Question

The ratio of coefficient of apparent expansions of the same liquid in two different vessels is 1:2. If ${\alpha }_1$and ${\alpha }_2$ are the coefficient of linear expansions then coefficient of real expansion of the liquid is

• A. $2{\alpha }_1-{\alpha }_2$
• B. $3{\alpha }_1-4{\alpha }_2$
• C. ${\alpha }_1-4{\alpha }_2$
• D. $6{\alpha }_1-3{\alpha }_2$

Answer 1

The correct option is D $6{\alpha }_1-3{\alpha }_2$

${\gamma }_r={\gamma }_a+{\gamma }_g={\gamma }_a+3{\alpha }_g$

Given,

The ratio of co-efficient of apparent expansions of the same liquid in two different vessels is 1:2.

$\frac{{\gamma }_{a1}}{{\gamma }_{a2}}=\frac{1}{2}$

${\gamma }_{a1}=x$ ${\gamma }_{a2}=2x$

${\gamma }_r=x+3{\alpha }_1=2x+3{\alpha }_2$

$\Rightarrow x=3{\alpha }_1-3{\alpha }_2$

$\therefore {\gamma }_r=x+3{\alpha }_1=3{\alpha }_1-3{\alpha }_2+3{\alpha }_1=6{\alpha }_1-3{\alpha }_2$