A metal rod has a length of 100cm at 200°C. At what temperature will its length be 99.4cm. If the linear expansivity of the material of the rod is 2 × 10\(^{-5}\)C\(^{-1}\)
L\(_1\) = 100cm, T\(_1\) = 200°C
L\(_2\) = 99.4cm, T\(_2\) = ?
α 2 × 10\(^{-5}\) C\(^{-1}\)
| α | = | L\(_2\) - L\(_1\)
L\(_1\)(T\(_2\) - T\(_1\)) |
| 2 | × | 10\(^{-5}\) | = | 110 - 99.4
100(200 - T\(_2\)) |
= | 0.6
100(200 - T\(_2\)) |
2 × 10\(^{-5} × 100(200 - T_2\)) = 0.6
| 200 | - | T\(_2\) | = | 0.6
0.002 |
= | 300°C |
T\(_2\) = 200 - 300 = -100°C
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