A metal rod has a length of 100cm at 200\(^oC\). At what temperature will its length be 99.4cm. If the linear expansivity of the material of the rod is 2 x 10\(^{-5}C^{-1}\)
L\(_1\) = 100cm, T\(_1\) = 200\(^o\)C
L\(_2\) = 99.4cm,T\(_2\) = ?
\(\alpha\) = 2 x 10\(^{-5}\)C\(^{-1}\)
\(\alpha\) = \(\frac{L_2 - L_1}{L_1(T_2 - T_1)}\)
2 x 10\(^{-5} = \frac{99.4 - 100}{100( T_2 - 200)} = \frac{-0.6}{100(T_2 - 200)}\)
2 x 10\(^{-5}\) x \(100(T_2 - 200) = -0.6\)
\(T_2 - 200 = \frac{-0.6}{0.002} = - 300^oC\)
\(T_2 = 200 - 300 = -100^oC\)
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