Question

An aluminium rod of $10m$ length at ${20}^{o}C$ expand when the temperature is changed from $0^{o}C$ to ${100}^{o}C$. The resultant change due to rod expansion (in mm) is
$\left[thermalexpansioncoefficient\right(\gamma )ofat{20}^{o}Cis25\times {10}^{-6}(1{/}^{o}C\left)\right]$

• A. 25

Answer 1

The correct option is A 25
If we have a rod of length $l_o$ at temperature $T_o$ & the temperature is raised to a new value $T$, the rod will be found to have a new value $l$. Then the relation is
$l=l_o[l+\gamma \Delta T]$

Where $\Delta T=T-T_0$

$\gamma =\text{linear thermal expansion coefficient}$

$At{0}^{o}C$

$l_1=10\times [1+25\times {10}^{-6}(0-20\left)\right]$

$=9.995m$

$At{100}^{o}C$

$l_2=10\times [1+2.5\times {10}^{-5}](100-20)]$

$=10.02m$

$\text{The rod expansion is}$

$l_2-l_1=25mm$