Question

The coefficient of apparent expansion of mercury in a glass vessel is $153 \times 10^{-6} /{ }^{\circ} C$ and in a 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

• A. $9 \times 10^{-6} / { }^{\circ}C$
• B. $6 \times 10^{-6}/{ }^{\circ} C$
• C. $36 \times 10^{-6} / { }^{\circ}C$
• D. $27 \times 10^{-6}/{ }^{\circ} C$

Answer 1

Answer: (A)

$\gamma_{\text {real }}=\gamma_{\text {app. }}+\gamma_{\text {vessel }}$
So $\left(\gamma_{\text {app. }}+\gamma_{\text {vessel }}\right)_{\text {glass }}=\left(\gamma_{\text {app }}+\gamma_{\text {vessel }}\right)_{\text {steel }}$
$\Rightarrow 153 \times 10^{-6}+\left(\gamma_{\text {vessel }}\right)_{\text {glass }}=144 \times 10^{-6}+\left(\gamma_{\text {vessel }}\right)_{\text {steel }}$
Further,
$\left(\gamma_{\text {vessel }}\right)_{\text {steel }}=3 \alpha=3 \times\left(12 \times 10^{-6}\right)=36 \times 10^{-6} /{ }^{\circ} C$
$\Rightarrow 153 \times 10^{-6}+\left(\gamma_{\text {vessel }}\right)_{\text {glass }}=144 \times 10^{-6}+36 \times 10^{-6}$
$\Rightarrow\left(\gamma_{\text {vessel }}\right)_{\text {glass }}=3 \alpha=27 \times 10^{-6} /{ }^{\circ} C$
$\Rightarrow \alpha=9 \times 10^{-6} /{ }^{\circ} C$