A metal rod has a length of 100cm at 200 oC At ... - JAMB Physics 2019 Question

A metal rod has a length of 100cm at 200 $^{o} C$ . At what temperature will its length be 99.4cm. If the linear expansivity of the material of the rod is 2 x 10 $^{- 5} C^{- 1}$

200 $^{o}$ C

300 $^{o}$ C

100 $^{o}$ C

-100 $^{o}$ C

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Correct Option: D

L $_{1}$ = 100cm,

T $_{1}$ = 200 $^{o}$ C

L $_{2}$ = 99.4cm,

T $_{2}$ = ?

$α$ = 2 x 10 $^{- 5}$ C $^{- 1}$

$α$ = $\frac{L_{2} - L_{1}}{L_{1} (T_{2} - T_{1})}$

2 x 10 $^{- 5} = \frac{100 - 99.4}{100 (200 - T_{2})} = \frac{0.6}{100 (200 - T_{2})}$

2 x 10 $^{- 5}$ x $100 (200 - T_{2}) = 0.6$

$200 - T_{2} = \frac{0.6}{0.002} = 300^{o} C$

$T_{2} = 200 - 300 = - 100^{o} C$

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