Question

An iron scale is calibrated at $0^{\circ }C$. The length of a zinc rod is measured to be $100cm$ by the scale when the rod and the scale both are at $0^{0}C$. What will be the length of the rod as measured by the scale when both are at ${100}^{\circ }C$. Given : ${\alpha }_{iron}=1.2\times {10}^{-5}{}^{\circ }{C}^{-1}$ and ${\alpha }_{zinc}=2.6\times {10}^{-4}{}^{\circ }{C}_{-1}$.

Answer 1

Initially both scale and rod will be at zero so iron scale will give correct radially at $100C$ both will expand.

Let the length of iron and zinc rod at $0^o$c

length of zinc rod at temperature $\left(t\right){100}^{o}C$ when measured by sacle that its self undergoes thermal expansion is given as

$=L_{z}t=L_{z0}[1+(a_z-{\alpha }_I\left)t\right]$

$=100[1+(2.6\times {10}^{-5}-1.2\times {10}^{-5}\left)100\right]$

$=100[1+[1+(1.4\times {10}^{-3})]$

$=100[1+0.0014]$

$=100\left[1.0014\right]$

$=100.14cm$