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 $\alpha$ is the coefficient of linear expansion for brass, the coefficient of linear expansion of tin is

• A. $\frac{X+Y+3\alpha }{3}$
• B. $\frac{X+3\alpha -Y}{3}$
• C. $\frac{X+Y-2\alpha }{3}$
• D. $\frac{(X+Y-2\alpha )}{2}$

Answer 1

Answer: (B)

Coefficient of expansion of liquid = [Apparent coefficient of expansion + Coefficient of expansion of vessel]
Let coefficient of expansion of liquid be $=x$
Then
$x=X+3{\alpha }_{\text{brass }}$
$x=Y+3{\alpha }_{\text{tin }}$
$X+3{\alpha }_{\text{brass }}=Y+3{\alpha }_{\text{tin }}$
${\alpha }_{\text{tin }}=\frac{3{\alpha }_{\text{brass }}-Y+X}{3}$
$=\frac{3\alpha -Y+X}{3}$