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. (a)`(l_(1)-l_(2))/(l_(2)t_(1)-l_(1)t_(2))`
B. (b)`(l_(1)-l_(2))/(l_(1)t_(1)-l_(2)t_(2))`
C. (c)`(l_(1)+l_(2))/(l_(2)t_(1)+l_(1)t_(2))`
D. (d)`(l_(1)+l_(2))/(l_(1)t_(1)+l_(2)t_(2))`

Answer

A

Explanation

Pressure at the bottom In both arms will be equal `((rho_(0))/(1+gammat_(1)))l_(1) = ((rho_(0))/(1+gammat_(2)))l_(2) = implies gamma = (l_(1) - l_(2))/(l_(2)t_(1) - l_(1)t_(2))`