When a bar of iron $50.0 c m$ long at $15^{o} C$ is heated in a furnace, it becomes $50.4 c m$ . If the coefficient of linear expansion of iron is $1.1 \times 10^{- 5} C^{o - 1}$ , find the temperature of furnace.

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Solution

Expansion of rod $= c o e f f i c i e n t o f e x p a n s i o n \times L \times Δ T$
$(50.4 - 50) \times 10^{- 2} = 1.1 \times 10^{- 5} \times .5 \times (T - 15)$
$0.4 \times 10^{- 2} = .55 \times 10^{- 5} (T - 15)$
$T = 15 + \frac{0.4 \times 10^{- 2}}{.55 \times 10^{- 5}} = 15 + 727 = 742^{o} C$

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