Answer:
(a) The height of the mercury on the open side if the gauge pressure is measured to be 13.3 kPa is 9.97395 cm
(b) When the gauge pressure is doubled;
The height of the mercury on the open side becomes 19.9479 cm
The height of the mercury on the side connected to the gas becomes 12.02605 cm
Explanation:
(a) The given parameters are;
The height of the mercury column on the side connected to the gas = 22.0 cm
The gauge pressure = 13.3 kPa
The gauge pressure is the pressure in the gas container relative to the atmospheric pressure, therefore, we have;
ΔP = P - P₀ = ρ × g × h
Where;
ΔP = The gauge pressure = P - P₀ = 13.3 kPa = 13,300 Pa
P₀ = The atmospheric pressure
P = The pressure of the gas in the container
ρ = The density of the mercury = 13593 kg/m³
g = The acceleration due to gravity = 9.81 m/s²
ΔP = ρ × g × h, by substitution gives
13,300 = 13593 × 9.81 × h
h = 13,300/(13593 × 9.81) ≈ 0.0997395 m = 9.97395 cm
The height of the mercury on the open side if the gauge pressure is measured to be 13.3 kPa is 9.97395 cm
(b) Given that the gauge pressure for the gas doubles, we have;
13,300 × 2 = 13593 × 9.81 × h
Therefore, h = 2 × 9.97395 = 19.9479 cm
The height of the mercury on the open side, h = 19.9479 cm
Therefore, the height of the mercury on the side connected to the gas becomes, 22 - 9.97395 = 12.02605 cm
