First slide

Thermal expansion

Question

The figure shows a glass tube (linear co-efficient of expansion is $α$ ) completely filled with a liquid of volume expansion co-efficient $γ$ . On heating length of the liquid column does not change. Choose the correct relation between $γ$ and $α$

Moderate

A

$γ = α$
B

$γ = 2 α$
C

$γ = 3 α$
D

$γ = \frac{α}{3}$

Solution

When length of the liquid column remains constant, then the level of liquid moves down with respect to the container, thus $γ$ must be less than 3 $α$ .
Now we can write $V = V_{0} (1 + γΔT)$
Since $V = {Al}_{0} = [A_{0} (1 + 2 αΔT)] l_{0} = V_{0} (1 + 2 αΔT)$
Hence $V_{0} (1 + γΔT) = V_{0} (1 + 2 αΔT) \Rightarrow γ = 2 α$

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