# Thermal Expansion - Long Question Answer | Physics Grade 11 Solution

### Long Question Solution # Thermal Expansion - Long Question Answer 3

Question: Describe how the cubical expansivity of liquid can be determined by the use of balanced columns.

Ans: By the use of balanced columns, a simple method to determine the coefficient of real expansion of a liquid is Dulong and Petit’s experiment. It is based on the principle of hydrostatic. The apparatus uses a u-shaped glass tube ABCD filled with a liquid whose real expansivity should be determined. Initially, the liquid is at equal height as shown in the figure. One arm of the tube is surrounded by an ice-water jacket and another arm is surrounded with a steam jacket. The temperature of each jacket is noted by the thermometer fitted on them. To prevent the transformation of heat, a wet cloth is kept in the middle. At different heights, the pressure at the base is same. Let, h1 and h2 be the height of the liquid column in limb AB and CD respectively,
ρ1 and ρ2 be the density of liquid column in limb AB and CD respectively,
θ1 and θbe the temperature of liquid column in limb AB and CD respectively,
Patm be the Atmospheric pressure, and
g be the acceleration due to gravity

For liquid to be in equilibrium, the hydrostatic pressure at B is equal to hydrostatic pressure at C
Total pressure at B = Total pressure at C
h1 ρg + Patm = hρg + Patm
hρ1 = hρ2 ……..(1)
We know that,
ρ2 = ρ1 / (1 + γ ∆θ) ……..(2)
Where, γ = coefficient of real expansion of liquid

From eqn.1 and eqn.2 we get
hρ1 = hρ1 / (1 + γ ∆θ)
h+ hγ ∆θ = h2
γ = (h2 - h1)/h1θ
This is the expression of determining absolute expansivity of liquid.

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