What is the expected height that water will rise in a tall evacuated tube when it is opened to atmospheric pressure?

• A. 1 m
• B. 5 m
• C. 10 m
• D. 20 m

Answer: (C)

When a tall evacuated tube is opened to atmospheric pressure, the height to which water will rise is determined by the balance between the atmospheric pressure and the hydrostatic pressure of the water column. The pressure exerted by a column of water can be calculated using the hydrostatic pressure formula:

[ P = \rho g h ]

where ( P ) is the pressure, ( \rho ) is the density of the liquid (in this case, water), ( g ) is the acceleration due to gravity, and ( h ) is the height of the liquid column.

The standard atmospheric pressure at sea level is approximately 101,325 Pascals. The density of water is about 1,000 kg/m³ and the acceleration due to gravity is approximately 9.81 m/s². By rearranging the hydrostatic pressure formula, you can solve for the height ( h ):

[ h = \frac{P}{\rho g} ]

Plugging in the values for atmospheric pressure, the density of water, and acceleration due to gravity:

[ h = \frac{101,325 , \text{Pa}}{(1,000 , \text{kg/m}^3) \cdot (