A U -tube has a liquid of density ρ 0 at 0 ° C . In the two limbs they are kept to a length l ⁡ 1 and l ⁡ 2 at a constant temperature of t 1 and t 2 respectively. Then, the cubical expansion coefficie

Question

A U -tube has a liquid of density ρ 0 at 0 ° C . In the two limbs they are kept to a length l ⁡ 1 and l ⁡ 2 at a constant temperature of t 1 and t 2 respectively. Then, the cubical expansion coefficient will be

TestHub · Accepted Answer

Pressure on each side has to be same or the level to be maintained.

$∴ l_{1} ρ_{1} g = l_{2} ρ_{2} g$

$∴ \frac{l_{1} ρ_{0}}{(1 + γ t_{1})} g = \frac{l_{2} ρ_{0}}{(1 + γ t_{2})} g$

$∴ l_{1} + l_{1} t_{2} γ = l_{2} + γ l_{2} t_{1}$

$γ (l_{1} t_{2} - l_{2} t_{1}) = l_{2} - l_{1}$

$γ = \frac{l_{2} - l_{1}}{l_{1} t_{2} - l_{2} t_{1}}$

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