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In a vertical U-tube containing a luquid...

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

A

`(l_(1) - l_(2))/(l_(2)t_(1) - l_(1)t_(2))`

B

`(l_(1) - l_(2))/(l_(1)t_(2) - l_(2)t_(2))`

C

`(l_(1) + l_(2))/(l_(2)t_(1) + l_(1)t_(2))`

D

`(l_(1) + l_(2))/(l_(1)t_(1) + l_(2)t_(2))`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `rho_(0), rho_(1)` and `rho_(2)` be the densites of the liquid at temperature `0, t_(-1)` and `t_(2)` respectively
To balance pressure, `rho_(1)l_(1)g = rho_(2)l_(2)g`
or `((rho_(0))/(1 +gammat_(1)))l_(1) = ((rho_(0))/(1 + gammat_(2)))l_(2)`
`rArr l_(1) + l_(1)gammat_(2) = l_(2) + l_(2)gammat_(1) gamma = ((l_(1) - l_(2))/(l_(2)t_(1) - l_(1)t_(2)))`
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