Question

The coefficient of apparent expansion of mercury in a glass vessel is 153 × ${10}^{-6}{/}^{\circ }C$ and in a steel vessel is 144 × ${10}^{-6}{/}^{\circ }C$. If afor steel is 12 × ${10}^{-6}{/}^{\circ }C$, 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

The correct option is A

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

${{\rm Y}}_{real}=g_{app}.+g_{vessel}$

So (${\gamma }_{app}.+{\gamma }_{vessel}{)}_{glass}=({\gamma }_{app}.+{\gamma }_{vessel}{)}_{steel}$

Þ $153\times {10}^{-6}+{\gamma }_{vessel}{)}_{glass}=(144\times {10}^{-6}+{\gamma }_{vessel}{)}_{steel}$

Further, (${\gamma }_{vessel}{)}_{steel}=3a=3\times (12\times {10}^{-6})=36\times {10}^{-6}{/}^{\circ }C$

Þ 153 × ${10}^{-6}+({\gamma }_{vessel}{)}_{glass}=144\times {10}^{-6}+36\times {10}^{-6}$

Þ $({\gamma }_{vessel}{)}_{glass}=3a=27\times {10}^{-6}{/}^{\circ }CÞa=9\times {10}^{-6}{/}^{\circ }C$