Question:
A bakelite beaker has volume capacity of 500 cc at \(30^\circ\)C. When it is partially filled with \(V_m\) volume (at \(30^\circ\)C) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If \(\gamma_{\mathrm{(beaker)}} = 6\times10^{-6}\ {}^\circ\mathrm{C^{-1}}\) and \(\gamma_{\mathrm{(mercury)}} = 1.5\times10^{-4}\ {}^\circ\mathrm{C^{-1}}\), where \(\gamma\) is the coefficient of volume expansion, then \(V_m\) (in cc) is close to ________.
A bakelite beaker has volume capacity of 500 cc at \(30^\circ\)C. When it is partially filled with \(V_m\) volume (at \(30^\circ\)C) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If \(\gamma_{\mathrm{(beaker)}} = 6\times10^{-6}\ {}^\circ\mathrm{C^{-1}}\) and \(\gamma_{\mathrm{(mercury)}} = 1.5\times10^{-4}\ {}^\circ\mathrm{C^{-1}}\), where \(\gamma\) is the coefficient of volume expansion, then \(V_m\) (in cc) is close to ________.
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The unfilled volume stays constant only if the beaker's volume expands by exactly as much as the mercury does.
Updated On: Nov 5, 2026
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Correct Answer: 20
Solution and Explanation
Unfilled volume \(= V_{beaker} - V_{Hg}\) is constant, so \(\Delta V_{beaker} = \Delta V_{Hg}\).
\(500\,\gamma_b\,\Delta T = V_m\,\gamma_m\,\Delta T\)
\(V_m = 500\times\dfrac{6\times10^{-6}}{1.5\times10^{-4}} = 500\times 0.04 = 20\) cc.
Answer: 20
\(500\,\gamma_b\,\Delta T = V_m\,\gamma_m\,\Delta T\)
\(V_m = 500\times\dfrac{6\times10^{-6}}{1.5\times10^{-4}} = 500\times 0.04 = 20\) cc.
Answer: 20
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