First slide

Thermal expansion

Question

The coefficient of apparent expansion of a liquid when determined using two different vessels A and B are $2 δ a n d δ$ respectively. If coefficient of linear expansion of vessel A is $α,$ the coefficient of linear expansion of vessel B is

Moderate

A

$\frac{2 α}{3}$
B

$\frac{α}{2}$
C

$(\frac{δ}{3} + α)$
D

$(\frac{2 δ}{3} + α)$

Solution

(3)
$\begin{array}{l} δ_{r e a l} = δ_{a p p} + δ_{v e s s e l} \\ F o r v e s s e l A, δ_{A} = (δ_{l} - 2 δ) \\ F o r v e s s e l B, δ_{B} = (δ_{l} - δ) \\ ∴ δ_{B} - δ_{A} = δ \\ \Rightarrow δ_{B} = δ_{A} + δ = (3 α + δ) \\ ∴ α_{B} = \frac{δ_{B}}{3} = (α + \frac{δ}{3}) \end{array}$

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