Question

: When the Italian physicist Evangelista Torricelli was trying to calculate the atmospheric pressure, he invented the mercury barometer . The main idea of this device is about balancing the pressure at the same layer between the weight of the mercury column and the weight of the air column above the open bath.

If the height of the mercury (13.6 g.cm-3) column was 60 cm at a specific place. Find:

1) The atmospheric pressure at that place.

2) The height of the air (0.001 g.cm-3) column at this place.

Answer 1

a) In the mercury barometer the height of the column is directly proportional to the atmospheric pressure (see https://en.wikipedia.org/wiki/Barometer#Equation):

$$P = \rho_m g h_m$$

where $\rho_m = 13.6\times 10^3\space kg/m^3$ is the density of mercury, $g = 9.8m/s^2$ is the gravitational acceleration, and $h_m = 60cm = 0.6m$ is the height of the mercury column. Thus, obtain:

$$P = 13.6\times 10^3\cdot 9.8\cdot 0.6 \approx 0.8\times 10^5Pa =$$

b) The height of the air column is given as follows:

$$h_a = \dfrac{P}{\rho_ag}$$

where $\rho_a = 0.001g/cm^3 = 1kg/m^3$ is the dencity of the air. Thus, obtain:

$$h_a = \dfrac{0.8\times 10^5}{1\cdot 9.8} \approx 8.2\times 10^3m$$

Answer. a) $0.8\times 10^5Pa$, b) $8.2\times 10^3m$.