Question

The ratio of coefficient of apparent expansions of a liquid in the containers A and B is 1:2. If $18\times {10}^{-6/0}C$ and $12\times {10}^{-6/0}C$ are the co-efficients of linear expansions of the containers A and B respectively, then the coefficient of real expansion of the liquid is

• A. $24\times {10}^{-6/0}C$
• B. $6\times {10}^{-6/0}C$
• C. $72\times {10}^{-6/0}C$
• D. $30\times {10}^{-6/0}C$

Answer 1

Answer: (C)

$72\times {10}^{-6/0}C$

${\gamma }_r={\gamma }_a+{\gamma }_g={\gamma }_a+3{\alpha }_g$
$\frac{{\gamma }_{a1}}{{\gamma }_{a2}}=\frac{1}{2}$
Let ${\gamma }_{a1}=x$
Let ${\gamma }_{a2}=2x$
Thus,
${\gamma }_r=x+3{\alpha }_1=2x+3{\alpha }_2$
$\therefore x+3\times 18\times {10}^{-6}=2x+3\times 12\times {10}^{-6}$
$\Rightarrow x=18\times {10}^{-6}$
${\gamma }_r=18\times {10}^{-6}+3\times 18\times {10}^{-6}=72\times {10}^{-6}$/ ${}^0$ C