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 o0f volume expansion of the liquid is equal to

Options

A. `(l_(1)-l_(2))/(l_(2)t_(1)-l_(1)t_(2))`
B. `(l_(1)-l_(1))/(l_(2)t_(1)-l_(2)t_(2))`
C. `(l_(1)+l_(2))/(l_(2)t_(1)+l_(1)t_(2))`
D. `(l_(1)+l_(1))/(l_(2)t_(1)+l_(2)t_(2))`

Answer

A

Explanation

`rho_(0)+rho_(t_(2))gl_(2)=rho_(0)+rho_(t_(1))gl_(1)`
`rho_(t_(2))l_(2)=rho_(t_(1))l_(1)`
`(rho_(0))/(1+gammat_(2))l_(2)=(rho_(0))/(1+gammat_(1))l_(1)`
`(1+gammat_(1))l_(2)=l_(2)-l_(2)`
`gamma(l_(2)t_(1)-l_(1)t_(2))=l_(1)-l_(2)`
`gamma=(l_(1)-l_(2))/(l_(2)t_(1)-l_(1)t_(2))`