Shown in the figure below is a U-tube with one end closed and the other end havi

Question

Shown in the figure below is a U-tube with one end closed and the other end having funnel of height 10 cm as shown. Mercury is poured into the funnel so as to trap the air in the tube, which is 24 mm in diameter and is 150 cm long. Assuming that the trapped air is compressed isothermally, what is the height h (in meters) of mercury (p_hg = 13.600 kg'm^3) in the tube when the funnel starts to run over Neglect capillary effects for this problem, and assume the trapped air acts as an ideal gas at 20 C .

Explanation / Answer

Pressure of air = rho * R * T

                       = 1.225 * 287 * 293

                       = 103.011 kPa

Pressure due to mercury column   = rho * g * h

                                                   = 13600 * 9.8 * (0.1 +h)

=> 13600 * 9.8 * (0.1 + h) = 103.011 * 10^3

      h = 67.23 cm

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