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 expanison of vessel A is `alpha` find the coefficient of linear expansion of vessel B.

Answer 1

We know that coefficient of real expansion fo liquid `(gamma_r)` = coefficient of apparent expansion of the liquid `(gamma_a)` + coefficient of volume or cubical expansion of the vessel `(gamma_v),` i.e.,`gamma_r = gamma_a + gamma_v = gamma_a + 3 alpha` Since the liquid is same in both the vessel, so value of `gamma_r` is same. From vessel A, `gamma_r = gamma_1 + 3 alpha_1 = gamma_1 + 3 alpha ( :. alpha_1 = alpha, given)`
For vessel B. `gamma_r = gamma_2 + 3 alpha_2 :. gamma_1 + 3 alpha = gamma_2 + 3 alpha_2`
or `alpha_2 = (gamma_1 + gamma_2)/(3) + alpha`