Question

The coefficient of apparent expansion of a liquid when determined using two different vessels A and B are ${\gamma }_1$ and ${\gamma }_2$ respectively. If the coefficient of linear expansion of the vessel A is $\alpha$, the coefficient of linear expansion of the vessel B is

• A. $\frac{\alpha {\gamma }_1{\gamma }_2}{{\gamma }_1+{\gamma }_2}$
• B. $\frac{{\gamma }_1-{\gamma }_2}{2\alpha }$
• C. $\frac{{\gamma }_1-{\gamma }_2+\alpha }{3}$
• D. $\frac{{\gamma }_1-{\gamma }_2}{3}+\alpha$

Answer 1

The correct option is D $\frac{{\gamma }_1-{\gamma }_2}{3}+\alpha$

${\gamma }_r={\gamma }_l+{\gamma }_g={\gamma }_r+3{\alpha }_g$
Given,
${\gamma }_r={\gamma }_1+3{\alpha }_1$ ....(1)
${\gamma }_r={\gamma }_2+3{\alpha }_2$ ....(2)
Equating (1) and (2),
${\gamma }_1+3{\alpha }_1={\gamma }_2+3{\alpha }_2$
$\therefore {\alpha }_2=\frac{{\gamma }_1-{\gamma }_2}{3}+{\alpha }_1$