Question

The co-efficient of apparent expansion of a liquid is $30\times {10}^{-6/0}$C. It is kept in a vessel whose coefficient of superficial expansion is $1.8\times {10}^{-5/0}$C. The co-efficient of real expansion of the liquid is :

• A. $22\times {10}^{-6}{/}^o$C
• B. $5.7\times {10}^{-5}{/}^o$C
• C. $1\times {10}^{-4}{/}^o$C
• D. $2.2\times {10}^{-5}{/}^o$C

Answer 1

Answer: (B)

$5.7\times {10}^{-5}{/}^o$C

${\gamma }_a=$30x${10}^{-6}$ as given
${\beta }_g=$1.8x${10}^{-5}=$18x${10}^{-6}$ as given
${\beta }_g=2{\alpha }_g$
${\gamma }_g=3{\alpha }_g$
$\therefore {\gamma }_g=\frac{3}{2}{\beta }_g=\frac{3}{2}\times 18\times {10}^{-6}$
${\gamma }_r={\gamma }_a+{\gamma }_g$
$\therefore {\gamma }_r=30\times {10}^{-6}+27\times {10}^{-6}=57\times {10}^{-6}=5.7\times {10}^{-5}{/}^{o}C$