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A metal rod has a length of 100cm at 200°C. At what temperature will its...

Physics
JAMB 2019

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\(^{-1}\)

  • A. \(300^0C\)
  • B. \(200^0C\)
  • C. \(100^0C\)
  • D. \(-100^0C\)
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Correct Answer: Option D
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

There is an explanation video available below.


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Explanation Video

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