Question

The apparent coefficient of expansion of a liquid when heated in a brass vessel is X and when heated in a tin vessel is Y. If α is the coefficient of linear expansion for brass, the coefficient of linear expansion of tin is?

Answer 1

Let the volume expansion of liquid be δ and linear expansion of tin be ${\alpha }_t$.

Apparent expansion = real expansion of vessel + real expansion of liquid

Therefore, X=3α+δ ...(1) and

$Y=3{\alpha }_t+\delta$ ...(2)

On rearranging equations (1) and (2), we get,

$\delta =X-3\alpha ...\left(1\right)and$

$\delta =Y-3\alpha ...\left(2\right)$

Equating (1) and (2)

$X-3\alpha =Y-3{\alpha }_t$

$\therefore 3{\alpha }_t=Y-X+3\alpha$

$\therefore {\alpha }_t=\frac{Y-X+3\alpha }{3}$