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# Calculate the increase in length of brass rod, which measures $100cm$ at ${10^0}C$, when it is heated to ${880^0}C$. ($\alpha$ for brass = $0.000018$ ${^0}C^{-1}$)A) $3.096$$cmB) 15.66$$cm$C) $26.22$$cmD) 81$$cm$

Last updated date: 19th Jun 2024
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Hint: To find the solution for this problem, the actual length of the rod at certain degree is given. We need to find the increase in length of the brass rod when it is heated to some degree of the temperature. The linear expansion of the brass is given as $0.000018$ ${^0}C^{-1}$.

${L_0} = 100$$cm$ at ${10^0}C$
Increase length = $= (\Delta {L_t} - \Delta {L_0})$
$t = {(880 - 10)^0}C$
The linear expansion of brass $\alpha = 0.000018$ ${^0}C^{-1}$
This is the formula to find the increase in length of the brass rod $\Delta L$ = $100 \times 0.000018 \times 870$ = $15.66$
So, the increase in length of the brass rod is $15.66cm$.