First slide

Thermal expansion

Question

A steel rod of length 1m is heated from 25°C to 75°C keeping its length constant. The longitudinal strain developed in the rod is (Given: Coefficient of linear expansion of steel = 12 x $10^{- 6} /^{0} C$ )

Moderate

A

$- 6 \times 10^{- 6}$
B

$- 6 \times 10^{- 5}$
C

$- 6 \times 10^{- 4}$
D

zero

Solution

Due to the Expansion of the rod due to heating it, the rod develops a strain, trying to resist the change in length. Thus the strain tends to reduce the length of the rod.
$Strain \Rightarrow \frac{∆ L}{L} = \frac{Lα ∆ θ}{L} \Rightarrow α ∆ θ$
Strain $\Rightarrow - 12 \times 10^{- 6} \times 50$
$\Rightarrow - 6 \times 10^{- 4}$

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