In a vertical `U`-tube containing a luquid, the two arms are maintained at different temperatures, `t_(1)` and `t_(2)` . The liquid coplumns in the two arms have heights `l_(1)` and `l_(2)` respectively. The coefficient of volume expansion of the liquid is equal to

Options

A. `(l_1 - l_2)/(l_2 t_1- l_2 t_2)`
B. `(l_1 - l_2)/(l_1t_2 - l_2t_2)`
C. `(l_1 + l_2)/(l_2t_1 + l_2t_2)`
D. `(l_1 + l_2)/(l_1 t_2 + l_2 t_2)`

Answer

A

Explanation

Let, l be the height before raising the temperature in each column . i.e `l_1 gt l and l_2 gt l`
`l = (l_1)/(1 + gammat_1)= (l_2)/(1 + gamma t_2)`
`rArr l_1 + gamma l_1 t_2 = l_2 + gamma l_2t_1 rArr gamma = (l_1-l_2)/(l_2 t_1 - l_2t_2)`