × 10^{-6} | 0.0065 |
| Co | 6.24 × 10^{-6} | 0.0053 |
| Ni | 6.84 × 10^{-6} | 0.0069 |
| Cu | 1.67 × 10^{-6} | 0.0043 |
| Ag | 1.59 × 10^{-6} | 0.0041 |
| Au | 2.35 × 10^{-6} | 0.0035 |
| Pd | 10.8 × 10^{-6} | 0.0037 |
| W | 5.3 × 10^{-6}(27°C) | 0.0045 |
| Pt | 9.85 × 10^{-6} | 0.0039 |
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