Question

A bakelite beaker has volume capacity of $500cc$ 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

Answer: 20

After increasing temperature
$\Delta V^{\prime }=\left(V_0^{\prime }-V_m^{\prime }\right)$
$\Delta V^{\prime }=\Delta V$
$V_0-V_m=V_0\left(1+{\gamma }_b\Delta T\right)$
$-V_m\left(1+{\gamma }_M\Delta T\right)$
$V_0{\gamma }_b=V_m{\gamma }_m$
$V_m=\frac{V_0{\gamma }_b}{{\gamma }_m}$
$=\frac{(500)\left(6\times 10^{-6}\right)}{\left(1.5\times 10^{-4}\right)}$
$=20CC$