A U-tube filled with a liquid of volumetric expansion coefficient 10–5/°C lies in a vertical plane. The height of liquid column in the left vertical limb is 100 cm. The liquid in the left vertical limb is maintained at a temperature = 0°C while the liquid in the right limb is maintained at a temperature = 100°C. The difference in levels in the two limbs is
Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.
Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA
The difference in levels arises due to thermal expansion. The liquid expands when heated, so the right column (100°C) rises while the left (0°C) stays at 100 cm. The density at a temperature T is given by ρT = ρ0/(1 + γΔT), where γ is the volumetric expansion coefficient (10–5/°C). The pressure at the bottom of the U-tube must be equal. For the left limb, pressure P = ρ0gh0. For the right, P = ρ100gh. Equating them: ρ0gh0 = [ρ0/(1+γ×100)]gh. Solving for h gives h = h0(1+γ×100) = 100(1+0.001) = 100.1 cm. The difference in height Δh = h - h0 = 0.1 cm. Since γ = 10-5/°C and h0=100cm, Δh = γ×100×h0 = 10-5 × 100 × 100 = 0.1 cm. This is independent of the specific option format, but the calculation shows a direct proportionality to the temperature difference.
Final Answer: T