The coefficients of apparent expansion of a liquid when determined using two different vessels A and B are `y_(1)` and `y_(2)` respectively. If the coefficient of liner expansion of the vessel A is `alpha`, the coefficient of linear expansion of the vessel B is

Options

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

Answer

D

Explanation

For vessel A,
`gamma_(real)=gamma_(app)+gamma_(g)`
`gamma_(real)=gamma_(1)+3alpha`
For vessel B,
`gamma_(real)=gamma_(2) + 3alpha_(B)`
`gamma_(1) + 3alpha = gamma_(2) + 3alpha_(B)`
`alpha_(B) = (gamma_(1) - gamma_(2) + 3alpha)/(3)`
`alpha_(B)= (gamma_(1) - gamma_(2))/(3) + alpha`