Question

A glass bulb of volume $250cc$ 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

• A. $3.06cc$
• B. $2.94cc$
• C. $6.12cc$
• D. $7.73cc$

Answer 1

The correct option is A $3.06cc$

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.