Question

The co-efficient of real expansion of liquid is ${\gamma }_r$ and the co-efficient of apparent expansions of the liquid is ${\gamma }_a$. The co-efficient of cubical expansion of the vessel is $\gamma$. If ${\gamma }_r:{\gamma }_a=4:1$ then ${\gamma }_a:\gamma$ is :

• A. 3:1
• B. 1:3
• C. 4:1
• D. 1:4

Answer 1

Answer: (B)

1:3

${\gamma }_r={\gamma }_a+{\gamma }_g$ ....(1)
Given, ${\gamma }_g=\gamma$
Given ${\gamma }_r$ : ${\gamma }_a=$4:1
Dividing (1) by ${\gamma }_a$,
$\frac{{\gamma }_r}{{\gamma }_a}=1+\frac{{\gamma }_g}{{\gamma }_a}=1+\frac{\gamma }{{\gamma }_a}$
$\Rightarrow 4=1+\frac{\gamma }{{\gamma }_a}$
$\Rightarrow \gamma =3{\gamma }_a$
$\Rightarrow {\gamma }_a$:$\gamma$ = $\frac{1}{3}$