Question

An aluminium rod with another alloy are bonded together at ${20}^{\circ }C$ to form a bimetal sensor. The length of the bimetal rod at ${20}^{\circ }C$ is $10m$. How much the rod will expand (in mm) when the temperature is changed from $0^{\circ }C$ to ${100}^{\circ }C?$ The expansion coefficient of aluminium is $2.5\times {10}^{-6}{/}^{\circ }C.$

• A. 25

Answer 1

The correct option is A 25
The expansion in the lengthof a metal due to tempertaure is given by,

$l=l_o(1+\gamma .\Delta T)$

$l_o=\text{Original length}\Delta T=(T-T_o)$

$\gamma =\text{liner expansion coefficient}$

$\therefore \text{at}{0}^{\circ }C\text{the length is :}$

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

$l_1=9.995m$

$\text{And at}{100}^{\circ }C\text{the length is}$

$l_2=10[1+25\times {10}^{-6}\times (100-20\left)\right]$

$l_2=10.02m$

$\text{Thus the expansion is:}$

$l_2-l_1=10.02-9.995$

$=25mm$