The coefficient of apparent expansion of a liquid when determined using two different vessle A and B are `gamma_(1)` and `gamma_(2,)` respectily. If the coefficient of linerar expansion of vesel A is `alpha.` Find the coefficient of linear expension of the vessel B.

Options

A. `(alpha Y_1 Y_2)/(Y_1 + Y_2)`
B. `(Y_1-Y_2)/(2a)`
C. `(Y_1 - Y_2 + alpha)/(3)`
D. `(Y_1 - Y_2)/(3) + alpha`

Answer

D

Explanation

`gamma_("actual") = gamma_("app") + gamma_("vessel")`
`as gamma _("vessel") = alpha`
For A `rArr gamma_(actual) = gamma_1 + 3 alpha_(A) = gamma_1 + 3 alpha`
For B `rArr gamma_("real") = gamma_(2) + 3 alpha_(B)`
`therefore gamma_(1) + 3 alpha = gamma_(2) + 3 alpha_(B) rArr alpha_(B) = (gamma_1 - gamma_2)/(3) + alpha`.