First slide

Thermal expansion

Question

By what temperature a rod should be heated so that its length becomes 2l_o if its initial length is l₀. Coefficient of linear expansion is α in that temperature range

Difficult

A

$\frac{\ln 2}{α}$
B

$α \ln 2$
C

ln 4
D

ln2

Solution

$\frac{d l}{l d θ} = α \Rightarrow \int_{0}^{△ θ} 1 . d θ = \frac{1}{α} \int_{l_{0}}^{2 l_{0}} \frac{1}{l} d l \Rightarrow △ θ = \frac{\ln 2}{α}$

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