In a vertical U-tube containing a liquid, the two arms are maintained at different temperatures, $t_{1}$ and $t_{2}$ . The liquid columns in the two arms have heights $l_{1}$ and $l_{2}$ respectively. The coefficient of volume expansion of the liquid is equal to

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Solution

The correct option is A
$L e t ρ_{0}, ρ_{1} a n d ρ_{2} b e t h e d e n s i t i e s o f t h e l i q u i d a t t e m p e r a t u r e s 0, t_{1} a n d t_{2} r e s p e c t i v e l y T o b a l a n c e p r e s s u r e, ρ_{1} l_{1} g = ρ_{2} l_{2} g o r (\frac{ρ_{0}}{1 + γ t_{1}}) l_{1} = (\frac{ρ_{0}}{1 + γ t_{2}}) l_{2} \Rightarrow l_{1} + l_{1} γ t_{2} = l_{2} + l_{2} γ t_{1} γ = (\frac{l_{1} - l_{2}}{l_{2} t_{1} - l_{1} t_{2}})$

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