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