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

Step-by-step solution

Pressure on each side has to be same or the level to be maintained. ∴ l ⁡ 1 ρ 1 g = l ⁡ 2 ρ 2 g ∴ l ⁡ 1 ρ 0 1 + γ t 1 g = 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 = l ⁡ 2 - l ⁡ 1 l ⁡ 1 t 2 - l ⁡ 2 t 1