First slide

Thermal expansion

Question

If the coefficient of real expansion γ_r is 1% more then coefficient of apparent expansion, linear expansion coefficient of the material is

Easy

A

$\large \frac {\gamma_r}{303}$
B

$\large \frac {100\gamma_r}{101}$
C

$\large \frac {101\gamma_r}{300}$
D

$\large \frac {101\gamma_r}{100}$

Solution

Given that $\large \gamma_r=\frac {101}{100}\gamma_a\Rightarrow \gamma_a=\frac {100}{101}\gamma_r$
We have $\large \gamma_r=\gamma_a+3\alpha_g\Rightarrow \gamma_r=\frac {100}{101}\gamma_r+3\alpha_g$
$\large \gamma_r\left [ 1-\frac {100}{101} \right ]=3\alpha_g\Rightarrow \alpha_g=\frac {\gamma_r}{303}$

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