A bakelite beaker has volume capacity of $500\ \text{cc}$ 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 varied. If $\gamma_{\text{beaker}} = 6\times10^{-6}\ ^\circ\text{C}^{-1}$ and $\gamma_{\text{mercury}} = 1.5\times10^{-4}\ ^\circ\text{C}^{-1}$, where $\gamma$ is the coefficient of volume expansion, then $V_m$ (in cc) is close to ______.
Numerical value type. Enter your answer.
Answer: 20
The unfilled volume stays constant if the beaker and the mercury expand by the same amount:
$$500\,\gamma_{\text{beaker}}\,\Delta T = V_m\,\gamma_{\text{mercury}}\,\Delta T \Rightarrow V_m = \frac{500\times6\times10^{-6}}{1.5\times10^{-4}} = 20\ \text{cc}$$
Solution by Sreeraj P, M.Sc Physics