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 gamma_(1) gamma_(2))/(gamma_(1) + gamma_(2))`
B. `(gamma_(1) - gamma_(2))/(2 alpha)`
C. `(gamma_(1) - gamma_(2) + alpha)/(3)`
D. `(gamma_(1) - gamma_(2))/(3) + alpha`

Answer

D

Explanation

`gamma_("real") = gamma_("app") + gamma_("vessel") = gamma_("app") + 3 alpha ( "as " gamma_("vessel") = 3 alpha)`
For vessel A, `gamma_("real") = gamma_(1) + 3 alpha`
For vessel B, `gamma_("real") = gamma_(2) + 3 alpha_(B)`
`:. Gamma_(1) + 3 alpha = gamma_(2) + 3 alpha_(B) or alpha_(B) = (gamma_(1) - gamma_(2))/(3) + alpha`