What is the ratio in pressure at the closed bottom of an open,1.5-m tall tube of mercury (density 13.7 g/cm³)to that at the top? Assume the laboratory air pressure is 101.5 kPa. A)0.34 B)0.83 C)1.2 D)2.0 E)3.0

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Quizplus · Accepted Answer

The pressure at the bottom of the tube is the sum of the air pressure above the mercury and the pressure due to the mercury column. The pressure due to the mercury column can be calculated using the formula $P = \rho gh$, where $\rho$ is the density of mercury (13.6 x $10^3$ kg/m$^3$), $g$ is the acceleration due to gravity (9.8 m/s$^2$), and $h$ is the height of the mercury column (1.5 m). This gives a pressure due to the mercury of approximately 200 kPa. Adding the atmospheric pressure (101.5 kPa) gives a total pressure at the bottom of approximately 301.5 kPa. The ratio of the pressure at the bottom to the pressure at the top (which is just the atmospheric pressure) is 301.5 kPa / 101.5 kPa = 2.97, which rounds to 3.0.

What Is the Ratio in Pressure at the Closed Bottom