The figure shows a glass tube (linear co-efficient of expansion is α α ) completely filled with a liquid of volume expansion co-efficient γ γ . On heating length of the liquid column does not change. Choose the correct relation between γ γ and α α
Text Solution
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When length of the liquid column remains constant, then the level of liquid moves down with
respect to the container, thus γ γ must be less than 3 α α .
Now we can write V = V 0 (1 + γ γ Δ Δ T)
Since V = Al 0 = [A 0 (1 + 2 α α Δ Δ T)] l 0 = V 0 (1 + 2 α α Δ Δ T)
Hence V 0 (1 + γ γ Δ Δ T) = V 0 (1 + 2 α α Δ Δ T) ⇒ ⇒ γ γ = 2 α α .
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