The atmospheric pressure in a certain area is determined to be 103.36 kPa using a mercury barometer shown in the figure below. (Acceleration due to gravity, g = 10 m/s², and density of mercury, \( \rho \) = 13.6 x 10³ kg/m³)
The height to which the mercury column rises is about:
A. 76 mm
B. 76 cm
C. 7.6 m
D. 760 cm
Answer (1)
To determine the height to which the mercury column rises, we need to relate the atmospheric pressure to the height of the mercury column in a barometer. The formula that relates these quantities is given by:
P = ρ ⋅ g ⋅ h
Where:
P is the atmospheric pressure, in pascals (Pa)
ρ is the density of mercury, in kilograms per cubic meter (kg/m³)
g is the acceleration due to gravity, in meters per second squared (m/s²)
h is the height of the mercury column, in meters (m)
Given:
Atmospheric pressure, P = 103.36 kPa = 103 , 360 Pa
Density of mercury, ρ = 13.6 × 1 0 3 kg/m³
Acceleration due to gravity, g = 10 m/s²
We can rearrange the formula to solve for h :
h = ρ ⋅ g P
Substituting the given values:
h = 13 , 600 × 10 103 , 360
h = 136 , 000 103 , 360
h ≈ 0.76 m
To convert meters to centimeters (since the options are in centimeters), we multiply by 100:
h ≈ 0.76 × 100 cm
h ≈ 76 cm
Therefore, the height to which the mercury column rises is approximately 76 cm .
The correct option is B. 76 cm .
