Question

When a liquid is heated in copper vessel its coefficient of apparent expansion is $6\times {10}^{-6}{/}^{o}C$. When the same liquid is heated is heated in a steel vessel its coefficient of apparent expansion is $24\times {10}^{-6}{/}^{o}C$. If the coefficient of linear expansion for copper is $18\times {10}^{-6}{/}^{o}C$, the coefficient of linear expansion for steel is:

• A. $20\times {10}^{-6}{/}^{o}C$
• B. $24\times {10}^{-6}{/}^{o}C$
• C. $34\times {10}^{-6}{/}^{o}C$
• D. $12\times {10}^{-6}{/}^{o}C$

Answer 1

Answer: (D)

$12\times {10}^{-6}{/}^{o}C$

Here, ${\gamma }_{real}={\gamma }_{app}+{\gamma }_{container}$

So, ${\gamma }_{app\left(Cu\right)}+{\gamma }_{Cu}={\gamma }_{app\left(S\right)}+{\gamma }_S$

or $6\times {10}^{-6}+3(18\times {10}^{-6})=24\times {10}^{-6}+3{\alpha }_S$ where $(\gamma =3\alpha )$

or ${\alpha }_S=12\times {10}^{-6}{/}^{o}C$