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. `(gamma_A + gamma_B)/(3 )`
B. `(gamma_A - gamma_B)/(3)`
C. `(gamma_A + gamma_B)/(3) - alpha `
D. `(gamma_A - gamma_B)/(3) + alpha `

Answer

D

Explanation

Coefficient of real expansion of liquid = Coefficient of apparent expansion of liquid + coefficient of cubical expansion of the vessel
i.e. `gamma_r = gamma_a + gamma_V = gamma_a +3 alpha_V`
For vessel A :
` gamma_r = gamma_A + 3 alpha_1 ` ....(i)
for vessel B:
` gamma_r = gamma_B + 3 alpha_2` ......(ii)
Comparing (i) and (ii)
` gamma_A + 3 alpha_1 = gamma_B + 3 alpha_2`
` rArr alpha_2 = (gamma_A - gamma_B)/(3) + alpha_1`
since `alpha_1 = alpha `
` alpha_2 = (gamma_A - gamma_B)/(3) + alpha `