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\(^{-1}\)
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Correct Answer: Option n
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
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