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 nod is 2 × 10(^{-5})C(^{-1})
Explanation
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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