The bulb volume of a mercury thermometer at 0°C is V₀ and the capillary area is A₀. Let $\alpha_{glass}$ be the linear expansion coefficient of glass and $\gamma_{Hg}$ the cubical expansion coefficient of mercury. If mercury just fills the bulb at 0°C, what is the capillary-column length at T°C?
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Question

The bulb volume of a mercury thermometer at 0°C is V₀ and the capillary area is A₀. Let α g l a s s \alpha_{glass} α g l a ss be the linear expansion coefficient of glass and γ H g \gamma_{Hg} γ H g the cubical expansion coefficient of mercury. If mercury just fills the bulb at 0°C, what is the capillary-column length at T°C?

Physics · Thermodynamics

G1 Physics · Accepted Answer

At T°C, the excess mercury volume over the expanded bulb volume is approximately ΔV=V₀(γHg-3αglass)T. The capillary area expands to A≈A₀(1+2αglassT). Hence column length h=ΔV/A=V₀T(γHg-3αglass)/[A₀(1+2αglassT)]. Option B.