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
$x=X+3 \alpha_{\text {brass }}$
$x=Y+3 \alpha_{\text {tin }}$
$X+3 \alpha_{\text {brass }}=Y+3 \alpha_{\text {tin }}$
$\alpha_{\text {tin }}=\frac{3 \alpha_{\text {brass }}-Y+X}{3}$
$=\frac{3 \alpha-Y+X}{3}$