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The coefficient of apparent expansion of mercury in a glass vessel is $153 \times 10^{-6} /{ }^{\circ} C$ and in steel vessel is $144 \times 10^{-6} /{ }^{\circ} C$. If $\alpha$ for steel is $12 \times 10^{-6} /{ }^{\circ} C ,$ then that of glass is
$9 \times 10^{-6} /{ }^{\circ} C$
$6 \times 10^{-6} /{ }^{\circ} C$
$36 \times 10^{-6} /{ }^{\circ} C$
$27 \times 10^{-6} /{ }^{\circ} C$
Solution
The real expansion is given as the sum of apparent expansion and the vessel expansion.
$\gamma_{\text {real}}=\gamma_{\text {app}}+\gamma_{\text {vessel}}$
$\therefore\left(\gamma_{\text {app}}+\gamma_{\text {vessel}}\right)_{\text {glass }}=\left(\gamma_{\text {app}}+\gamma_{\text {vessel}}\right)_{\text {stee }}$
$153 \times 10^{-6}+\left(\gamma_{\text {vessel}}\right)_{\text {glass }}=144 \times 10^{-6}+\left(\gamma_{\text {vessel}}\right)_{\text {steel }}$
$\left(\gamma_{\text {vessel}}\right)_{\text {steel }}=3 \alpha=3 \times 12 \times 10^{-6}=36 \times 10^{-6} /{ }^{\circ} C$
The expansion of glass comes out be,
$153 \times 10^{-6}+\left(\gamma_{\text {vessel}}\right)_{\text {glass }}=144 \times 10^{-6}+36 \times 10^{-6}$
$\left(\gamma_{\text {vessel}}\right)_{\text {glass }}=3 \alpha=27 \times 10^{-6} /{ }^{\circ} C$
$\alpha=9 \times 10^{-6} /{ }^{\circ} C$
