The gas pressure inside the box is determined by adding the atmospheric pressure to the pressure exerted by the mercury column, calculated using the equation P = ρgh. The total pressure is 103.592 kPa.
The gas pressure inside the box shown in Figure 1 is equal to the atmospheric pressure plus the pressure exerted by the mercury column in the left leg of the U-tube. The pressure exerted by the mercury column is calculated using the following equation:
P = ρgh
where:
P is the pressure in Pascals (Pa)
ρ is the density of the fluid 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 fluid column in meters (m)
In this case, the density of mercury is 13600 kg/m³, the acceleration due to gravity is 9.81 m/s², and the height of the mercury column is 0.16 m. Therefore, the pressure exerted by the mercury column is calculated as follows:
P = (13600 kg/m³)(9.81 m/s²)(0.16 m) = 2292 Pa
Therefore, the gas pressure inside the box is equal to the atmospheric pressure plus 2292 Pa. Atmospheric pressure is typically about 101.3 kPa, so the gas pressure inside the box is calculated as follows:
P = 101.3 kPa + 2292 Pa = 103.592 kPa
Therefore, the gas pressure inside the box shown in Figure 1 is 103.592 kPa.