Show work problems: A \"U-shaped\" tube has one end open the atmosphere and the

Question

Show work problems: A "U-shaped" tube has one end open the atmosphere and the other end attached to a closed chamber. Initially the gas inside the chamber is the same as the air outside, 0.9400 atm, and liquid mercury sits at the bottom of the tube with its level equal on both sides. If the pressure inside the chamber is pumped up to an absolute pressure of 1.08 atm, what will happen to the level of the mercury on the two sides of the tube? What will be the difference in level when the pressure change is complete? (5 points) 1. in

Explanation / Answer

1. When the pressure inside the chamber is raised compared to the pressure outside, the mercury in the inside arm of the U shaped tube will beginnto fall down and the arm which is exposed to atmosphere will rise in height.

The increase in hight inside will be such that the pressure difference due to unequal heights of mercury column must be equal to the difference in the pressure at the two surfaces.

Density of mercury = 13.69 x 103 kg/m3

Pressure difference dP = 1.08 - 0.94 atm = 0.14 atm = 0.14 x 1.013 x 105 Pa

Let d is height difference between two columns, hence

d (13.69 x 103) g = 0.14 x 1.013 x 105

d = 0.14 x 1.013 x 105/(13.69 x 103 x 9.81) = 0.105 m = 10.5 cm

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