Question

A vertical glass tube closed at bottom contains mercury up to a height of 500 mm at a temperature of 10°C. The height of mercury column at 30°C changes by

(γ_Hg = 18 x 10^-5(°C)^-1 ; α_glass = 0.8 x 10^-5 C^-1)

(1) – 0.2 mm

(2) + 1.6 mm

(3) – 1.6 mm

(4) + 0.2 mm

Answer 1

(2) + 1.6 mm

Let a₁, l₁, p₁ and v₁ denote area of cross-section length of mercury column; density of mercury and volume of mercury in glass tube at 10°C. The corresponding quantites at 30°C are a₁, l₂, p₂ and v₂ respectively. The mass of mercury in tube remains same, therefore

Also,

From Eqns. (1), (2) and (3) we have

The change in height of mercury in tube = 501.6–500 = 1.6 mm