A U-tube is filled with a liquid of volumetric coefficient of expansion $10^{- 5} /^{0} C$ lies in a vertical plane. The height of liquid column in the left vertical limb is 100cm. The liquid in left vertical limb is maintained at a temperature of 0⁰C while the liquid at the right limb is maintained at 100⁰C. Find the difference in the levels of the two limbs.

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10cm

0.1cm

1cm

1.01cm

answer is B.

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Detailed Solution

$\begin{array}{l} P_{1} = ρ_{0^{0} C} \times g \times 100 \\ P_{2} = ρ_{100^{0} C} \times g \times y \end{array}$

$\begin{array}{l} ρ_{0^{0} C} \times g \times 100 = ρ_{100^{0} C} \times g \times y \\ ρ_{0^{0} C} \times g \times 100 = \frac{ρ_{0^{0} C}}{(1 + γ Δ θ)} \times g \times y \end{array}$

$\begin{array}{l} 100 = \frac{1}{(1 + γ Δ θ)} \times y \\ y = 100 (1 + 10^{- 5} \times 100) = 100 \times 1.001 = 100.1 c m \end{array}$

So, change is y = 0.1cm

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