First slide

Thermal expansion

Question

What should be the lengths of a copper rod and a brass rod be at $0^{ο} C$ , so that the difference in the lengths of the copper and brass rods remains 10 cm at all temperatures? Given $α_{b} = 1.8 \times 10^{- 5} / K and α_{c} = 1.6 \times 10^{- 5} / K$ .

Moderate

A

$L_{b} = 50 c m, L_{c} = 60 c m$
B

$L_{b} = 100 c m, L_{c} = 110 c m$
C

$L_{b} = 90 c m, L_{c} = 100 c m$
D

$L_{b} = 80 c m, L_{c} = 90 c m$

Solution

Let the length of brass rod at $0^{o} C i s L$
$∴$ Length of copper rod at $0^{o} C = (L + 10)$
Since $α_{c} L_{c} = α_{b} L_{b}$ ,
we can write, $1.6 \times 10^{- 5} \times (L + 10) = 1.8 \times 10^{- 5} \times L \Rightarrow L = 80 c m$
$∴$ Length of copper rod $= (80 + 10) c m = 90 c m$

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