The resistance of a wire of length $l$ and cross section area $A$ is given by $R = \rho l / A$, where $\rho$ is the *resisitivity* (SI units: $\mathrm{\Omega\,m}$). Over reasonably narrow temperature ranges, $R$ increases with temperature linearly:
$$
R(T) = R_0[1+\alpha(T-T_0)],
$$
where $\alpha$ is a constant.
Fit a straight line to the following data sets and determine $\rho$ for copper and iron at the reference temperature $T_0 = 300\;\mathrm{K}$. The data are measured for a wire of circular cross sectional radius $0.1\;\mathrm{mm}$ and length $100\;\mathrm{m}$.

$T\;/\mathrm{K}$ | $R(\mathrm{Cu})\;/\mathrm{\Omega}$ | $R(\mathrm{Fe})\;/\mathrm{\Omega}$ |
---|---|---|

220.0 | 0.33 | 1.89 |

250.0 | 0.51 | 2.31 |

280.0 | 0.59 | 2.77 |

310.0 | 0.44 | 3.25 |

340.0 | 0.64 | 3.71 |

370.0 | 0.70 | 4.25 |

400.0 | 0.73 | 4.66 |

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