First slide

Thermal expansion

Question

A copper rod of 88 cm and an aluminium rod of unknown length have their increase in length independent of increase in temperature. The length of aluminium rod is $(α_{Cu} = 1.7 \times 10^{- 5} K^{- 1} and α_{Al} = 2.2 \times 10^{- 5} K^{- 1})$

Moderate

Solution

$As per question, {Δl}_{Cu} = {Δl}_{Al}$
$or, l_{Cu} α_{Cu} ΔT = l_{Al} α_{Al} ΔT l_{Al} = \frac{l_{Cu} α_{Cu}}{α_{Al}} = \frac{88 \times 1.7 \times 10^{- 5}}{2.2 \times 10^{- 5}} = 68 cm$

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