Using two different containers A and B, the coefficients of apparent expansion of a liquid are found to be `gamma_(1) " and " gamma_(2)` respectively. If the coefficient of linear expansion of the material A is `alpha`, find that of the material B.

Explanation

We have, `gamma=gamma^(.)+gamma_(g) " or, " gamma=gamma^(.)+3alpha`
[`gamma^(.)=` Coefficient of apparent expansion of the liquid, `gamma=` coefficient of real expansion of the liquid , `gamma_(g)=` coefficient of volume expansion of the material of the container.]
For container A,
`" "gamma=gamma+gamma_(g)=gamma_(1)+3alpha`
and for container B,
`" "gamma=gamma_(2)+3alpha^(.)`
[`alpha^(.)=` coefficient of linear expansion of the material of the container B]
`therefore " " gamma_(2)+3alpha^(.)=gamma_(1)+3alpha`
or, `" "3alpha^(.)=gamma_(1)+3alpha-gamma_(2) " or, " alpha^(.)=1/3(gamma_(1)-gamma_(2))+alpha.`