Question

The coefficient of apparent expansion of mercury in a glass vessel is $153\times {10}^{-}6/{}^{o}C$ and in a steel vessel is $144\times {10}^{-6}/{}^{o}C$. If a for steel is $12\times {10}^{-6}/{}^{o}C$, then that of glass is

• A. 9 × 10^-6/ºC
• B. 6 × 10^-6/ºC
• C. 36 × 10^-6/ºC
• D. 27 × 10^-6/ºC

Answer 1

The correct option is A

9 × 10^-6/ºC

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