Question

how much will a bar of aluminium ,100 cm long ,expand when heated from 20 celcius to 100 celcius? co efficient of linear expansion of aluminium is 2.5*10 to the power of -5 degree celcius inverse 

Answer 1

$\alpha = \frac{\Delta\l}{l_1\Delta\ T}$
Where, α=expansion on heating=2.5*(10)^{-5} °C
$l_1$ = initial length (100cm)
$\Delta\l$ = Change in length, $l_1=100cm$ $l_2=?$
$\Delta\T$ =  change in temperature = 100°C-20°C=80°C
Using the above formula,
$\alpha l_1\Delta\T=\Delta\l$
$\alpha l_1\Delta\T=l_2-l_1$
Substituting values:-
$2.5*10^{-5}*100*80=l_2-100$
Solve, you get
$l_2=100.2cm$

Answer 2

$\Delta L= \alpha *L*\Delta T\\\\.\ \ \ \ =2.5*10^{-5}*100*(100-20)\\\\.\ \ \ \ =0.2\ cm$

So the aluminium bar of length 100 cm will expand by 0.2 cm and the bar will expand to 100.2 cm total length.