One atmosphere of pressure will push a column of mercury to a height of 760 mm when the closs sectional area of the column is 1.00 cm.what would be the height of the column of mercury supported by the atmosphere if its cross sectional area were 0.500cm? How High would the mercury column be if the area were 2cm?

Question

One atmosphere of pressure will push a column of mercury to a height of 760 mm when the closs sectional area of the column is 1.00 cm.what would be the height of the column of mercury supported by the atmosphere if its cross sectional area were 0.500cm? How High would the mercury column be if the area were 2cm?

Answer 1

To find the height of the column of mercury supported by the atmosphere, we can use the formula:

h = (P * A) / ρg

where:
- h is the height of the column of mercury
- P is the pressure (1 atmosphere or 760 mmHg)
- A is the cross-sectional area of the column
- ρ is the density of mercury (13.6 g/cm^3)
- g is the acceleration due to gravity (9.8 m/s^2)

Let's calculate the height for each given cross-sectional area:

For a cross-sectional area of 0.500 cm^2:
h = (760 mmHg * 0.500 cm) / (13.6 g/cm^3 * 9.8 m/s^2)
h = (760 * 0.500) / (13.6 * 9.8)
h ≈ 0.275 m or 27.5 cm

For a cross-sectional area of 2.000 cm^2:
h = (760 mmHg * 2.000 cm) / (13.6 g/cm^3 * 9.8 m/s^2)
h = (760 * 2.000) / (13.6 * 9.8)
h ≈ 1.100 m or 110 cm

Therefore, the height of the column of mercury supported by the atmosphere would be approximately 27.5 cm if the cross-sectional area were 0.500 cm^2, and approximately 110 cm if the area were 2.000 cm^2.

Answer 2

To solve this problem, we can use the concept of pressure and Pascal's law. Pascal's law states that a change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container.

Given:
- One atmosphere of pressure will push a column of mercury to a height of 760 mm when the cross-sectional area of the column is 1.00 cm.

Question 1: What would be the height of the column of mercury supported by the atmosphere if its cross-sectional area were 0.500 cm?

To find the height, we can set up a proportion using the known values:

1.00 cm / 760 mm = 0.500 cm / x

Cross-multiplying:

1.00 cm * x = 0.500 cm * 760 mm

x = (0.500 cm * 760 mm) / 1.00 cm

x = 380 mm

Therefore, the height of the column of mercury would be 380 mm.

Question 2: How high would the mercury column be if the area were 2 cm?

Using the same method as above:

1.00 cm / 760 mm = 2 cm / x

Cross-multiplying:

1.00 cm * x = 2 cm * 760 mm

x = (2 cm * 760 mm) / 1.00 cm

x = 1520 mm

Therefore, the height of the column of mercury would be 1520 mm.