First slide

Thermal expansion

Question

A horizontal uniform tube, open at both ends, is containing a liquid of certain length at some temperature. When the temperature is changed, the length of the liquid in the tube is not changed. If $α$ is the coefficient of linear expansion of the material of the tube and $γ$ is the coefficient of volume expansion of the liquid, then [EAMCET 2013]

Moderate

A

$γ = 2 α$
B

$γ = 3 α$
C

$γ = 4 α$
D

$γ = α$

Solution

Coefficient of superficial expansion of the material of the tube = $2 α$
Expansion of volume of the liquid =A( $γ L)$ $△ t$ and expansion of volume of tube = A $[2 α] L . △ t$ $A γ L . △ t = A (2 α) L . △ t \Rightarrow γ = 2 α$
Therefore

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