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,

$153 \times 10^{-6}+\left(\gamma_{\text {vessel}}\right)_{\text {glass }}=144 \times 10^{-6}+36 \times 10^{-6}$

$\left(\gamma_{\text {vessel}}\right)_{\text {glass }}=3 \alpha=27 \times 10^{-6} /{ }^{\circ} C$

$\alpha=9 \times 10^{-6} /{ }^{\circ} C$