A glass bulb of volume $250 c c$ is filled with mercury at $20^{o} C$ and the temperature is raised to $100^{o} C$ . If the coefficient of linear expansion of glass is $9 \times 10^{- 6} /^{o} C$ . Coefficient of absolute expansion of mercury is $18 \times 10^{- 5} /^{o} C$ . The volume of mercury overflows

3.06 c c

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2.94 c c

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6.12 c c

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7.73 c c

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Solution

The correct option is A $3.06 c c$
Expansion of mercury = Vm×γm×ΔT = 250×1.8×10-4×80 ....................(1)
where Vm, γm and ΔT are original volume of mercury, coefficient of absolute expansion of mercury and rise in temperature.
Expansion of glass container = Vg×γg×ΔT = 250×3×9×10-6×80 ...................(2)
where Vg, γg and ΔT are original volume of container, coefficient of volume expansion of glass and rise in temperature.
Spill over volume ΔV of mercury will be obtained by subtracting (2) from (1)
ΔV = 250×80×{ 1.8 - 0.27 } ×10-4 = 3.06 cc.

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A glass bulb of volume 250cc is filled with mercury at 20oC and the temperature is raised to 100oC. If the coefficient of linear expansion of glass is 9×10−6/oC. Coefficient of absolute expansion of mercury is 18×10−5/oC. The volume of mercury overflows