Question

The coefficient of apparent expansion of a liquid when determined using two different vessels A and B are ${\gamma }_1$ and ${\gamma }_2$ respectively. If the coefficient of linear expansion of the vessel $A$ is $\alpha$, then the coefficient of linear expansion of vessel $B$ is found to be $\frac{{\gamma }_1-{\gamma }_2+3\alpha }{x}$. The value of $x$ is

Answer 1

For the two vessels, we can equate the coefficients of cubical expansion of liquids as,
${\gamma }_l={\gamma }_1+3{\alpha }_1={\gamma }_2+3{\alpha }_2\Rightarrow {\alpha }_2=\frac{{\gamma }_1-{\gamma }_2+3{\alpha }_1}{3}$