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Linear Expansion

A metal rod h...

Question

A metal rod has the length of $50 c m$ at $20^{o} C$ . When it is heated to $95^{o} C$ , its length becomes 50.06 cm. Find the length of the rod at $0^{o} C$ .

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Solution

$α = \frac{△ L}{L_{1} △ T} (1) L_{1} = 50 c m L_{2} = 50.06 c m △ L = 0.06 c m T_{1} = 20 ℃ T_{2} = 95 ℃ △ T = 75 ℃$

Putting value in $(1)$ to find coefficient of Linear expansion
$α = \frac{0.06}{(50) (75)} α = 16 \times 10^{- 6} ℃^{- 1}$
Now, temperature at $0^{o} C$
Length at $0^{o} C = L_{3}$
$L_{3} = L_{2} (1 + α △ T) △ T = 0 - 20 ℃ △ T = - 20 ℃ L_{3} = 50 [1 + 16 \times 10^{- 6} \times (- 20)] L_{3} = 49.984 c m$

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