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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$$cm$
B) $15.66$$cm$
C) $26.22$$cm$
D) $81$$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 $0.000018$ ${^0}C^{-1}$.

Complete step by step answer:
This problem is based on thermal expansion. In thermal expansion, the increase in volume of the material will also increase the temperature. It can be expressed that fractional change in length or a volume per unit temperature change.

In linear expansion coefficient it is actually describing the expansion of the solid and a volume expansion coefficient is also more in liquid or a gas. The expansion is uniform in all dimensions of the crystal only when the crystalline solid is isometric. There is different expansion for different crystallographic directions and the crystal also changes the shape and temperature, only when it is not isometric.
The given data in the problem are,
${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 $15.66cm$.
Therefore Option (B) is correct.

Note: In the concrete road are poured with an expansion joint between the slabs for allowing the thermal expansion joints are also cause of thumping noise commonly experienced only when traveling on a concrete highway. The difference in expansion will also cause the bimetallic strip to bend the temperature when it is changed. This also includes the thermostat to control the temperature for oven thermometers to measure the temperature and also switches to regulate toasters.