Question

A bakelite beaker has volume capacity of $500 cc$ at $30^{\circ} C$. When it is partially filled with $V _{ m }$ volume (at $30^{\circ}$ ) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If $\gamma_{\text {(beaker) }}=6 \times 10^{-6}{ }^{\circ} C ^{-1}$ and $\gamma_{(\text {mercury })}=1.5 \times 10^{-4}{ }^{\circ} C ^{-1},$ where $\gamma$ is the coefficient of volume expansion, then $V _{ m }$ (in $cc$ ) is close to________.

Answer 1

After increasing temperature
$\Delta V ^{\prime}=\left( V _{0}^{\prime}- V _{ m }^{\prime}\right)$
$\Delta V ^{\prime}=\Delta V$
$V _{0}- V _{ m }= V _{0}\left(1+\gamma_{ b} \Delta T \right)$
$- V _{ m }\left(1+\gamma_{ M } \Delta T \right)$
$V _{0} \gamma_{ b }= V _{ m } \gamma_{ m }$
$V _{ m }=\frac{ V _{0} \gamma_{ b }}{\gamma_{ m }}$
$=\frac{(500)\left(6 \times 10^{-6}\right)}{\left(1.5 \times 10^{-4}\right)}$
$=20 CC$