Question

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

Answer 1

Volume capacity of beaker, $V_0=500\text{cc}$

According to the question,

$\Delta V_{\text{beaker}}=\Delta V_{\text{mercury}}$

$V_0{\gamma }_{\text{beaker}}\Delta T=V_m{\gamma }_m\Delta T$
$V_m=\frac{V_0{\gamma }_{\text{beaker}}}{{\gamma }_m}$
$\therefore V_m=\frac{500\times 6\times {10}^{-6}}{1.5\times {10}^{-4}}=20\text{cc}$